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Illustrating the PhaenomenaCelestial cartography in Antiquity and the Middle Ages$

Elly Dekker

Print publication date: 2012

Print ISBN-13: 9780199609697

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199609697.001.0001

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The Mathematical Tradition in Medieval Europe

The Mathematical Tradition in Medieval Europe

Chapter:
(p.337) Chapter Five The Mathematical Tradition in Medieval Europe
Source:
Illustrating the Phaenomena
Author(s):

Elly Dekker

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199609697.003.0005

Abstract and Keywords

The oldest extant medieval globe made in the Latin West dates from ca. 1320-1340. It is a precession globe built in keeping with Ptolemy's description and does not fit in any known medieval tradition. The oldest celestial maps in the mathematical tradition were made around 1425 by Conrad of Dyffenbach. His trapezoidal projection appears to be completely new. Another of his maps is based on the polar equidistant projection. This latter projection was also used in ca. 1435 for a pair of celestial maps attributed to Reinardus Gensfelder and closely connected to the Vienna globe making enterprise. The stereographic projection was used for celestial maps other than astrolabes only in the second half of the fifteenth century. The globe by Hans Dorn of 1480 exemplifies the Viennese tradition in globe making. This globe and the other extant celestial globe of 1492 by Johannes Stöffler were designed to help the astrologer to fix the mundane houses. The constellations on Stöffler's globe show the impact of Michael Scot's iconography.

Keywords:   projection, precession, trepidation, celestial maps, globes, precession globe, astrology, Ptolemy, Dyffenbach, Johannes Dorn, Johannes Stöffler, Michael Scot

5.1 The Mathematical Tradition: The Islamic Legacy

The transmission of knowledge from Muslin Spain to the Latin West started with the introduction of the astrolabe at the turn of the tenth century. This is why the astrolabe is often seen as foreshadowing the spread of Islamic science in Latin Europe, and it is for that reason the best studied medieval scientific instrument. Many scholars, starting with Bubnov in 1899, have collected and studied sources which could shed light on the assimilation of astrolabe knowledge in Latin Europe.1 Despite their efforts a great deal of uncertainty still exists about the channels through which the knowledge needed for the construction and use of the instrument was transferred.

In the study of written sources it is generally assumed that the diffusion started with a rather primitive translation of an Arabic treatise which was subsequently reworked and improved. Yet, no manuscript has so far been found testifying to this first stage of transmission. Only one early eleventh-century Latin astrolabe text, the Sententie astrolabii, appears to include fragments translated from an Arabic work.2 Further, most early Latin texts are confusing, not to say wrong, and it is not clear what help they could offer a reader apart from feeding his imagination.

Studies of extant early artefacts are rarely conclusive in establishing their past history and more often than not differences in opinion prevail, especially where an interesting object such as the astrolabe discovered and first described by Destombes is concerned.3 Many scholars consider this astrolabe to have been made in the tenth century thus representing the earliest trace of the instrument in Latin Europe. Another early astrolabe in the collection of the National Maritime Museum, shown in Fig. 5.1, illustrates clearly the transmission from Muslim Spain to the Latin West. The instrument may have been copied in Paris around 1223 (or 1233) from an astrolabe of Spanish-Islamic origin, that was made there in 1070 or there about.4 Seen against (p.338)

The Mathematical Tradition in Medieval Europe

Fig. 5.1 Medieval astrolabe, ca. 1230. (Courtesy of the National Maritime Museum Greenwich, Inventory number AST0570.)

this background, it is no coincidence that the shape of the rete of this astrolabe (Fig. 5.1) fits well into the style of astrolabes made in the second half of the eleventh century in Northern Spain, with characteristics such as prayer niches on the outer frame and the style of the pointers.5 It is not difficult to understand that instruments were among the first transmitters of new mathematical knowledge to the Latin speaking world. An instrument is the sort of curiosity that attracts the attention of a wider audience, whereas tables in learned treatises may turn people off. From that point of view it is all the more remarkable that so few globes have survived from the Middle Ages.

5.1.1 Alfonsine astronomy

Among the many works translated in the twelfth century is the Latin translation of the Almagest made around 1175 by Gerard of Cremona from the Arabic versions circulating in Muslim Spain.6 Gerard's translation became very influential in the Middle Ages and was printed in 1515. In the thirteenth century a group of Jewish and Christian scholars composed a series of works comprising translations, adaptations, and original texts in Spanish (or better old Castilian) under the supervision of King Alfonso X of Castile, a patron of literature and learning who reigned from 1252 until 1284.7 Not all texts survive intact. For example, only the canons (sets of instruction for use) of the Castilian Alfonsine Tables survive.8 These Tables, written in Toledo around 1270, served to calculate the positions of the planets. Other texts such as the Libros del saber de astronomía, also written in Castilian on astronomical instruments, and related texts are completely preserved.9 In the Libros del saber one finds in the first book a description of the 48 Ptolemaic constellations and their stars which—although not a direct translation—is based predominately on al-Ṣūfī's Book on the Constellations of the Fixed Stars (see Section 4.3).10 It includes many of al-Ṣūfī's indigenous star names and his coordinate tables, but the longitudes are increased by the Alfonsine value 17° 8´. The epoch mentioned is not the beginning of the reign of King Alfonso X of Castile (1252), but the year 1256.11 (p.339) I shall return to this the Alfonsine value 17° 8´ in more detail below.

Al-Ṣūfī's work on uranography was also transmitted along another line, which is known as the Ṣūfī Latinus corpus, consisting of eight manuscripts with a specific type of illustrated star catalogue.12 The oldest representative of this group of manuscripts is Paris, Bibliothèque nationale de France, MS Arsenal 1036. The star catalogue of this corpus is Gerard's Latin translation from the Arabic adapted to al-Ṣūfī's epoch 964 by adding 12° 42´ to the longitudes of the stars. And for each constellation there is a drawing that stems from an Arabic al-Ṣūfī manuscript. Through these illustrations al-Ṣūfī's iconography left its traces in the Latin West.13

A star catalogue in the translation of Gerard of Cremona with longitudes exceeding the corresponding Ptolemaic ones by 17° 8´ is also usually included in the Parisian Alfonsine Tables, so-called because they were written in Paris.14 Although the precession correction is the same as that used in the catalogue in the Libros del saber, the epoch of the latter (1256) is slightly later than that of the Parisian Alfonsine star catalogue, which is said to be the Alfonsine epoch of June 1252.

The Parisian Alfonsine Tables, written around 1320 and first printed in 1483, are a reworking of the earlier and now lost Castilian Alfonsine Tables.15 Although the lines of transmission from Spain to Paris are far from clear it must have been from Toledo that the Parisian astronomers learned about the idea of accession and recession. The theory presented in chapters 49–50 of the Toledan Alfonsine canons refer to a model by Arzarquiel and differs from the oldest Latin text in the Liber de motu octave spere (Book on the Motion of the Eighth Sphere).16 Both early theories differ in turn from the most common theory of precession used in the Middle Ages included in the Parisian Alfonsine Tables. This latter Parisian theory includes precession tables based upon two components: a motion of accession and recession characterized by a period of 7000 years, an amplitude of 9°, and a motion of a constant rate of precession with a period of 49,000 years.17

Application of the Parisian precession tables predicts that in June 1252 the longitudes of the stars will have increased with respect to Ptolemy (ad 137) by 15° 22´ 9˝.18 Or to put it another way, the Parisian precession tables predict that the stellar longitudes in June 1252 exceed the Ptolemaic ones by 17° 8´ only if the Ptolemaic epoch was ad 16 instead of ad 137.

A number of modern scholars have tried to explain this difference. One suggestion is that the Alfonsine astronomers made an error in their calculation (adding instead of subtracting), another that they did not know the precise value of the Ptolemaic epoch (ad 16 instead of ad 137).19 The most promising explanation so far is that by Chabás and Goldstein who suggest that the Alfonsine correction of 17° 8´ came into being within the framework of the catalogue for the epoch 1256 in the Libros del saber  which goes back to al-Ṣūfī's star catalogue for the epoch 964 and a precession correction of 12° 42´. Using al-Ṣūfī's rate of precession of 1° in 66 years, the difference 4° 26´ between the precession corrections 17° 8´ (p.340) and 12° 42´ is equivalent to 292.6 years which agrees with the difference between the epoch 1256 and 964.20 Chabás and Goldstein further suggest that the Parisian astronomers borrowed the Alfonsine correction of 17° 8´ from the Libros del saber and used it for the Alfonsine epoch June 1252 independently of the Parisian precession tables.21

Gerard's version of the Ptolemaic star catalogue adapted to epochs other than that of Alfonso X can be found in many medieval manuscripts. Often these catalogues are illustrated.22 The precession corrections in these later medieval star catalogues (for epochs later than 1252) are usually calculated with the Parisian precession tables through their excess with respect to the Alfonsine value 17° 8´. An example of an illustrated catalogue of special interest to this study is the one in Vienna, Österreichische Nationalbibliothek, MS 5415, ff. 217r–251v, which is adapted to the epoch 1424 by adding 1° 48´ to the Alfonsine value 17° 8´ for 1252 (f. 217r: ‘Et addunt super stellas verificatas per Alfoncium 1 gradum et 48 minuta in longitudine sed nichil in latitudine’).23 Thus in the star catalogue in Vienna MS 5415 the longitudes of the stars exceed the corresponding Ptolemaic ones by 18° 56´. Since it was obtained by adding to the Alfonsine value 17° 8´ for 1252 this latter value refers tacitly to a Ptolemaic epoch ad 16!24

5.1.2 Globe treatises

In the early corpus of astrolabe-related texts is a Latin fragment that is clearly a translation from the Arabic, Incipit de horologic seconded alkoram, id est speram rotundam, which some believe to describe a spherical astrolabe and others a celestial globe.25 Samsó proposed that it was related to Battānī's bayda, but the text itself cannot discriminate between the various suggestions. The first complete text with instructions for making a (precession) celestial globe in the Latin West is included in Gerard's translation of the Almagest. The oldest still extant globe made in medieval Europe, Cusanus's globe discussed below in Section 5.2, was made following these instructions.

Another text on the construction and use of the globe is part of the series of descriptions of astronomical instruments included in the Libros del saber.26 This Alfonsine globe treatise is a Castilian translation of Kitāb calā l-kura (Book concerning the Globe) written by Qusṭā ibn Lūqā, discussed in Section 4.2. The translators Yehūdah ibn Mosheh ha-Kohen and Johan Daspa revised their work in 1277, and it is this later version that is part of the Libros del saber. Preceding the 65 books by Qusṭā ibn Lūqā are four new chapters on the construction of the globe assumed to be the work of Isḥāq ibn Sīd, in which a number of technical details such as the advantages and disadvantages of the use of various materials such as wood, copper, and brass, are discussed.27 Following the 65 books is another newly written text by Don Mosheh on the use of auxiliaries such as a quadrant and a semicircular device for (p.341) finding the boundaries of the mundane houses after the prime vertical method.28 In Qusṭā ibn Lūqā's treatise a method for determining the mundane houses is discussed in chapter 55 based on the standard method.29 The collection of treatises on instruments in the Castilian Libros del saber was translated in 1341 into Italian in Seville but never into Latin.

The 65 chapters of Qusṭā ibn Lūqā's globe treatise were also directly translated from the Arabic into Latin and Hebrew. The Latin translation by an unknown translator, the Liber in opera sphera uolubilis, is known from eight manuscripts.30 The Hebrew translation is by Jacob ben Makhir ibn Tibbon (ca. 1236–ca. 1305), also known as Profatius. Some of the Hebrew versions have a section on the construction of the globe. Profatius's text was in turn translated into Latin by Stephanus Arlandi of Barcelona in 1301. He added also a chapter on globe making (at the end of his text).31 Thus in addition to a Castilian and an Italian version, two Latin translations were ultimately made of Qusṭā ibn Lūqā's globe treatise.

Another Latin treatise on the construction of the celestial globe, Tractatus de sphaera solida, circulated in the fourteenth and later centuries.32 Lorch has suggested from the style of writing that this treatise is also a translation from the Arabic, but an original has so far not been identified. The identity of the author of the Tractatus de sphaera solida is uncertain. Some suppose that the text is by Accursius of Parma, since his name is mentioned in the copy of the treatise in Florence, Bibliotheca Laurenziana MS Plut. 29.46: ‘Astrolabium sphaericum compositum anno domini 1303 Dominus Accursius de Parma fuit principium huius operis’.33 Lorch suspects that Accursius is the scribe of the Florentine text and that the other person often quoted in the treatise, John of Harlebeke, wrote it. His name occurs more often in copies of the treatise as for example in London, British Library, MS Arundel 268: ‘Tractatus de spera solida, sive astrolabio sperico, compositus a magistro Johanne de Harlebeke medico, anno domini 1303 Parisiis’.34 Very little is known about John of Harlebeke. He seems to have lived in the second half of the thirteenth century and was known as a priest and astronomer, and according to the text cited above worked in Paris as a physician.35 He is also mentioned as a monk of the Benedictine abbey of St Martin, Tournai.36 Of the two candidates, John of Harlebeke seems to have the best credentials. Whoever the author may be, there is general agreement that the text dates from 1303. It is known in more than 30 manuscripts and appears to have been most influential in medieval Europe.37 In the first decades of the sixteenth century three printed editions of the Tractatus de sphaera solida appeared.38 A German translation was made in the fifteenth century.39 This German translation is manifest to the growing interest in celestial cartography in German-speaking countries during the fifteenth century.

Treatises on the construction and use of the astrolabe available to the medieval astronomer outnumber by far those on the construction of globes. The success of the astrolabe may explain (p.342) the plea of John of Harlebeke in favour of the use of globe for solving astronomical problems in a prologue to the Tractatus de sphaera solida:

‘The root and basis of all astronomical theory, and also its immense prolixity and inexhaustible depth of ingenuity, take their beginning from things that are observed with appropriate instruments. It is agreed amongst all the authorities on this subject that without instruments there would be no way of discovering the motions of the celestial bodies.

There is a great number of these instruments, but in this there generally seems to be agreement: that they all imitate the motion of the Heavens and are made in a likeness of it as if from the original, which not Man but God (may His name be blessed) has made. In the judgement of all those who philosophize aright, the Heavens are spherical. Hence, if it is also agreed that a copy is formed in a likeness to the original, it is plain that a spherical instrument is more similar to the spherical Heavens than all other instruments. In accordance with this, Ptolemy - being cognizant of the matter we have spoken of - made an armillary instrument with wonderful ingenuity [and described it] in the Almagest. The figure of the sphere is reflected in the form of this [instrument], but, contained only by the appropriate arrangement of circles, it had none of the stars in its composition - among the figures of the Heavens there is an empty space to mark the stars. By being so awkward, it is found unsuited to determine the daily configurations of the Heavens.

Moreover, Ptolemy's astrolabe is elaborated in the likeness of that sphere [sc. of the Heavens], for it should be conceived as a sphere spread out in a plane. The geometrical proofs in this are ingenious, but in conceiving it the mind is affected by tedium, because things that are seen directly in the sphere we must there [in the astrolabe] conceive obliquely. Nor are the figures [imagines] in the sky [accurately] portrayed. [The astrolabe] is also partly truncated: it does not represent stars that are south of the tropic of Capricorn - not from necessity, but from custom and convenience. To place the latitudes of the planets in it is also difficult, if not impossible. It sometimes happens that the less experienced are misled in this matter and think that a planet in the East is above the Earth when it is below the Earth, and vice versa - and similarly for the other angle. In the judgement of the experienced the astrolabe is deservedly held, by virtue of its ingenuity, numerous uses, simple operation, and portability, as nobler and better than the other instruments of the venerable Ancients.

The same Ptolemy mentioned a spherical instrument in the Almagest, and indicated that the stars are inscribed in it according to longitude and latitude and that the celestial figures and constellations are drawn on it. But he does not intimate how this instrument might be brought to perfection so that it could be put to everyday uses, i.e. [finding] ascendants, equations of the houses, and other things necessary in this application [i.e. astrology]. We do not here set down the construction and uses of the astrolabe, as being sufficiently treated by the ancients. But what, by God's mercy, has come to us of the construction and uses of the instrument called “sphera solida” or “spherical astrolabe” we treat with the Lord's help - at the instance of some of my friends and for the use of those who might wish to look at this treatise.

We treat first, the construction of this instrument with all its parts, and secondly its uses. The instrument will be easy enough to construct, handsome and delightful in appearance, and because of its many uses, much desired and sought-after by the experienced. Of all other instruments it is the root and exemplar, except the two instruments that are called “perfect”- that is, they are universal - and other, imperfect, or particular, [instruments], such as the quadrant, cylinder, triquetrum, and shadow-instruments. Of these [latter] the everyday uses are few and they are, as it were, obtainable as parts of the perfect instruments. The Ancients have treated these carefully enough.

(p.343) But enough of these things. We come now, by invoking divine help, to the book. The prologue ends.’40

After this prologue the globe is subsequently described in the first part of nine chapters. It consists of a wooden sphere marked—as is prescribed in most treatises—by a number of great circles: the Equator graduated in 360º, the ecliptic graduated twelve times 0º–30º and great circles through the ecliptic poles for every 30º. Since such great circles through the ecliptic poles are found on many Arabic globes, their prescription suggests that an Arabic globe or a treatise may have been one of the sources.41 Also the value of the obliquity of the ecliptic, 23º 33´, is borrowed from an Arabic source. The sphere is mounted in a meridian ring and set in a hemispherical bowl with four vertical cords to support the instrument's particular mounting. In some manuscripts the bowl is said to be placed on a central piece instead of hanging on the four cords.42

The construction is notable for a number of points. There are two circles drawn around the north and south pole with a radius ε, the obliquity of the ecliptic, which obviously represents the north and south polar circles. Although polar circles became a regular feature in Western celestial maps and globes these circles are properly speaking not a meaningful part of celestial cartography. It is not known when the polar circles were first introduced in celestial cartography and when they came to replace the ever-visible and invisible circles used in Antiquity. The means to adjust the globe for geographical latitude could account for the disappearance of the ever-visible and invisible circles. Indeed, these latter circles are not seen on the early Islamic globes discussed in Section 4.4, but neither are polar circles. Their introduction in the Tractatus de sphaera solida could have been inspired by the five terrestrial zones described by the author of the Tractatus de sphaera solida.43 In fact, the polar circles are relevant to understanding phenomena of the climates and so on, and separate regions of excessive cold from the temperate zones, and maps of these zones were common in the Middle Ages.44 Another interesting feature in John of Harlebeke's globe treatise is the combination of scales of the zodiac and the calendar scales on the horizon ring. This combination serves to find the place of the Sun in the zodiac on a certain day of the year, which information is used in many applications of the globe. The author of the Tractatus de sphaera solida tells his reader that this information can be found on the back of astrolabes.45 Indeed, the zodiac with calendar is a common element of Western Arabic and Latin astrolabes, but not of Islamic globes.46 The scales on the horizon and the polar circles became standard features of Western globes.

5.2 Ptolemy’s Precession Globe

In 1444 Cardinal Nicolas of Cusa or Nicolas Cusanus (1401–64), a famous German polymath, paid a visit to the Reichstag in Nuremberg and there bought a number of manuscripts and three instruments for the amount of 38 florins: (p.344)

1444 Ego Nicolaus de Cusza, prepositus monasterii Treverensis dyocesis, orator pape Eugenii in dieta nurembergensi, que erat ibidem de mense Septembris ob ereccionem antipape felicis ducis Sabaudie factam Basilee per paucos sub titulo concilii, in qua dieta erat fridericus romanorum rex cum Electoribus, emi Speram Solidam magnam, astrolabium et turketum, Jebrum super almagesti cum aliis libris 15, pro XXXVIII florenis renensibus.47

All three instruments—the solid globe, the astrolabe, and the torquetum—have been preserved in accordance with Cusanus's wishes. His entire inheritance was bequeathed to a charitable institution that he had founded as a home for the aged in Bernkastel-Kues (St. Nikolaus Hospital). When Hartmann visited the place in 1913 he found next to the three instruments a small brass globe, which had clearly never been finished.48 In addition to a grid, there are the first 45 stars described in the Ptolemaic star catalogue on it, belonging to the constellations Ursa Minor, Ursa Maior, and Draco. Hartmann has measured their positions and compared them with the longitudes in the star catalogue of al-Ṣūfī. He showed that the stellar longitudes on the brass globe on the average exceed al-Ṣūfī's precession correction by 4.6º ± 0.2º. Since al-Ṣūfī's longitudes differ from the corresponding Ptolemaic ones by 12º 42´, the positions on the small brass globe appear to be consistent with those in the Alfonsine star catalogue (17° 8´ added to the Ptolemaic longitudes of the stars). This implies that the small globe could have been made any time after 1325, when the Alfonsine star catalogue was commonly appended to the Alfonsine Tables. From the style of the lettering, Hartmann has suggested the middle of the fifteenth century as the date of construction of this small globe.

The other globe in Bernkastel-Kues, the ‘spera solida magna’, although now incomplete, is designed as a precession globe, very much after the model described in Ptolemy's Almagest. It is described in Appendix 5.2 (WG1). In Ptolemy's time, precession was a very novel feature, the understanding of which was crucial to discussing the main theme of the Almagest, the motions of the Sun and the planets. It is for this reason that Ptolemy included a description of a relevant demonstration model:

‘But we also wish to provide a representation [of the fixed stars] by means of a solid globe in accordance with the hypotheses which we have demonstrated concerning the sphere of the fixed stars, according to which, as we saw, this sphere too, like those of the planets, is carried around by the primary [daily] motion from east to west about the poles of the equator, but also has a proper motion in the opposite direction about the poles of the sun's, ecliptic circle.’49

Cusanus's globe is the only extant medieval artefact that recalls this description of Ptolemy's precession globe. It deviates in construction from Islamic and later European globes which are made for a fixed epoch.50 The spera solida magna consists of a wooden hollow sphere, about 27 cm in diameter. The sphere is closed by a circular disc (Fig. 5.2) and covered by a thin layer of plaster and cloth. The maker did not follow Ptolemy in making ‘the colour of the globe in question somewhat deep, so as to resemble, not the day- time, but rather the nighttime sky, in which the stars actually appear’.51 Instead he painted the (p.345)

The Mathematical Tradition in Medieval Europe

Fig. 5.2 Construction detail of the sphere of Cusanus's globe. (Reproduced from Hartman 1919, Plate XI.)

sphere with layers of white oil paint to smooth the surface. On the surface of the sphere in principle only two great circles are drawn. The first circle represents the ecliptic (see Fig. 5.3) which is divided into units of 1° by dots. The other (Fig. 5.4) is perpendicular to the ecliptic and passes through Sirius (α CMa). The intersection of this circle with the ecliptic is the fixed starting point for marking the stars on the sphere as explained by Ptolemy:

‘Since it is not reasonable to mark the solstitial and equinoctial points on the actual zodiac of the globe (for the stars depicted [on the globe] do not retain a constant distance with respect to these points), we need to take some fixed starting-point in the delineated fixed stars. So we mark the brightest of them, namely the star in the mouth of Canis Major [Sirius], on the circle drawn at right angles to the ecliptic at the division forming the beginning of the graduation, at the distance in latitude from the ecliptic towards its south pole recorded [in the star catalogue].’52

The choice of the brightest star Sirius (α CMa) as the reference star may seem obvious but one may well wonder how convenient this choice is from the point of view of globe construction. All longitudes in the star catalogue in the Almagest (fixed for the epoch 28 August 137) have to be reduced by subtracting Sirius's longitude Gem 17° ⅔´. One is tempted to think that the choice of Sirius was suggested by the fact that on Hipparchus's globe the longitude of Sirius must have been close to Gem 15°. Later Ptolemy switched to another reference star, Regulus (α Leo), the longitude of which in the Ptolemaic star catalogue is Leo 2° ½´.53

(p.346)

The Mathematical Tradition in Medieval Europe

Fig. 5.3 The ecliptic close to Aries on Cusanus's globe. (Reproduced from Hartman 1919, Plate IV.)

Returning to Cusanus's globe, the sphere is mounted in a peculiar way that follows Ptolemy's description of his precession model closely. At the north and south ecliptic poles two brass circular discs are fixed by four nails. A brass ring is attached to these discs such that it can rotate around the sphere. Half of the ring is 8 mm thick, but the size of the other half is cut out such that one side of the ring coincides precisely with a great circle through the poles (see Fig. 5.5). This thinner ring through the ecliptic poles is divided into units of 5° and subdivided into 1°, but is not numbered. This ring is one of the pair that has to be prepared as follows:

‘In the middle of the convex face of each ring we draw a line accurately bisecting its width. Using these lines as guides, we cut out one of the latitudinal sections defined by the line over half of the circumference, and divide [each of] the semi-circular recessed sections [thus created] into 180 degrees.’54

The thinner part of the ring fixed at the ecliptic poles could then be used to mark the positions of the stars on the sphere:

‘Then, for each of the other fixed stars in the catalogue in order, we mark the position by rotating the ring with the graduated recessed face about the poles of the ecliptic: we turn the face of its recessed section to that point on the [globe's] ecliptic which is the same distance from the beginning of the numbered graduation (at Sirius) as the star in question is from Sirius in the catalogue; then we go to that point on the graduated face which we have [thus] positioned which is, again, the same distance from the ecliptic as the star is in the catalogue, either towards the north or towards the (p.347)

The Mathematical Tradition in Medieval Europe

Fig. 5.4 The colure through Sirius (α CMa) on Cusanus's globe. (Reproduced from Hartman 1919, Plate VI.)

south pole of the ecliptic as the particular case may be, and at that point we mark the position of the star; then we apply to it a spot of yellow colouring (or, for some stars, the colour they are noted [in the catalogue] as having), of a size appropriate to the magnitude of each star.’55

The maker of Cusanus's globe did not number the ecliptic scale. For a globe with varying equinoxes and solstices this seems to make good sense although it is cumbersome to plot the stars without numbers. The maker also did not follow Ptolemy's advice of using a yellow colour for marking the stars in a blue background. On Cusanus's globe the stellar positions are indicating by small holes drilled into the sphere and filled with red wax showing the stars in red against an originally white background.

After having served as an auxiliary for locating the stars on the sphere, the ring attached to the ecliptic poles is next used for mounting the sphere. In two points of the brass ring, at a distance of about 24°, are provisions for fixing another larger brass ring that can rotate around these two points (Fig. 5.5). These provisions demonstrate that in this construction the smaller ring is supposed to represent the solstitial colure passing through the ecliptic and equatorial poles. Of the larger ring Ptolemy says:

‘Then we attach the larger of the rings, which will always represent a meridian, to the smaller ring which fits around the globe, on poles coinciding with those of the equator. These points [the poles of the equator] are, in the case of the larger, meridian [ring], attached, again, at the diametrically opposite ends of the recessed and graduated face (which will represent the [section of the meridian] above the earth); but in the case of the smaller ring, [which passes] through both poles, they will be fixed at the ends of the diametrically opposite arcs which stretch the 23; 51º of the obliquity from each of the poles of the ecliptic. We leave small solid pieces in the recessed parts of the rings, to receive the bore-holes for the attachments [of the pins representing the poles].’56

It is not difficult to see that Cusanus's globe fits this Ptolemaic description well, even in the absence of the now lost larger meridian ring. Had it been there the globe mounted in its meridian ring could have been placed in a stand with a horizon ring and then would be ready for use.

A user interested in demonstrating the heavenly phenomena in his own time would have to (p.348)

The Mathematical Tradition in Medieval Europe

Fig. 5.5 Detail of the mounting of Cusanus's globe. (Reproduced from Hartman 1919, Plate VIII.)

determine the position of the solstitial colure passing through the ecliptic and equatorial poles as Ptolemy explains:

‘Now the recessed face of the smaller of the rings must, clearly, always coincide with the meridian through the solstitial points. So on any occasion [when we want to use the globe], we set it to that point of the ecliptic graduation whose distance from the starting-point defined by Sirius is equal to the distance of Sirius from the summer solstice at the time in question (e.g. at the beginning of the reign of Antoninus, 12⅓° in advance57). Then we fix the meridian ring in position perpendicular to the horizon defined by the stand [of the globe], in such a way that it is bisected by the visible surface of the latter, but can be moved round in its own plane: this is in order that we may, for any particular application, raise the north pole from the horizon by the appropriate arc for the latitude in question, using the graduation of the meridian [to place the ring correctly].’58

The action to fix the meridian ring for a specific epoch has left its traces on Cusanus's globe. Along the circle at a distance of about 24° from the north and south ecliptic poles one finds several holes, presumably indicating the equatorial poles for a number of epochs (Fig. 5.6). Hartmann has carefully measured the positions of these holes which are schematically summarized in Scheme 5.1 following his example.59 One of the holes (A in Scheme 5.1) lies 12.4° east of the great circle through Sirius and, since the longitude of Sirius in the Ptolemaic star catalogue is Gem 17° ⅔´, this hole obviously represents the north equatorial pole for the epoch of the (p.349)

The Mathematical Tradition in Medieval EuropeThe Mathematical Tradition in Medieval Europe

Fig. 5.6 a–b Holes connected with the mounting of Cusanus's globe. Left: Holes in the area around the north ecliptic pole; right: around the south ecliptic pole. (Photo: Elly Dekker.)

Almagest (AD 137). Two other holes (B and C in Scheme 5.1.) are shifted with respect to the great circle through Sirius 20.5° east and 3.3° west, respectively. The presumed solstitial colures through these holes are located respectively 8.1° east and 15.7° west with respect to the Ptolemaic solstitial colure through A.

Around the points A and C are traces of a small circle and a series of points (Fig. 5.6) which were caused by the nails with which a circular disc was fixed to the sphere at the equatorial poles at A and C. Hartmann also found traces of the equators corresponding to the equatorial poles at A and C. These markings show that the equatorial poles A and C were actually used and must have had a particular interest for the maker or user of the globe. The absence of traces of a circular disc with nails around point B suggests that the hole at B was not used in the same way as those at A and C.

The interest in Ptolemy's epoch (point A) does not require much explanation. For determining the epoch corresponding to hole C one needs to know which theory of precession was applied by the user. For example, with the method used by the Alfonsine astronomers for calculation the epoch of the star catalogue in the Libros del Saber, one finds an epoch by a simple calculation. The excess of 15.7° of the colure through point C with respect to Ptolemy's exceeds that of al-Ṣūfī's catalogue of 964 by 3º (12º 42´ = 12.7º). Using a constant rate of 1º in 66 years this difference of 3º is equivalent to 200 years, that is, an epoch of 1164 for point C. However, this epoch can be rejected because it violates a constraint indicated by the iconography of Perseus (Fig. 5.3). Already Hartmann noticed the peculiar helm worn by Perseus, and pointed out that this type came into use at the (p.350)

The Mathematical Tradition in Medieval Europe

Scheme 5.1 The configuration of holes around the north ecliptic pole on Cusanus's globe.

end of the thirteenth century.60 Thom Richardson of the Royal Armouries has confirmed that ‘the “pointed top” group are first illustrated in 1285 and go on until about 1340’.61

The most common theory in use before 1444, the year in which Cusanus bought the globe, was the Parisian Alfonsine trepidation theory. This theory predicts an epoch of 1292 ± 50 for the solstitial colure 15.7° west (point C) of the Ptolemaic one (Point A) for ad 137.62 In assessing this epoch I have taken into account the fact that the uncertainty in the position of the holes according to Hartmann is ½°, which in terms of epochs is equivalent to about 50 years.63 Note that this epoch 1292 postdates the Alfonsine epoch 1252 while the excess of 15.7° associated with point C is less than 17° 8´, the value by which the longitudes in the Alfonsine star catalogue exceed the Ptolemaic ones. As explained in Section 5.1 above the value 17° 8´ agrees (p.351) effectively with the theory for the epoch ad 16. When counted from ad 16 the value of 15.7° west (point C) would correspond to an epoch of 1125 ± 50 which can be rejected for the reasons explained above. Indirectly this shows that the user had no copy of the Alfonsine star catalogue but used the copy of Gerard of Cremona in his translation of the Almagest and calculated the precession correction with respect to ad 137.

An epoch between 1242 and 1342 predicted by the Parisian Alfonsine trepidation theory offers in my opinion the best prospects for interpreting point C. Considering that the Parisian Alfonsine precession theory was constructed around 1320, a date before 1320 is not likely. I think that one can exclude the possibility that the user intended to set the equatorial poles for the Alfonsine epoch at 1252 because then the value 17° 8´ would have been used.64 Thus the best assessment of point C is that it represents a date between 1320 and 1342 consistent with the range in dates indicated by Perseus's helm mentioned above.

About the epoch associated with point B one can only speculate. The absence of traces of the use of a circular disc around this hole could mean that it was created only after the meridian ring with the circular disc was lost. However that may be, Hartmann suggested that the pole at B was used to verify an old pre-Ptolemaic text since there are also traces on the surface of the globe of a number of parallel circles centred on pole B which seem to represent the tropics and the ever-visible and ever-invisible circles at geographical latitude 35º, but in the absence of other clues the meaning of pole B remains obscure.65

5.2.1 The constellations

In the description of his solid globe Ptolemy gives the following instructions for drawing the constellations on the sphere after the stars have been marked on it:

‘As for the configurations of the shapes of the individual constellations, we make them as simple as possible, surrounding66 the stars within the same figure only by lines, which moreover should not be very different in colour from the general background of the globe. The purpose of this is, [on the one hand], not to lose the advantages of this kind of pictorial description, and [on the other] not to destroy the resemblance of the image to the original by applying a variety of colours, but rather to make it easy for us to remember and compare when we actually come to examine [the starry heaven], since we will be accustomed to the unadorned appearance of the stars in their representation on the globe too.’67

All constellation images on Cusanus's globe are simple line drawings with very few elaborations, as Ptolemy's instruction prescribes. When I examined the globe in 1992 it was difficult to make good photographs as a result of wear. I have therefore reproduced the pictures published by Hartmann in Figs 5.25.5 and 5.75.10. One should be aware that Hartmann did manipulate his photographs before publishing them. After enlarging his pictures he copied the constellation figures with a pencil and, after reducing these drawings to their original sizes, combined these drawings with the original photograph. Some of the drawings are incomplete. (p.352)

The Mathematical Tradition in Medieval Europe

Fig. 5.7 Auriga, Orion, Gemini, Cancer, and Canis Minor on Cusanus's globe. (Reproduced from Hartman 1919, Plate V.)

The most striking examples are the absence of Bootes's stick and the incomplete figure of Cygnus (compare my photographs in Figs 5.115.12 with Hartmann's in Fig. 5.9). Despite these few shortcomings Hartmann's pictures are good reproductions of the originals.

As these pictures show, most human figures are nude, the exceptions being the female figures Andromeda and Virgo. The human figures seem to have very similar heads, hands, and curly hair, but there is some differentiation among their faces. Some human constellations, that is Bootes, Cassiopeia, Perseus, Auriga, and Orion, have their heads drawn in profile. The faces of others, such as Cepheus, Hercules, Andromeda, Gemini, Virgo, Aquarius, and Centaurus, are drawn full faced. Most animal constellations are drawn in

The Mathematical Tradition in Medieval Europe

Fig. 5.8 Ursa Maior and Leo on Cusanus's globe. (Reproduced from Hartman 1919, Plate VII.)

profile. These include Ursa Maior, Pegasus, Equuleus, Delphinus, Leo, Capricornus, Pisces, Hydra, Cetus, Lepus, Canis Maior, Canis Minor, and Lupus. Two constellations, Cancer and Scorpius, are as usual seen from above. Birds like Aquila and Cygnus are drawn in flight. Aries and Taurus have their heads turned to look backwards. Some animals, such as Ursa Minor and Ursa Maior, have scanty hair around the head and Cetus has some on the head and on his back, whereas Leo's head and Aries's fleece receive the full treatment. Wings are usually well worked out, not only in Cygnus and Aquila but also in the mythological figures Pegasus and Virgo. Finally the artist has a very characteristic way of drawing watery features, as for example his images of Aquarius's stream of water (compare Fig. 5.2) and Eridanus. Since most human (p.353)
The Mathematical Tradition in Medieval Europe

Fig. 5.9 Bootes, Ophiuchus, Serpens, Corona Borealis, Hercules, Draco, Lyra, and Cygnus on Cusanus's globe. (Reproduced from Hartman 1919, Plate IX.)

constellations are nude their design seems to have at first sight little to offer as far as dating is concerned. However, the head gear of some of the constellations is telling. As mentioned above Perseus's helm was used between 1285 and 1340. Also the hunting hat of Cepheus and Bootes points to the first half of the fourteenth century.68

A most conspicuous feature of Cusanus's globe is that all human constellations are presented in front view, a mode of constellation design common among Islamic globe makers. This would suggest that the model used by the maker was an Islamic globe. This is supported by

The Mathematical Tradition in Medieval Europe

Fig. 5.10 Centaurus, Lupus and Ara on Cusanus's globe. (Reproduced from Hartman 1919, Plate X.)

the fact that contrary to earlier antique sources and later Western globes, the Bears are not drawn back to back (see Section 4.4). However, here the agreement between Arabic iconography and that expressed on Cusanus's globe ends. This becomes clear when the constellation figures on Cusanus's globe are compared with, say, the constellation drawings presented in Bernkastel-Kues, Cusanusstift, MS 207. According to Krchňák, who examined the codices which today are still kept in the Cusanusstift, this manuscript was among the codices acquired in 1444 and may have the same provenance as the globe.69

Bernkastel-Kues MS 207 dates to 1301–34 and according to Krchňák was written in (p.354)

The Mathematical Tradition in Medieval Europe

Fig. 5.11 Bootes on Cusanus's globe. (Photo: Elly Dekker.)

Prague.70 On ff. 124v–135r is a cycle of constellation drawings which belongs to the star catalogue on ff. 116v–121v. This catalogue is part of the Ṣūfī Latinus corpus albeit of the augmented type.71 The drawings in MS 207 differ considerably from the main types but the connection with the Ṣūfī Latinus tradition is recognizable in many ways. Since Krchňák connects this codex with Cusanus's globe a comparison is of interest. Below I have listed the images on the globe that deviate from those in the Ṣūfī Latinus tradition, as exemplified in Bernkastel-Kues MS 207.

CEPHEUS (Fig. 5.5) is naked and has no tiara but wears instead a medieval hat. The kneeling attitude is in line with the stellar configuration

The Mathematical Tradition in Medieval Europe

Fig. 5.12 Cygnus on Cusanus's globe. (Photo: Elly Dekker.)

described in the Ptolemaic catalogue. In MS 207, f. 125r he is also naked but here he wears a high cap in keeping with the Ṣūfī Latinus tradition.

BOOTES (Fig. 5.9) is standing as is expected from the Ptolemaic stellar configuration, with his western arm raised and a stick in his eastern hand. Apart from his hat, which is the same as that of Cepheus, and a girdle he is naked. In MS 207 f. 125v he is also naked but here he holds a sword in keeping with the Ṣūfī Latinus tradition.

CORONA BOREALIS (Fig. 5.9) is a crown with six petals, three of which are drawn on the outside and the other three on the inside of the ring. In MS 207 f. 125v it is a represented by a ring in keeping with the Ṣūfī Latinus tradition.

(p.355) HERCULES (Fig. 5.9) is a naked figure with a beard. His eastern foot is above the head of Draco and he kneels on the (western) knee in keeping with the ‘Kneeler’ described in the Ptolemaic catalogue. However, he carries the attributes of Hercules: the club in his raised western hand and a lion's skin in his other outstretched hand. In MS 207, f. 125v this constellation is also naked but here the figure holds only a sickle in his raised left hand in keeping with the Ṣūfī Latinus tradition.

LYRA (Fig. 5.9) is depicted as a musical instrument, the lyre. In MS 207 f. 126r Lyra is drawn as a vase in keeping with the Ṣūfī Latinus tradition.

PERSEUS (Fig. 5.3) is drawn naked with a helm on his head. In his hand above his head he holds a curved sickle-like weapon with teeth. In his other hand he carries a female head, representing the decapitated head of Medusa. In MS 207, f. 126r Perseus is also naked but here he holds a sword and carries the head of Ghūl, the desert demon in keeping with the Ṣūfī Latinus tradition.

AURIGA (Fig. 5.7) is a naked figure with curly hair. On his right shoulder is the head of a goat and on his right wrist is a smaller goat. In MS 207, f. 126r Auriga is also naked but there are no goats and Auriga holds a rein in his hand in keeping with the Ṣūfī Latinus tradition.

VIRGO (Fig. 5.8) is a female figure with long hair and wings. She wears a long dress with a girded top. Her head is turned in profile to the north. The left hand is on her breast. In MS 207, f. 130r Virgo is also dressed but here she is drawn without wings in keeping with the Ṣūfī Latinus tradition.

LIBRA (Fig. 5.10) is presented as the Claws of Scorpius as described in the Ptolemaic catalogue. In MS 207, f. 130v Libra is drawn as a pair of scales in keeping with the Ṣūfī Latinus tradition.

ORION (Figs 5.4 and 5.7) is a naked kneeling figure. He holds a shield in his raised western arm and carries a club in his raised eastern hand. He has around his middle a belt to which a sword in a scabbard is attached, as described in the Ptolemaic catalogue. In MS 207, f. 132r Orion is also naked but here he has a lengthened sleeve instead of a shield in keeping with the Ṣūfī Latinus tradition.

CENTAURUS (Fig. 5.10) is partly a horse and partly a nude figure with curly hair on top. His left hand holds the right foreleg of Lupus, and his right hand touches the belly of Lupus. In MS 207, f. 134v Centaurus holds a branch with leaves in keeping with the Ṣūfī Latinus tradition.

From this comparison it is clear that the constellation drawings on the globe have little in common with the Ṣūfī Latinus tradition seen in a number of manuscripts. Whatever the origin of the constellation drawings on Cusanus's globe, it should not be sought among the Arabic influences dominating the mathematical tradition in the Latin West around 1300. The only remarkable agreements between the constellation drawings in Bernkastel-Kues MS 207 and on the globe are first of all the nudity of most human figures. In this respect the constellation drawings in MS 207 deviate from the norm of the Ṣūfī Latinus corpus. A second common feature is the wavy-like borders of the river Eridanus. On the globe the same characteristic is used for the presentation of Aqua, but in MS 207 the borders of the stream of water are presented as straight lines. And third it is worth noting that the typical hat worn by Cepheus and Bootes on Cusanus's globe is also seen on the left shoulder of Jupiter in MS 207, f. 115v.72 Interesting as this is, it is not (p.356) sufficient to establish a straightforward relation between the globe and the codex.

Whereas the date of production of the globe seems fairly well established it is not clear where the globe was made. Around 1300 instrument making was not yet an established trade. Instruments were made through cooperation between scholars and artists, working in wood and metal. Such a grouping of people could be found in monasteries, at royal courts, and in commercial cities. Hartmann believed that one of Cusanus's instruments, the torquetum, could be connected with Nuremberg. And since he could date this instrument to 1434 he thought that there might be a connection with a certain Nicholas of Heybech from Erfurt. Astronomical tables of this Nicolas were included in Bernkastel-Kues MS 211, the same codex in which he had found the note by Cusanus on the acquisition of the instruments and sixteen codices.73 His next step was to suggest that this astronomer from Erfurt might have been identical with a certain Magister Nicolao orlogista, who was recorded in Nuremberg around 1431/4.74 Thus it seemed not unreasonable to presume that the codices and the other instruments were once the property of this Nicholas of Heybech from Erfurt.75 In 1963 Krchňák showed that Hartmann's thesis was untenable because Nicholas of Heybech must have been older than 70 in 1431.76

Examining the codices connected with Cusanus, Krchňák developed a completely different thesis. The interpretation of the extant Cusanus codices is complex. Not all manuscripts can be supposed to have been part of the sixteen codices which Cusanus bought in 1444 together with three instruments. Some have been lost, others have been separated and bound differently and a few are now in other libraries. Among the extant codices Krchňák found four originating from Germany (MS 211, parts of MS 210 and of MS 212, MS Harley 3702), three from Paris (MS 209, part of MS 212, MS 213), one from Toulouse (MS 214), three from Prague (MS 207, MS 208, MS 210), one from Toledo (MS Harley 3734) and one from Italy (MS Harley 5402). These various backgrounds suggest strongly that many extant codices were not necessarily part of the acquisition made in 1444. Yet Krchňák believes that MS 207, MS 208, and MS 210 belong to those acquired in 1444.

The connection of Bernkastel-Kues MS 207 and Cusanus's globe is far from clear. Krchňák presumes a common origin of the codex and the globe because of the hunting hat occurring in MS 207 on f. 115v and on the globe. His other argument for connecting the codex and the globe is the agreement in artistic style. The line drawings, nakedness, and hair styles of the human figures would connect Bernkastel-Kues MS 207 with Prague, and in its trace also Cusanus's globe.77 However, it has not been shown that the hunting hat and the style of drawings were localized to Prague.

His analysis of MS 208 and MS 210 serves to add to his claim that Cusanus's globe would have been made in Prague. Glosses in these manuscripts show that around 1300 connections existed between the court in Prague and two astronomers from Spain. Krchňák identified one of them as Alvaro de Oviedo, a translator from (p.357) Toledo, but this has been questioned.78 However that may be, Krchňák believes that these Spanish astronomers brought Cusanus's astrolabe from Spain to Prague. He also believes that the presence of these Spanish astronomers in Prague indirectly confirms that Cusanus's globe was made there around 1300. He presents, however, no evidence for either presumption.

I do not question the presence of Spanish astronomers working at the Prague court around 1300, but I am not convinced that the globe was built there by them. One could reason that the location of the solstitial colure through pole C 15.7º west of the colure for Ptolemy's epoch shows that the user was familiar with the Parisian Alfonsine Tables which were available from 1320 on, but this argument is not decisive if the maker and the user are not the same person. My main reason for doubting a Spanish maker is that the design of Cusanus's globe is so very unlike a globe from Muslim Spain. Although all human constellations are presented in front view as they are on Islamic globes the constellation drawings on Cusanus's globe recall the very opposite of Arabic traditions in constellation design. In fact the globe's constellations are even unlike anything known from the Middle Ages and one would even be inclined to date them to the fifteenth century.79 However, Perseus’ helm contradicts such a hypothesis. As long as the origin of the constellation drawings remains the puzzle it is today, any guess on its place of origin is premature. All the same, this globe of the second quarter of the fourteenth century is closest to what I imagine a Greek model of Ptolemy's precession globe would have looked like.

5.3 MAPS IN THE MATHEMATICAL TRADITION

In the fifteenth century a revival in map making in central Europe took place which, through the work of Dana Bennett Durand, became known as the Vienna-Klosterneuburg map corpus. The greater part of the material is centred on geographical problems, such as finding the correct coordinates of places, their latitudes and longitudes, and so on. Two sketches prepared by Conrad of Dyffenbach are based on a modified version of the list of coordinates included in the Toledan Tables.80 These early Dyffenbach terrestrial maps are preserved in Vatican City, Biblioteca Apostolica Vaticana, MS Palat. lat. 1368, ff. 46v–47v and ff. 65v–66r. Preceding the latter map are, on ff 63r–64v, four celestial maps.

Already in 1915 Saxl had recorded in his description of Vatican City MS Palat. lat. 1368 the existence of four celestial maps on ff. 63r–64v of an unusual design.81 They were first studied in 1937 by Uhden, but gained significance when Durand discussed them in the context of the Vienna map corpus.82 The part of the codex with the maps appears to have been written around 1426 by Conrad of Dyffenbach, witness of which is a remark made at the end of the astrological treatise (f. 45r): ‘Et sic finitur centiloquium Ptholomei scriptum per me Conradum de Dyffenbach anno domini 1426, festo epiphanie domini etc’.83

Conrad of Dyffenbach matriculated at Heidelberg University in 1399 and later became a (p.358) prebendary of the church of St Peter in Aschaffenburg. Conrad was probably either a student or a colleague of Johannes of  Wachenheim, who matriculated in 1377 in Prague and then moved to Heidelberg University where he became Rector in 1387. Johannes later obtained a canonry in the church of St Cyriac at Neuhausen near Worms and was also known as Johannes de Wormacia.

It is not known whether Conrad of  Dyffenbach was the author of the celestial maps or only the copyist. The maps are preceded by an illustrated star catalogue on ff. 51r–56v said to have been verified by Johannes of Wachenheim for 1420, and on ff. 56v–58v there is a list of stars with their planetary natures and another listing their place in the zodiacal signs for 1400.84 On ff. 59r–62v there follows a series of drawings of the discs of an equatorium, a device for calculating the positions of the planets. The celestial maps on ff. 63r–64v are followed by a terrestrial map (ff. 65v–66r, labelled by Durand Dyffenbach II) which Durand suggests may have been inspired by the celestial maps. Before discussing the context of the celestial maps, something must be said about their projection.

5.3.1 The Dyffenbach projection

There are four celestial maps divided over four pages (Figs 5.135.16), which are described in more detail in Appendix 5.1 as M1a–d. One of the maps, labelled here M1a, is circular and extends from the ecliptic north pole to the ecliptic. It is marked by a grid consisting of a series of equidistant circles centred around the ecliptic north pole, which represent parallels for every 5°, and a series of straight lines extending from the ecliptic north pole to the ecliptic, which represent great circles for every 5°. In modern terms this map is a polar azimuthal equidistant projection of the northern celestial hemisphere. Examples of celestial maps with equidistant circles centred on the equatorial north pole were known in the Middle Ages (Section 3.2) and may indicate that such maps were known in Antiquity. The surviving medieval examples show however that the very notion of a projection does not yet underline the construction of these maps. A typical ‘error’ in these medieval maps is that oblique circles are presented as circles whereas in the polar azimuthal equidistant projection such circles are mapped onto higher order curves which are difficult to draw. The first thorough treatment of this projection is given by the ninth-century Arab astronomer and mathematician Ḥabash al-Ḥāsib.85 As discussed in Chapter 4, al-Bīrūnī mentioned and rejected this projection since one has to present the celestial sphere into two halves, with the result that the borders of each cut through the zodiacal constellations and would divide them over the two hemispheres ‘and that is far from what is sought’.86 The objection raised here is, however, not restricted to the polar azimuthal equidistant projection but applies to any presentation of the celestial sphere in two maps bounded by the ecliptic. The constellations located in the zodiac are, generally speaking, half north and half south of the ecliptic. Considering the importance attached to the zodiac such a division of the zodiacal constellations is not commendable. Extending the maps to include the zodiacal constellations completely, as was done with the Vienna maps discussed below, has the disadvantage that the (p.359) circles parallel but south to the ecliptic have a greater diameter than the ecliptic. The objection raised by al-Bīrūnī is certainly of interest in discussing the Dyffenbach maps because it may explain why next to the map of the northern hemisphere bounded by the ecliptic there are

The Mathematical Tradition in Medieval Europe

Fig. 5.13 Part of the Dyffenbach map M1a in Vatican City, MS Palat. lat. 1368, f. 63v. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.)

also three maps (M1b–M1d) in another projection centred on the zodiac. Overstepping the boundaries was clearly no option for the author of the Dyffenbach maps.

This alternative way to map the zodiac was investigated by Uhden and most of his (p.360) conclusions were taken over by later authors. Uhden associated the zodiacal maps M1b–M1d with the trapezoidal projection—calling it the oldest known example of it. Uhden noticed that the ratio of the longitude intervals at respectively the parallel for a latitude 30° and at the ecliptic (latitude 0°) is 2:3 whereas in the Donis projection,

The Mathematical Tradition in Medieval Europe

Fig. 5.14 Part of the Dyffenbach map M1a and map M1c in Vatican City, MS Palat. lat. 1368, f. 64r. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.)

which maintains the correct proportion of the longitude intervals, such a ratio holds only for a latitude of 48°. Thus Uhden concluded:

‘In determining the size of the latitudinal degree, then, the author of this map must have proceeded from a premise very different from that of Nicolaus (p.361)

The Mathematical Tradition in Medieval Europe

Fig. 5.15 The Dyffenbach map M1b in Vatican City, MS Palat. lat. 1368, f. 63r. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.)

Donnus. The former's [Dyffenbach] method becomes clear only when compared with the map described above. Measurement shows that the trapezoidal projection plan was derived directly from the equidistant planisphere. The distances between the meridians on the celestial equator and those on the parallels at 30° both follow the system of azimuthal projection and form the basis of the drawing of the second map. A most curious method, indeed, a second example of which can scarcely exist and which hardly deserves imitation.’87

This statement induced Durand to say that ‘in fact the network of the trapezoidal Dyffenbach star maps appears to have been derived not by true projection from a globe, but rather by measurements from the azimuthal frame constructed on f. 63v’, that is the polar map.88 Uhden's conclusion that the size of the latitudinal degree was determined by measuring ratios on the polar map is not convincing. Besides, the method used in constructing the three zodiacal Dyffenbach maps follows a simple mathematical principle and may therefore be marked as a proper projection. The Dyffenbach projection—as I propose to call it—consists of a series of equidistant straight lines, representing parallels to the ecliptic, (p.362)

The Mathematical Tradition in Medieval Europe

Fig. 5.16 The Dyffenbach map M1d in Vatican City, MS Palat. lat. 1368, f. 64v. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.)

and a series of straight lines extending from the ecliptic north and south pole to the ecliptic, representing great circles. The basic structure is shown in Scheme 5.2.

Simple geometry shows that in this Dyffenbach projection the ratio of the lengths of a degree at respectively latitudes 30° and 0° is proportional to CD:AB = PR:PS = 2:3. Generally, the ratio of the lengths of a degree at latitudes b and 0° is equal to EF:AB = PQ:PS = (90°-b): 90°. Note that the projection does not require a central meridian, the position of the poles P and T can be placed anywhere along the lines at a distance of 90° from the ecliptic. The Dyffenbach projection differs thus in its defining characteristics from the Donis projection in which the ratio of the lengths of a degree at respectively latitudes b and 0° is proportional to cos b.89

In a way one could place the Dyffenbach projection between the polar azimuthal equidistant projection and the Donis projection but conceptually it is closer to the former. The Dyffenbach projection could have been developed from the polar azimuthal equidistant projection simply by (p.363)

The Mathematical Tradition in Medieval Europe

Scheme 5.2 Construction underlying the Dyffenbach projection.

replacing the series of equidistant circles centred on the pole by a series of straight parallel lines. The connection between the polar map M1b and the zodiacal map M1c. on f. 64r might suggest this since both maps are centred on the summer solstitial colure. However, this is misleading because the zodiacal map is drawn upside-down with respect to the north–south orientation of the polar map, and as such is not a continuation of the polar map.

Looking now at the details of the Dyffenbach maps we note that each map is based on a grid of 5° × 5° in longitude and latitude. The parallels 5° north and south of the ecliptic are not drawn but are replaced by lines 6° north and south of the ecliptic, conforming to the antique concept of the zodiac consisting of a band bounded by the circles parallel to the ecliptic 6° north and south of it. Each map extends in longitude by roughly four signs of the zodiac. It would have been astronomically perhaps more logical to make four zodiacal maps covering each three signs, corresponding to the four seasons. The choice to make three instead of four maps must have had a practical reason.

If we look at the size of the maps in latitude the situation is less systematic. The map on f. 63r (Fig. 5.14/M1b), covering the first four signs of the zodiac (Aries, Taurus, Gemini, Cancer), extends from latitude 30° north to 55° south of the ecliptic to include such southern constellations as Eridanus and Canis Maior. The other two maps on respectively f. 64r (Fig. 5.15/M1c), covering the second set of four signs (Leo, Virgo, Libra, Scorpius) and on f. 64v (Fig. 5.16/M1d), covering the last set of four signs (Sagittarius, Capricornus, Aquarius, Pisces) extend both from latitude 30° north to 30° south of the ecliptic. There are also a few non-zodiacal constellations sometimes only presented by some of their stars but all have latitude less than 30° north or south. Taken together one gets the impression that the author of the maps was exploring the scope of his projection and, after the trial seen in map M1b (Fig. 5.14) to extend further south, decided that this did not deserve following up in the other maps, presumably because the ratio of the lengths of a degree at respectively latitudes 55° and 0° is equal to (90°-55°):90° = 0.39. This should be compared to the corresponding value cos 55 ° = 0.57 in the polar azimuthal equidistant projection and the Donis projection.

5.3.2 Astronomical significance

Looking at the astronomical features of the maps it is clear that the polar and the zodiacal maps share a few aspects in construction. In setting out (p.364) the scales in longitude the signs run from left to right on both the polar map and the zodiacal ones except in the zodiacal map M1c where the longitude runs from right to left because the map is upside-down. It is not clear how consciously this choice was made. In Western writing authors precede from left to right naturally. However, the result is that the east–west order of the stars is presented in the maps as these are seen on a globe and not as in the sky.

Using the map's grid the position of each star is indicated according to its longitude and latitude recorded in the Ptolemaic star catalogue but corrected for precession. The brightest stars are indicated by a starry symbol and nebulous stars by a dot surrounded by a small dotted circle. However, most stars are marked by a number, which indicates its brightness. In the Ptolemaic catalogue there are 15 stars of the first, 45 stars of the second, 208 stars of the third, 474 stars of the fourth, 217 stars of the fifth, and 49 stars of the sixth magnitude. In addition there are 9 faint stars, 5 nebulous, and 3 in Coma. It is clear that stars of the fourth magnitude are the most numerous and therefore the number 4 is found most frequently in the maps.

Next to the magnitude the map maker also added short descriptions of the location of the stars within the constellation to which they belong. Astrological information is also added. Occasionally a proper name is added to well-known stars. For example, the brightest star in Canis Minor (shown in the enlarged picture in Fig. 5.17) is marked by a starry symbol with its medieval name algomesa and the other star belonging to this constellation is indicated by the number 4, its magnitude, and described as the neck (collo) of algomesa. The name used for the constellation in medieval times stemming from the Arabic was also used for its brightest star.

The Mathematical Tradition in Medieval Europe

Fig. 5.17 Detail of the Dyffenbach map M1b in Vatican City, MS Palat. lat. 1368, f. 63r. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.)

In the area south of Canis Minor are two stars which attract attention because they should not be there. These stars belong to the constellation Navis (nos 44 and 45). According to the Greek and Arabic versions of the Ptolemaic star catalogue both stars should lie at southern latitude of respectively -75º and -71º 45´.90 In the Latin translation of Gerard of Cremona, star no. 44 of Navis, described as ‘in remo sequente et dicitur canopus et est suhel’, is of the first magnitude and its latitude is -29°. On the map this star is marked by an asterisk, labelled ‘canap[. . .] in navi/in remo/saturni [et] jouis’, and its position agrees with Gerard's value -29°. Star no. 45 of Navis, described in the catalogue as ‘Reliqua sequens earum’, is of the third magnitude and its latitude is -21° 50´. On the map this star is marked by the number 3 and labelled ‘sequens canap[. . .]’, and its position agrees also with the erroneous latitude −21° 50´ recorded in the Latin translation of Gerard of Cremona.91

The erroneous positions of stars nos 44 and 45 of Navis tell us that Durand's assumption that (p.365) the star catalogue preceding the maps on ff. 51r–56v by Johannes of Wachenheim was used in constructing the maps is incorrect.92 The latitudes of stars nos 44 and 45 of Navis in this star catalogue are respectively -75° and -71° 50´. In related star catalogues, such as in Vatican City, Biblioteca Apostolica Vaticana, MS Palat. lat. 1377, ff. 183r–194v for the epoch AD 137, the latitude of star no. 44 is given as -29° but this is followed by a correction to

-75° and the latitude of no. 45 is given as -71° 50´.93 And in Oxford, Bodleian Library, MS Rawl. C. 117, ff. 145r–157r for the Alfonsine epoch 1252 (17º 8´), the erroneous value of no. 44 (-29°) is changed to -69° and that of no. 5 (-21° 50´) is left unchanged. It seems that there was a certain awareness that the values of the latitudes of these stars in Gerard's catalogue were wrong. The entries in these various catalogues show that the maker of the Dyffenbach maps used a copy not far removed from the Latin translation of Gerard of Cremona but of course corrected for precession. The erroneous positions of stars nos 44 and 45 in Navis also tell us that the star catalogue in Vienna MS 5415, corrected for precession by 18° 56´ for the epoch 1424, was not used in constructing the Dyffenbach maps because the latitudes of stars nos 44 and 45 are given there as -75° and -77° 45´ (instead of -71° 45´!). The reason to suppose a relation between the Dyffenbach maps and this Vienna star catalogue is that both sources represent Bootes with a stick in one hand and a bow in the other. This image of Bootes is very unusual and must stem from a common source, a thesis supported by the images of Cepheus in both the Vienna catalogue and the polar map M1a.

In order to determine the epoch of a map or a globe it is usually best to select a number of stars close to the ecliptic and subsequently determine the differences between the longitudes of the stars on the map and those in the Ptolemaic catalogue for the epoch ad 137. The mean value of these differences generally speaking gives a fair estimate of the required precession correction for the map or globe. For the Dyffenbach maps I have limited the selection to those stars marked by an asterisk because only for these can a fairly good position be determined. The longitudes of these stars (MLon) and their latitudes (MLat) are shown in Table 5.1, together with the Ptolemaic values (PLon and PLat) and the differences in longitude (DLon) and latitude (DLat).

If all 14 stars are included the precession correction is equal to 19.3º ± 0.17º, which in terms of the Alfonsine trepidation theory corresponds to the period between 1446 and 1482. Among these 14 stars there are 2 which have values of Dlon which differ 1.5 times the standard deviation from the mean value. If these stars are rejected a new mean value can be determined which, using the same criterion, allows one to reject one more star. This process converges after the rejection of four stars (nos 11–14 in Table 5.1). Three of the four stars are located on the zodiacal map M1b which extends far to the south. The location of the fourth star, α PsA, is hard to determine. Anyway, when these four stars are left out, the precession correction is equal to 18.93º ± 0.10º, which in terms of the Alfonsine trepidation theory corresponds to the period between 1415 and 1441 which agrees well with the date of the maps. If only the four stars of the polar map M1a are used (nos 1–4 in Table 5.1) the precession correction is equal to 18.96º ± 0.09ºm which is close to the values obtained for (p.366)

Table 5.1 Stellar longitudes on Dyffenbach's maps compared to Ptolemaic values

No.

BPK

Modern

PLon

MLon

PLat

MLat

DLon

DLat

1

110

α

Boo

177.0

196.0

31.5

31.0

19.0

-0.5

2

197

α

Per

34.8

54.0

30.0

30.0

19.2

0.0

3

222

α

Aur

55.0

74.0

22.5

23.0

19.0

0.5

4

223

β

Aur

62.8

81.5

20.0

20.0

18.7

0.0

5

393

α

Tau

42.7

62.0

-5.2

-5.5

19.3

-0.3

6

469

α

Leo

122.5

141.0

0.2

0.0

18.5

-0.2

7

488

β

Leo

144.5

163.0

11.8

12.0

18.5

0.2

8

510

α

Vir

176.7

195.5

-2.0

-2.0

18.8

0.0

9

735

α

Ori

62.0

81.5

-17.0

-17.5

19.5

-0.5

10

818

α

CMa

77.7

96.5

-39.2

-39.0

18.8

0.2

11

670

α

PsA

300.0

320.0

-23.0

-23.0

20.0

0.0

12

768

β

Ori

49.8

70.0

-31.5

-32.0

20.2

-0.5

13

892

α

Car

77.2

97.5

-29.0

-29.0

20.3

0.0

14

848

α

CMi

89.2

109.5

-16.2

-16.0

20.3

0.2

Mean value of all 14 stars

19.30

-0.07

Standard deviation of all stars

0.64

0.29

Error in the mean

0.17

0.08

Mean value of all but stars nos 11–14

18.93

-0.07

Standard deviation of all but stars nos 11-14

0.32

0.30

Error in the mean

0.10

0.09

all maps. This shows that the maker was capable of updating the catalogue he used.

For unknown reasons the maps were not finished. On the polar map M1a only 7 of the 21 northern constellations in the Ptolemaic star catalogue have been completed (Ursa Minor, Ursa Maior, Draco, Cepheus, Bootes, Corona Borealis, and Auriga). In addition some of the stars belonging to the constellations Perseus and Ophiuchus have been plotted.

On the zodiacal map M1b Aries, Taurus, Gemini, Cancer, and Leo (the western part) are presented. North of the ecliptic one finds Triangulum and south of it Cetus (the eastern part), Eridanus, Orion, Lepus, Canis Maior, and Canis Minor. Next to the erroneous stars nos 44 and 45 of Navis, discussed above, one finds east of Canis Maior a few more stars that belong to Navis, but the contour of the ship is not drawn.

On the zodiacal map M1c Leo (the eastern part), Virgo, Libra, and Scorpio are drawn. North of the ecliptic one finds the three stars of Coma Berenices (Leo 6e–8e), marked oc, oc, and ne, with a note saying that they lie between the tail of Leo and Ursa Maior. Another star plotted north of Virgo is probably the northernmost of the three stars in the leg of Bootes (Boo 20). South of the ecliptic one finds Crater and Corvus, but not Hydra and two stars that belong to Lupus (Lup 1–2).

On the zodiacal map M1d Sagittarius, Capricornus, Aquarius, and Pisces are presented. North of the ecliptic are four stars of Pegasus, the identifications of which are troublesome. At first sight they seem to represent the bright stars of second magnitude in the square of Pegasus (Peg 1–4) but these stars ought to lie more to the east. South of the ecliptic one finds Piscis Austrinus (p.367) and Cetus. A few stars of Sagittarius are misplaced. Sgr 23 and 24 are off by 5°, and Sgr 25 in the front right hock of Sagittarius is off by 20°, thus creating the curious shape of this constellation. These incorrect positions may have been part of the star catalogue but could also have been introduced by the maker of the map.

The constellations drawn on the zodiacal map raise many questions. One might think that the presentation of the constellation figures was not the first concern of the maker of the maps. As mentioned in Section 5.2 Ptolemy advises making the shapes of the individual constellations as simple as possible, surrounding the stars within the same figure only by lines. Yet, Ptolemy must have meant recognizable figures, not the vague forms drawn in the Dyffenbach maps. Some figures are worse than others. On map M1b (Fig. 5.14) Eridanus and Leo are more easily recognized than Taurus and the Gemini, whereas on map M1c (Fig. 5.15) Crater and Corvus are barely discernible as a bowl and a bird. It is not so difficult to identify Aquarius with his stream of water ending in Piscis Austrinus on map M1d (Fig. 5.16) but Cetus is presented as a curiously shaped animal. The often oddly shaped constellations in the zodiacal maps contrast with the figures drawn in the polar map. Especially the images of Bootes and Cepheus show that the map maker—although not a gifted artist—had access to a model for drawing the constellation figures. The best explanation for the clumsy figures in the zodiacal maps is, in my opinion, that the map maker consciously ignored existing iconographic traditions and tried to draw the constellations from the descriptions of the Ptolemaic star catalogue. His result shows that in the absence of a good model this is not at all easy.

This does not change the fact that the maps are novel in a number of ways: the choice of the projection; the choice of marking the stars by the number of their magnitude instead of by dots of different sizes; the choice of adding information of the location of the stars with respect to the constellation figure. All this seem to point to a search for a method of mapping the celestial sphere on a plane such that most of the information in the star catalogue was made available graphically.

5.3.3 The Vienna maps

The next step in the development of mathematical celestial cartography in Europe is connected with the codex Vienna, Österreichische Nationalbibliothek, MS 5415, which contains a number of interesting astronomical texts. On ff. 161r–191r one finds the treatise on globe making, the Tractatus de sphaera solida, and on ff. 192r–210v there follows another one, the Tractatus de spera volubili of Qusṭā ibn Lūqā. After a number of empty pages (ff. 211r–216r) a short note follows on f. 216v about how to prepare the grid of maps representing the northern and southern hemispheres. This is in turn followed on ff. 217r–251v by a star catalogue for the epoch 1424 with stellar longitudes 18° 56´ in excess of the Ptolemaic longitudes.

The Tractatus de sphaera solida in Vienna MS 5415 stands out for its graphic presentations. Next to the usual schematic drawings of the mounting in the shape of a hemispherical bowl an image of a celestial globe is included on f. 180v (see Fig. 5.26 below), which in all respects has the appearance of a real globe almost as we know it today. Preceding these various schemata are two celestial maps, on f. 168r and f. 170r (see Figs 5.18 and 5.19). These maps are described in more detail in Appendix 5.1 and shall here be referred to as the Vienna maps.

According to Durand, Vienna MS 5415 was among the four manuscripts (the three others are (p.368)

The Mathematical Tradition in Medieval Europe

Fig. 5.18 The northern celestial hemisphere in Vienna MS 5415, f. 168r. (Courtesy Österreichische Nationalbibliothek, Vienna, Picture Archive.) See also Plate VI.

(p.369)
The Mathematical Tradition in Medieval Europe

Fig. 5.19 The southern celestial hemisphere in Vienna MS 5415, f. 170r. (Courtesy Österreichische Nationalbibliothek, Vienna, Picture Archive.) See also Plate VII.

Vienna MS 5418, Munich Clm 56, Munich Clm 10662) written by Reinardus Gensfelder (ca. 1385–1457?).94 This ‘wandering scholar’ was born in Nuremberg. He received his university education in Prague where he became magister artium in 1408. Thereafter he continued his studies in Padua. Between 1433 and 1436 Gensfelder seems to have spent some time in Salzburg, possibly in the monastery of St Peter. In 1436 he entered the monastery of Reichenbach but he continued to (p.370) travel. In 1439 he went to Vienna, in 1440 to Passau, and in 1441 he was in Klosterneuburg. In 1444 Gensfelder became a priest in the parish of Tegernheim close to Regensburg. He appears to have died before1457.

When and where Gensfelder produced Vienna MS 5415 has been a topic of debate. Dates mentioned in the literature vary from 1435 to 1444. The former date 1435 is mentioned on f. 191r: ‘Explicit tractatus…finitus anno 1435o currente’.95 The later date 1444 occurs on f. 159v: ‘Explicit tractatus Albionis finitus anno Christi 1444o currente etc.’, and on f. 180r: ‘anno Domini 1444o’.96 It has been argued that the date on f. 159v is a writing error of 1434 and that the date on f. 180r might refer to an adjustment made on that page because on f. 191r it is clearly stated that the Tractatus de sphaera solida was finished in 1435.97 However that may be, for the maps a date of 1435 seems most probable because they are closely connected to the Tractatus de sphaera solida.

The question of the place of production of Vienna MS 5415 must be left open since there is no consensus among scholars on where the manuscript was produced. Durand claims that it was copied in 1435 during Gensfelder's visit to Salzburg and that he also prepared the maps included in the codex there.98 This visit to Salzburg is, according to Durand, attested ‘by the subscriptions of several of the sections in the two Vienna manuscripts (i.e., Codices 5415 and 5418), also in Palat. lat. 1374, f. 112v’.99 Unfortunately this cannot be confirmed.100 It has also been argued from the coats of arms of Vienna, Austria, and Klosterneuburg on f. 33v of the MS 5415 that Gensfelder was in or around Vienna in the years 1433–35.101 This is why Vienna and Klosterneuburg have also been proposed as the place where Gensfelder might have copied the manuscript.102 Wherever the place of production of Vienna MS 5415 might have been, scholars agree that this important manuscript is closely connected with the activities of the Vienna astronomical school. Its most prominent member was John of Gmunden (ca. 1384–1442), an astronomer and mathematician, who lectured at Vienna University.103 John is famous for his educational texts on devices of all sorts. His collection of instruments, which included among others a celestial globe, an astrolabe, and an armillary sphere, was bequeathed to the University of Vienna.104 Georg Müstinger (born before 1400–42) was another important member of the Vienna school. Müstinger was prior of the Augustinian monastery of Klosterneuburg, and also vicar general of the archdiocese of Salzburg. The ties between Salzburg on the one hand and Vienna and Klosterneuburg on the other are, for example, expressed on the Klosterneuburg map, the centre of which is close to Salzburg while the basic radius line runs between Vienna and Klosterneuburg.105

(p.371)

The Mathematical Tradition in Medieval Europe

Scheme 5.3 The main grid of the northern and southern hemispheres in Vienna MS 5415, f. 168r and f. 170r.

There can hardly be a greater contrast than that existing between the Dyffenbach and the Vienna maps. While the Dyffenbach maps show the hesitant search for method in constructing celestial maps, the maker of the Vienna maps seems to have solved most problems associated with such an enterprise. The difference between the Dyffenbach and the Vienna maps is especially visible in the drawings of the constellations, but before discussing this a few remarks on the projection of the Vienna maps must be made.

The Vienna maps serve in the first place as a model for drawing the constellations on a celestial globe, as described in the Tractatus de sphaera solida. This does explain why the maker chose the equidistant projection for his maps, as applied in Dyffenbach's map M1a. However, when compared to this latter map, the number of great circles through the ecliptic pole in the Vienna maps is greatly reduced. The stars and their constellations are outlined with respect to a grid that consists of an outer boundary circle and 12 straight lines representing respectively the ecliptic and 12 great circles through the ecliptic pole (see Scheme 5.3). Added to this basic grid are a number of circles centred on the equatorial pole (N and S in Scheme 5.3) which do not occur on the Dyffenbach map.

One pair of circles represents the polar circles described in the Tractatus de sphaera solida. The other equatorial circle drawn on the Vienna maps passes through the first points of Aries and Libra and extends on one side beyond the ecliptic. It presumably represents the Equator. By definition the Equator should not only pass through the equinoxes but also through the points T located on the solstitial (p.372) colures through the first points of Cancer and Capricornus, at a distance equivalent to 90° from the equatorial poles (compare Scheme 5.3). However, since in the equidistant projection oblique circles like the Equator are projected as ovals instead of circles, the Equators drawn on both hemispheres do not pass through the points T in Scheme 5.3.

In the northern hemisphere two more circles are drawn (dotted in Scheme 5.3). The smaller of these two circles is centred on the north equatorial pole N. It has been suggested that this smallest circle of a diameter equivalent to 4.7° traces the daily rotation of the star at the end of the tail of Ursa Minor (α UMi). The ecliptic coordinates of α UMi for 1424 using the Ptolemaic catalogue are longitude 79.1° (Gem 19° 6´) and latitude 66°. When converted to equatorial coordinates we obtain a right ascension of 358.5° and a declination of 85.6°. Thus α UMi would have been 4.4° from the north equatorial pole which is only slightly less than 4.7°. The smallest circle could therefore represent the daily rotation of the star at the end of the tail of Ursa Minor (compare Fig. 5.18). However, this explanation cannot be the whole story, if only because the northernmost intersection of the small circle with the solstitial colure (point P in the northern hemisphere in Scheme 5.3, where a dot is clearly visible) is the centre of another circle which passes through the equinoxes. How this greater circle should be understood is not evident. In the southern hemisphere this centre (point P in the southern hemisphere in Scheme 5.3) is also marked, although the corresponding circle through the equinoxes is not drawn. There is a trace of a small circle around point P instead of around the south equatorial pole S (see Fig. 5.19). The meaning of this small circle is also unclear. My guess is that the map maker tried to compensate for the fact that the Equator did not pass through the solstices, but understandably did not succeed in finding an alternative solution. In that sense the additional circles in the maps are best seen as trials of drawing the Equator correctly. It shows that the polar equidistant projection was not yet fully understood by the map maker.

As already mentioned above, there is no detailed grid to plot the stars on the Vienna maps. The most likely method used by the map maker for marking the stellar positions is by using a ruler with an equidistant scale in latitude in analogy to the use of a great circle centred on the ecliptic pole for indicating the stellar positions on the sphere as described in the Tractatus de sphaera solida. By using the scale along the ecliptic and that of the ruler the position of the star was marked by a point (or hole) in the parchment at the latitude of the star. The map maker next added a number to the point to identify the star with its position in the constellation figure as described in the star catalogue. Once the stars belonging to one and the same constellation were marked, the constellation itself could be drawn around the group of stars. An interesting aspect of the northern hemisphere of the Vienna maps is that the zodiacal constellations extend across the ecliptic. The reason for this is clearly to avoid the zodiacal constellations becoming divided between the two hemispheres which—as al-Bīrūnī had argued—is unacceptable.

In plotting the stars the map maker or the maker of its model must have used a star catalogue which must account for the following characteristics:

  1. 1. The longitudes of its stars differ with respect to the corresponding Ptolemaic values by (p.373) 18° 53´ ± 21´, which mean value and standard deviation was obtained by measuring the ecliptic longitudes of 18 stars located close to the ecliptic.

  2. 2. The numbering of the stars within the constellation Andromeda deviates from that in most medieval star catalogues. For example, the stars that are listed in modern editions as nos 11–14, 15, 16–23 in the description of Andromeda are in the map numbered 20–23, 19, and 11–18, respectively.

  3. 3. The numbering of the stars within the constellation Auriga deviates from that in most medieval star catalogues. Two stars are missing: one is a star in the left arm, Aur 9, and the other is in the right knee, Aur 14. As a result the stars, that are listed in modern editions as nos 10–13 in the description of Auriga, are in the map numbered nos 9–12, respectively, and since Aur 14 is missing altogether, no. 12 is the last star in Auriga.

  4. 4. There are a few positions that deviate from those common in most medieval star catalogues. The stars Ari 9 and Ari 10 in the tail of Aries are south of the ecliptic instead of north and the star Navis no. 45 lies south instead of north of Navis no. 44.

  5. 5. The names of the stars presented on the Vienna maps, summarized in Table 5A.1 in Appendix 5.1, include quite a number of unusual Arabic star names that do not occur in most medieval star catalogues.

The features 1–5 define a catalogue tradition which is exemplified by Vienna star catalogue in Vienna MS 5415 on ff. 217r–251v.106 This catalogue is greatly inflated with star and constellation names compiled from several sources including texts translated from the Arabic, which accounts for most of the star names on the Vienna maps.107 The stellar longitudes in the Vienna star catalogue are adapted for precession for the epoch 1424 by adding 18° 56´ to the Ptolemaic longitudes consistent with the mean value 18° 53´ ±21´ quoted above. The numbers of the stars in Andromeda deviate from the more usual order. The entry of Auriga consists of 12 stars only. The latitudes of Ari 9–10 are south instead of north of the ecliptic and the latitudes of stars nos 44 and 45 of Navis are respectively given as -75° 0´ and -77° 45´. The latter value deviates from the latitude -71° 45´ given in most medieval star catalogues, with the result that the star Navis no. 45 is south instead of north of Navis no. 44. There is one inconsistency: in the Vienna catalogue the latitude of Arcturus (Boo 1e) is given as 25° instead of 31° 30´ but on the map the latter correct value is used. Clearly, a very close copy of this Vienna catalogue was used in the construction of the maps or its model.

The most outstanding feature of the constellation designs of the Vienna maps is that all human figures are without exception seen from the rear.108 No example of this way of presentation from earlier times existed in the Middle Ages. The only other document that comes close to the Vienna maps in this respect, but not quite, is the Farnese globe discussed in Section 2.6. In medieval illustrated manuscripts the constellations are sometimes drawn face-on, sometimes as seen from behind. Arabic globes present the constellation figures consistently in front view as the mirror images of the figures as seen in the sky. In short, the constellation images on the Vienna (p.374) maps do not fit into a specific medieval tradition and as such represent a unique highlight in celestial cartography.

In 1927 Saxl suggested that the Vienna maps are a precise copy of an oriental model.109 Saxl's argument is based on certain Arabic elements in the presentations of some constellations. As mentioned before, Arabic pictorial traditions in celestial cartography were transmitted to the Latin West mostly by way of the Ṣūfī Latinus corpus. The illustrations in the constellation cycle of this corpus are all connected through typical features of al-Ṣūfī's uranography as, for example, the sickle in Hercules's raised hand, the head of Ghūl carried by Perseus, an extended sleeve of Orion and a bunch of branches in the hand of Centaurus. The characteristics of Hercules and Perseus are included on the Vienna maps but those of Orion and Centaurus are not. To complicate matters I like to mention the image of Lyra which on the map is drawn as a bird. This image results from a translation of an old Arabic name of Lyra or a few stars thereof, ‘an-nasr al-wāqic’, meaning ‘the Falling Eagle’.110 The Latin name vultur cadens was introduced in the Latin West through star tables used in constructing astrolabes and through Gerard of Cremona's star catalogue and this is behind Lyra's image of a bird occurring in Western iconographic traditions but not in constellation cycles belonging to the Ṣūfī Latinus corpus.111 The examples mentioned here show that the background of the iconography of the Vienna maps is complex and that the author/artist of its model seems to have borrowed from a variety of existing traditions. It also shows that Saxl's thesis of an oriental exemplar for the Vienna maps cannot be maintained, the more so since an Arabic tradition can neither explain presentations of the constellations in rear view nor can it account for the representation of the Milky Way drawn on the Vienna maps.

As an alternative for explaining the unusual style of the constellations Roland suggested that in addition to Arabic influences there may have been antique examples at hand in Vienna.112 It is hard to substantiate this possibility. Considering the close connection between the maps and Gerard of Cremona's Latin translation from the Arabic of the Ptolemaic star catalogue, I doubt that in particular the rear-view presentations of constellations on the Vienna maps can be explained by antique examples. It may not be satisfying to conclude that the constellation designs of the Vienna maps are not connected with a specific constellation cycle, yet in the absence of a clear link to any such cycle the thesis that especially its rear-view iconography was newly created while making a celestial globe is worth considering. Indeed, in shaping the constellations into rear view the astronomer/artist may have adapted images from a variety of sources, and this may account for one aspect of the complex background of the Vienna maps.

Since the presentations on the Vienna maps are internally consistent, in the sense that all human constellation figures are seen in rear view, the maker of the exemplar (model globe) of the Vienna maps must have applied a specific rule. The rule could have been suggested by the descriptive part of the Ptolemaic star catalogue, explaining where, in which part of the body, left (p.375) or right and so on, a star had to be located. By insisting that a star described by Ptolemy in the right hand or in the left foot ends up on the globe in the right hand or in the left foot of a constellation all human figures are automatically presented from the rear. At the same time the shapes and attitudes of the constellations would agree with the Ptolemaic iconography as discussed in Section 4.4. The awareness of the significance of these descriptions in drawing constellations is seen in the Dyffenbach maps M1b– M1d, although there the maker did not succeed in drawing recognizable figures. The images in the Vienna maps may well be the final result of a number of now lost trials in this respect. Anyhow, the demand for correspondence between text and images gained importance in the fifteenth century. On most fifteenth- and sixteenth century maps and globes the human constellation figures are without exception drawn in rear view.

But let me return to Vienna MS 5415. As mentioned before, the star catalogue in this codex must have been very close to the one used for the Vienna maps and the question arises of how in particular the constellation designs in the maps and the star catalogue are related. The styles of the drawings in the Vienna catalogue and of those on the Vienna maps point to work by different artists.113 Also the iconography of a number of the constellation figures in the star catalogue clearly differs from that in the maps. In the catalogue Cepheus is drawn upright instead of kneeling and he carries a sceptre and a globus cruciger, Bootes is equipped with an additional bow, Hercules is drawn in the star catalogue face on and carries a lion's skin in his extended left hand, Cassiopeia is dressed and sits with outstretched arms on a throne holding a small sphere in her left hand, and Orion's tunic is turned into a more military outfit with a helm and a horn. The images of these constellations are not comparable with those in the maps. Those of Bootes and Cepheus point to a constellation cycle in a star catalogue which left its trace on the Dyffenbach map M1a. Other constellations such as Hercules, Cassiopeia, and Orion may derive from the same cycle. But what can be said about the other constellations?

Looking at the zodiacal constellations one finds that some (Aries, Cancer, Leo, Libra, Capricornus, and Pisces) are close to the images on the maps and others (Taurus, Virgo, Sagittarius, and Aquarius) are the reverse of those on the map. Indeed, on both the map and in the catalogue Taurus extends his left leg in front of him, Virgo points with her right finger to her head, Sagittarius holds the bow in his left hand, and Aquarius the urn under his right arm. Thus the catalogue images of Taurus, Virgo, Sagittarius, and Aquarius have the same left and right characteristics as those on the Vienna maps. Provided that the artist knew how to reverse an image it is possible that a number of zodiacal constellations on the maps were copied from the catalogue or vice versa. Of special interest in this respect is the image of Gemini in the catalogue. In Scheme 5.4 the schematic images of Gemini on the Vienna maps and in the Vienna star catalogue are presented. I have also added the image of Gemini in the map in Munich, Clm 14583, discussed later. The image in Munich, Clm 14583 in Scheme 5.4 is slightly adapted to correct the deformations caused by the binding in the manuscript (see Figs 5.18 and 5.20).

It is clear that all three images present the twins in rear view, showing their backs. The attitude of the Gemini, especially the western orientation of their legs on the Vienna map and on the maps in Munich Clm 14583, are consistent with the stellar (p.376)

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Scheme 5.4 The images of Gemini in Vienna MS 5415 f. 168r, f. 233v, and in Munich Clm 14583, f. 70v.

configuration as seen on a globe as it is described in the Ptolemaic star catalogue. The image of the Gemini in the Vienna star catalogue, on the other hand, is clearly the mirror image—not the reversed image—of the other two (ignoring the bunches of flowers)! This mirror image of Gemini is significant because it cannot be traced to an Islamic celestial globe. It could only be derived ultimately from a globe in the Western, mathematical tradition as presented on the Vienna maps. The example of Gemini suggests strongly that a number of zodiacal constellations in the catalogue were copied from a globe or a map and not the other way round. The image on the map in Munich, Clm 14583 in Scheme 5.4 confirms this. It suggests a scenario in which the artist of the star catalogue used a source related to a globe or map as his model, and copied some constellation images without modification (Aries, Cancer, Leo, Libra, Capricornus, and Pisces), reversed a few others (Taurus, Virgo, Sagittarius, and Aquarius) from globe-view to sky-view and presented one by its mirror image (Gemini). Such a scenario is confirmed by a few non-zodiacal constellations in the star catalogue. Most human figures are again presented face on, as seen in the sky. The catalogue images of Ophiuchus and Andromeda could easily have been obtained by reversing the images on a globe or map. And here too one finds an exception. Centaurus (f. 249r) is presented in rear view and he holds the lance with his left hand, whereas on the southern map in Vienna 5415 and on the map in Munich, Clm 14583 he holds it in his right hand. Thus the catalogue image of Centaurus is the mirror image of the figure depicted on the southern map in Vienna 5415 instead of the reversed image. Taken all together, the iconography of the constellations in the Vienna star catalogue seems the result of merging an existing constellation cycle with images borrowed from a source stemming from the Vienna maps or its model. A glimpse of this mix may be seen on f. 247v where Crater is drawn twice: as a wooden tub with two handles placed on Hydra, as on the Vienna maps, and independently as a vase.

As an aside I note that this scenario for the origin of the constellation designs is not contradicted by the relation between the illustrations in the Vienna star catalogue and those in Klosterneuburg, (p.377) Augustiner-Chorherrenstift, MS 125, ff. 6r–16r.114 This latter codex includes a constellation cycle illustrating excerpts of a text of Michael Scot (fl. c.1235), court astrologer to Emperor Frederick II.115 At the request of Frederick II Scot composed a work on astronomy and astrology, which includes a descriptive star catalogue Liber de signis. This medieval text includes a number of constellations which do not occur in the mathematical tradition and vice versa omits a few that are part of it.116 When the images in Klosterneuburg MS 125 are compared to those in the star catalogue in Vienna MS 5415, one sees that the presentations of the zodiacal constellations, among which is that of Gemini, agree. This holds also for a number of non-zodiacal constellations among which are Ursa Maior, Ursa Minor, Draco, Corona Borealis, Ophiuchus, Bootes (with sword in MS 125 and with traces thereof in MS 5415), a slightly adapted Perseus, Orion (with an ox-hide in MS 125), Navis, Canis Minor, Canis Maior, and Lepus. The presentations of a number of constellations, for example Hercules, Auriga, Andromeda, Eridanus, Centaurus, and Ara, in Klosterneuburg MS 125 are on the other hand in keeping with the characteristic iconography associated with Scot's text.117 These typical Scot-illustrations are not found in the Vienna catalogue. For example, the image of Auriga in Klosterneuburg MS 125 is a driver on a wagon, which fits Scot's iconography well in contrast to that in MS 5415 which seems to be the reverse of an image defined by the stellar configuration as it is described in the Ptolemaic star catalogue and as it is depicted on the Vienna maps. And although traces in the image of Andromeda in the catalogue in Vienna MS 5415 show that the artist intended originally an image of this chained woman with trees at her side in keeping with Scot's iconography, the attitude of the final image of Andromeda agrees with the reverse of an image defined by the Ptolemaic stellar configuration as it is depicted on the Vienna maps. These examples of Auriga and Andromeda suggest that the artists of both cycles had access to more than one source, one being closely connected to Michael Scot's star catalogue, the other a globe-related one. Alois Haidinger proposed that the images in Klosterneuburg MS 125, which can be dated to 1440 by watermarks, were taken partly from Vienna MS 5415 and partly from a cycle in the Scot tradition.118 This would explain indeed the agreements and disagreements between the two constellation cycles, but does not help us to understand the designs of a number of constellations in the catalogue in Vienna MS 5415 and their relation to the Vienna maps.

The complex background of constellation designs of the Vienna maps and of cycles created in or around Vienna in the first half of the fifteenth century shows at any rate that the artist of the globe-related source had a clear understanding of the reversal of images. Drawing the constellations on a globe such that the left and right characteristics in the Ptolemaic catalogue descriptions are preserved was clearly an issue in Viennese scientific circles. Although this does not answer unambiguously the question of the origin of the iconography of the Vienna maps, a globe-making thesis would allow an astronomer/artist to create his own rear-view (p.378)

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Fig. 5.20 Map of the zodiac and UMi, UMa, and Dra in Munich, Munich Clm 14583, ff. 70v–71r. (Courtesy of the Bayerische Staatsbiliothek, München.)

designs from a variety of sources that must have been available to him in or around Vienna.

5.3.4 Other fifteenth-century maps

The 1512 inventory of Regiomontanus's estate mentions Imagines celj et alia.119 According to Zinner this refers to a now lost pair of maps like that in Vienna MS 5415, which supposedly were accompanied by a star catalogue for the epoch 1424 but which by 1512 would have become separated from that catalogue.120 The same maps may have been recorded in the 1522 catalogue of Bernard Walther who acquired a substantial part of the instruments and books of Regiomontanus:’ Facies stellarum fixarum. In pergameno depictae in duabus tabellis’.121 Celestial maps are also listed in inventory of the Wiener Hofbiblothek made by Conrad Celtis, and a letter of 1512 by Johannes Cuspinianus, a member of the Vienna humanist circle, mentions another pair entitled: ‘imagines coeli australes et boreales in planum proiectas et artificiose formatas’.122 All these maps may have been modelled on the Vienna copies. Today two sets of manuscript maps remain, which are described in more detail in Appendix 5.1.123 One set survives in Munich Clm 14583, ff. 70v–73r (Figs 5.205.22), (p.379)

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Fig. 5.21 Map of the constellations north of the ecliptic in Munich, Munich Clm 14583, ff. 71v–72r. (Courtesy of the Bayerische Staatsbiliothek, München.)

the other set is known as the Nuremberg maps of 1503.

The codex Munich Clm 14583 was copied between 1447 and 1455 by Fredericus(Friedrich Gerhart), an industrious monk of St. Emmeram in Regensburg.124 In the period from 1436 to 1464 he transcribed in all eight codices on scientific topics. It is not clear what education Frederick received. According to Zinner he measured the altitude of the Sun with the help of a globe but could not design the face of a sundial.125 In 1453 Fredericus was in Salzburg where he calculated a solar eclipse for 30 November of that year. He may have visited Vienna in 1456 but he was again in St. Emmeram in 1459, where he stayed until he died in 1463.126

The maps are in the first part of the codex with astronomical texts (ff. 1–76). The first 43 pages contain astronomical tables which are (p.380)

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Fig. 5.22 Map of the constellations south of the ecliptic in Munich Clm 14583, ff. 72v–73r. (Courtesy of the Bayerische Staatsbiliothek, München.)

followed by a star catalogue with the title Composicio spere solide (ff. 44r–62v). At the end of the catalogue it says that it was written in Reichenbach in 1451. The star catalogue in Munich Clm 14583 is not illustrated and the longitudes of its stars are adapted to the epoch 1444 by a precession correction of 19° 6´. The stars are not numbered but those in Andromeda follow the same deviant order as in the catalogue in Vienna MS 5415. The latitudes of Navis nos 44 and 45 are respectively -75° 0´ and -21° 45´. The latter value should be -71° 45´. The catalogue in Munich Clm 14583 is no doubt part of the complicated transmission pattern behind the Vienna catalogue, but it is not a direct copy of it. The catalogue is followed by a number of empty pages (ff. 63r–69v). On f. 70r, the page preceding the maps on ff. 70v–73r, is a list of the Ptolemaic constellations with the incipit: ‘Rota 48 ymagines celi’, dated 1454. On the pages following the maps, ff. 73v–76v, is a list of constellation names and the number of their stars stemming from the descriptive tradition and simple drawings of the constellations without text. These drawings (p.381) belong to a fifteenth-century tradition associated with Book III of Hyginus, De Astronomia.

The maps are but poor copies astronomically speaking. One map, on ff. 70v–71r, presents the zodiacal constellations and Ursa Minor, Ursa Maior, and Draco (see Fig. 5.20). The zodiacal constellations are drawn north of the ecliptic instead of extending beyond it as they should. Another map on ff. 71v–72r presents all the non-zodiacal constellations north of the ecliptic (see Fig. 5.21). The third map on ff. 72v–73r shows all the non-zodiacal constellations south of the ecliptic (see Fig. 5.22). There are no stars marked in the maps nor are the constellations labelled. Only the names of the zodiacal signs are added in the maps. The style and shape of all figures agrees with those on the Vienna maps. The bunches of flowers in the hands of Gemini is the only feature that does not occur on the Vienna maps.

How did this small difference between the maps in Munich Clm 14583 and the Vienna maps come about? Either Gemini's bunches of flowers were part of the exemplar used for copying the maps or they were not. The latter possibility can be dismissed because it would require a specific initiative from a rather careless copyist. Gemini's bunches of flowers would thus have been on the exemplar, which implies that the Munich and the Vienna maps derive from a common exemplar rather than the one being a slightly adapted copy of the other. One can therefore reject Durand's suggestion that Gensfelder had taken his celestial maps (that is to say, presumably those in Vienna MS 5415) to Reichenbach where they supposedly could have served as the example for Fredericus.127

5.3.5 The Nuremberg maps

In 1943 Voss published a study of a pair of manuscript maps, here referred to as the Nuremberg maps (Figs 5.235.24), which appeared to be closely related to the better known pair produced by Albrecht Dürer (1471–1528), Conrad Heinfogel (1470–1530), and Johannes Stabius (d. 1522), and published in 1515.128 These latter maps, usually referred to as Dürer's maps because it was he who cut the wood blocks, proved extremely successful throughout the sixteenth century. Their iconography served as the model for the planisphere published by Peter Apian (1495–1552) in 1536 and reprinted with a different typeset in his Astronomicum Caesarum in 1540.129 Dürer's figures were also used on the manuscript celestial globe of 1532 and the printed globe of 1536 by Caspar Vopel (1511–61), on that of 1537 produced by Gemma Frisius (1508–55) together with Gaspar van der Heyden (c.1496–after 1549) and Gerard Mercator (1512–95), and, for example, on the manuscript celestial globe made under the supervision of Johannes Praetorius (1537–1616) in 1566.130

Like Dürer's maps of 1515 the production of the Nuremberg maps of 1503 was a cooperative undertaking, the participants of which are associated with poems in the corners of the southern hemisphere. In the right top corner is a poem paying tribute to Konrad Heinfogel (d. 1517) and Nuremberg. Below the poem is (p.382)

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Fig. 5.23 The northern hemisphere of 1503 (Courtesy Germanisches Nationalmuseum, Nuremberg, Inv. Nr. Hz 5576.)

Heinfogel's coat of arms. Heinfogel entered the University of Erfurt in 1471 but spent most of his creative life in Nuremberg. He is especially remembered for his German translation of the Sphere of Sacrobosco and for his contribution to the production of Dürer's maps of 1515.131 He seems to have worked with Bernard Walther (1430–1504), a wealthy Nuremberg merchant with a passion for astronomy who collaborated with Regiomontanus in making astronomical observations.132

In the bottom left corner is a poem on winds by the Dutch physician Theodorius Ulsenius (c.1460–1508) who spent much time abroad, especially in Germany (Nuremberg, Augsburg, Mainz, Freiburg, and Cologne).133 Ulsenius was not only a physician but also a poet and a close friend of Conrad Celtis.134 He published in 1496 in Nuremberg an astronomical-medical poem on syphilis which was illustrated by Dürer. Ulsenius left Nuremberg in 1501 when he moved to Mainz. He returned to his native country in 1507.

(p.383)

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Fig. 5.24 The southern hemisphere of 1503 (Courtesy Germanisches Nationalmuseum, Nuremberg, Inv. Nr. Hz 5577.)

Perhaps the most prominent person connected with the maps is Sebastianus Sperancius (d. 1525) presented in the bottom right corner as the man holding an armillary sphere as is explained in the text below him. He was a student of Celtis at the University of Ingolstadt. From 1499 until 1503 Sperancius lectured in Nuremberg and there made a sundial outlined by the mathematician Johannes Stabius (d. 1522) that still exists.135 In the following three years (1503–1506) he taught at the University of Ingolstadt but then moved to Brixen where he became secretary of Bishop Mattäus Lang. In 1521 Sperancius became Bishop of Brixen in which capacity a pair of globes was dedicated to him in 1522.136

The core of the Nuremberg maps, the stars and their constellations, recalls in many respects the Vienna maps. It is easy to see that the 1503 maps are based on a star catalogue belonging to (p.384) the Vienna tradition. For example, the numbers of the stars in the constellation Andromeda follow the deviant order occurring in the Vienna star catalogue. The dependence of the Nuremberg maps on the Vienna catalogue is confirmed by the fact that on the northern hemisphere the stars Ari 9 and Ari 10 in the tail of Aries are south of the ecliptic instead of north, and on the southern hemisphere the star Navis no. 44 lies north of Navis no. 45. Also the precession correction applied to the stellar longitudes in the Nuremberg maps recalls the Vienna star catalogue. Voss has shown that the map's stellar longitudes exceed the corresponding Ptolemaic ones for the epoch AD 137 by 18° 58´ ± 11´, which is close to the value of 18° 56´ used in Vienna star catalogue and the Vienna maps.137 However, the two stars missing in Auriga in the Vienna star catalogue are included in the Nuremberg maps with the result that the stars are listed as nos 1–14. The Nuremberg maps are thus not straightforward copies of the Vienna maps.

The most significant deviation from the Vienna maps is that the 1503 maps present the northern and southern hemisphere in stereographic projection. This means that the stars were plotted by using a latitude scale designed for stereographic projection using techniques known from the construction of astrolabes. This technique was known to Heinfogel, who used it on a parchment astrolabe preserved in his copy of Johannes Stöffler's Almanac of 1499.138 It is not clear why stereographic projection was preferred above equidistant projection. Perhaps this choice was induced by the fact that the maps did not serve as a model for globe making, or because by this choice the problems of drawing oblique circles in the equidistant projection are avoided since in stereographic projection all circles, inclusive of oblique ones, are presented as circles (or straight lines). It is worth noting that next to the polar circles small circles have been drawn around the north and south equatorial pole of the Nuremberg maps, as on the Vienna maps. The presence of these incomprehensible small circles suggests that a copy of the Vienna maps was at hand while the Nuremberg maps were constructed. Zinner has suggested that this copy may well be the lost maps of Regiomontanus.139 If these lost maps were faithful copies of the Vienna maps, quite a number of changes have been introduced on the 1503 maps in addition to the change in projection. For example, the Milky Way is left out of the Nuremberg maps and no star names have been added. The names of the constellations are written in capital letters and some names on the Nuremberg maps (OPHIVLCVS (sic), SAGITTA, EQVVS PEGASVS, ERIDANVS, ARA, and PISCIS NOTVS) replace the corresponding names on the Vienna maps (Serpentarius, ystius, equus volans, fluuius, sacrum thuribulum, and piscis meridionalis).

The constellation designs on the Nuremberg maps follow closely those on the Vienna maps in the sense that all are drawn from behind, although the artist of the Nuremberg maps has made a greater effort to turn the heads to show their faces. But there are also a number of iconographic differences. On the Vienna maps Cepheus, Bootes, Hercules, and Orion are dressed but on the Nuremberg maps they are nude. On the Vienna maps the constellations Hercules and Perseus show the Arabic impact on constellation design but on the Nuremberg (p.385) maps this has vanished: Hercules hold a lion's skin and a club while Perseus holds a proper Medusa head and has wings on his feet, in agreement with Greek-Roman mythology. Other iconographic adaptations are the ox head of Orion's pelt and the presentation of Navis as only half a ship. The ox hide is mentioned by Michael Scot when he let Jupiter say: ‘excoria vitulum saginatum et pellem pone in urina tua et viri tui septem diebus, et nascetur tibi filius cui nomen erit Orion’.140 The image of Orion holding an ox hide is not exceptional in the fifteenth century. It occurs, for example, in Klosterneuburg, MS 125, f. 13v, a constellation cycle related to the cycle in Vienna MS 5415, and on Stöffler's globe as discussed below.141

Although the artist of the Nuremberg maps is unknown he left his personal stamp on the maps through his style of drawing the constellations and the decorative elements in the corners of the maps. In the northern hemisphere are the images and the names of the four elements and the gods associated with them. On the southern hemisphere four compass directions are added across the celestial map and at the border of the map are sixteen wind heads and their names. Heinfogel's preoccupation with winds is manifest from a manuscript drawing in his copy of Johannes Stöffler's Almanac of 1499, with a compass rose and the names of 16 compass directions entitled: ‘Sunt in summa 64 ventorum species secundum Ulsenium frisium’.142 The addition of compass directions and wind heads in a celestial chart centred on the ecliptic is not functional since the relation between the horizon and the celestial sky is not fixed. Compass directions and wind heads are more often added to maps of the world, depicting the lands and seas on earth where east and west have a permanent meaning. These and other decorative elements in the Nuremberg maps should be understood as an expression of an idea of the universe which extends beyond celestial charts such as the Vienna maps. By introducing images of the planets, the four elements, and the winds around the celestial maps the designers of the Nuremberg maps have conceptually added a cosmographic dimension to celestial cartography. As Voss has shown, this approach fitted well into the humanist outlook on the world in which celestial cartography was just a lesser aspect. This may explain why no effort was made to number the scale along the ecliptic or to adapt the stellar positions to 1500, a time close to the date of construction. From the point of view of celestial cartography the most conspicuous aspects of the Nuremberg maps are its use of stereographic projection and the introduction of the new humanist approach in constellation design based on classical form.143

5.3.6 A planisphere by an anonymous maker

The oldest extant celestial map with constellations images in stereographic projection made in the Latin West (that is, not counting the retes of astrolabes which show only a selection of 20–50 stars) is a planisphere drawn on the back of a brass instrument known as the albion. Maps of this type are extremely rare. The only comparable map is John Blagrave's Astrolabium uranicum of 1596.144 For a long time the present albion in the collection of the Museo Astronomico e (p.386)

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Fig. 5.25 Planisphere on the back of an albion. (Reproduced from Turner (G) 1991, p. 70.)

Copernicano in Rome was listed among the objects stolen from the museum in 1984.145 Recently it became clear that it was mistakenly placed on that list. The present discussion is based on a picture of the map (Fig. 5.25) which allows only a few superficial remarks.146

The map in the stereographic projection extends from the north equatorial pole to a declination of around 35° south. The planisphere thus differs from the Nuremberg maps which are drawn in stereographic projection centred on the ecliptic poles. Since positions in star catalogues are usually available in ecliptic coordinates only, the maker of the present planisphere has inaccurately engraved a grid consisting of great circles through the ecliptic pole and parallels to the ecliptic. How to draw such a grid was well known from the construction of astrolabes since it coincides with a grid of lines of constant altitude and azimuth for a plate for (geographical) latitude equal to 90°-ε, where ε is the obliquity of the ecliptic. In a range extending 6° north and south of the ecliptic the parallels to the ecliptic have been engraved for every 1° to mark the zodiacal band. In addition the Equator and the tropics are engraved. A scale for declination numbering every 6° is added along the solstitial colure and a scale for ecliptic latitude numbering every 6° along the great circle passing through the ecliptic pole and the equinoxes.

The stars are marked by small crosses of different sizes. Not all constellations engraved on the plate are drawn as seen on a globe and not all of the 48 Ptolemaic constellations are presented. Since the map is cut-off at a southern declination of 35°, a number of constellations are incomplete. The tip of the tail of Scorpius and the legs of Sagittarius are absent and only the westernmost part of Navis, the head of Centaurus, and the legs of Lupus are seen. Completely absent are Ara and Corona Australis.

The design of the constellations has a number of conspicuous features. Cetus is drawn in an attitude that makes him stand more or less face on. Hydra is presented with dragon's wings. Aquarius is naked apart from a piece of cloth drawn around his body and he holds an urn in his right hand. Virgo is drawn face on, with wings and her northern hand pointing upwards where it is cut by the Tropic of Cancer. The branch held in her northern hand recalls the image of the ivy leaf on some Islamic globes (see for example Fig. 4.17). Yet, the present map does not exhibit many Arabic features. Hercules is presented with a club and a lion's skin, Perseus has wings around his feet, Lyra is drawn as a lyre, and Orion has a piece of cloth or skin in his left hand, not an extended (p.387) sleeve. Neither does the iconography of the planisphere fit into the Vienna map tradition. This raises the question of where and when the map was made.

The albion was invented in 1326 by Richard of Wallingford (1292?–1336), abbot of St. Albans.147 It is part of a class of instruments designed for calculating the positions of the Sun, the Moon, and the planets. Usually these instruments consist of a series of plates but the albion, meaning ‘all-by-one’, combines the various discs into one plate. North, who studied the treatise written by Wallingford in great detail, proposed a date for the present albion/planisphere in the fourteenth or early fifteenth century.148 The Viennese astronomer John of Gmunden revised and expanded the treatise by Richard of Wallingford in the first quarter of the fifteenth century.149 The albion was among the collection of instruments bequeathed by John of Gmunden to the university of Vienna and the albion is also mentioned among a series of instruments in the abbey of Reichenbach.150 According to Poulle it is not possible to decide from what is left of the present albion whether its construction follows the description of Richard of Wallingford or that of John of Gmunden.151

Stellar positions are sometimes helpful in establishing a date. Although it is not possible to measure the stellar positions accurately from the picture in Fig. 5.25, one can say that the map is compatible with an Alfonsine epoch of 1252. For example, with an Alfonsine precession correction of 17º 8’, the star on the end of the front leg of Canis Maior (CMa 9) is west of the solstitial colure and the more advanced of the stars in the left knee (CMa 10) is east of it.152 The positions of the stars in the legs of Canis Maior on the planisphere agree with these positions. If correct, the epoch of the planisphere (1252) is not indicative for the date of production of the planisphere. Although the use of an Alfonsine epoch is not inconceivable, a more detailed study of the star positions on the instrument is needed to confirm this hypothesis.

A date can also be surmised from the style of some the constellations drawings. The image of a dragon with wings, used on the planisphere for Hydra, occurs in a cycle of constellation drawings stemming from Michael Scott in Oxford, Bodleian Library, MS Can. Misc. 554 (north Italy, second quarter of the fifteenth century).153 In the illustrated manuscript of the fifteenth century with Germanicus's Aratea, Florence, Biblioteca Laurenziana, Plut 89, sup 43 (Florence, 1470), Cetus is a presented on f. 43r as a winged dragon.154 The iconographical characteristics of the images of Draco, Serpens, Cetus, and Hydra are easily transferred from one constellation to another. The wings of Hydra on the present planisphere fit into this and are compatible with a date in the fifteenth century and possibly Italy as the place of production. Hopefully a detailed study of the instrument is feasible in the near future and a better assessment of its date and place of production can be made.

(p.388) 5.4 Globes in the Service of Astrology

The first Western globe maker known by name is Jean Fusoris (ca. 1365–1436) who studied medicine at the University of Paris.155 He obtained his bachelor's degree in 1379 and his master's in 1391. He had a workshop in Paris, the first of its kind, where he made all sorts of instruments, especially astrolabes. After a visit to England he was accused of espionage and exiled to Mezieres-sur-Meuze and later to Reims. He continued to make instruments while in exile. Before he left for England Fusoris had written a text on globes, compositio revolutionum spere solide, presumably to accompany the globe he made for King Henry V. Another globe was made in 1410 for Pope John XXIII. Unfortunately nothing more is known about these Fusoris globes.

More can be said of the sphaera solida mentioned in the will of Johannes of Gmunden.156 This globe was almost certainly made after the instructions in the treatise Tractatus de sphaera solida in Vienna MS 5415 (f. 161r–191r) mentioned above. The detailed drawing of a globe in this treatise on f. 180v (Fig. 5.26) may give a fairly good idea of John's globe.

The sphere is mounted at the equatorial poles in a meridian ring which is placed in a stand with four legs (only three are seen in the drawing) supporting the horizon ring. The meridian ring has three graduated scales: one scale for declination and another for its complement. The outermost scale for altitude is not described in the treatise Tractatus de sphaera solida. This scale depends on geographical latitude. The location of the north equatorial pole on the altitude scale in the globe drawing shows that a latitude of around 48º for Vienna is used, suggesting that the drawing represents a real globe. A noticeable feature on the horizon ring is its combination of scales of the zodiac and the calendar. This combination serves to find the place of the Sun in the zodiac at a certain day of the year and, as mentioned in the Tractatus de sphaera solida, was commonly engraved on the back of astrolabes.157 In addition to the scales of the zodiac and the calendar, there is a scale for the azimuth. On the outer border of the horizon ring the names of the points of the compass are added. In this picture the celestial sphere itself is marked by a number of circles: the Equator graduated four times 0º–90º, the ecliptic graduated twelve times 0º–30º, the circles of constant longitude for every 30º, the tropics and the north polar circle, as described in the Tractatus de sphaera solida. How the constellations would have been drawn on the sphere of John's globe is shown by the Vienna maps discussed above.

John's globe was probably one of a series made by members of the Vienna astronomical school. In his Viri Mathematici the Viennese mathematician and astronomer Georg Tannstetter (1480/82–1530/35) described short biographical notes on fourteenth and fifteenth century astronomers. Of Georg Peurbach (1423–61), the Viennese astronomer and inventor of instruments, it says that he made several ‘spaeras solidas’.158 These globes would in all probability also be designed after the Vienna pattern.

In the second half of the fifteenth century globes were also made in Rome. Bills dated 1477 mention globes by Nicolaus Germanus (p.389)

The Mathematical Tradition in Medieval Europe

Fig. 5.26 Drawing of a celestial globe in Vienna MS 5415, f.180v. (Courtesy Österreichische Nationalbibliothek, Vienna, Picture Archive.)

(p.390) (ca. 1420–ca. 90).159 Germanus started his scientific career in the monastery of Reichenbach, where successive abbots fostered his interest in astronomy.160 His skill in globe making may well be connected with the Viennese tradition. His globes are listed in an inventory of 1481 of the Vatican Library: an Octava Sphera (a celestial globe), and a Cosmographia (a terrestrial globe) exhibited in the Pontificia (the Library), and again in an inventory of 1487 where it is said: ‘Spera in qua et terrae et maria ex Ptolemaeo cum orizonte. Spera in qua signa caelestia cum suis polis et elevationibus’.161

Today only two celestial globes of the fifteenth century remain, which are described in more detail in Appendix 5.2.162 One of the extant globes was owned by Martin Bylica (1433/4?–93?), a famous astrologer.163 Bylica entered the University of Cracow in 1452, where a chair in astrology was held by Andreas Grzymalas. In 1456 Bylica received his bachelor's degree and three years later his master's. He lectured at Cracow University from 1459–1463. In 1463 he continued his studies in Italy, at the universities of Padua and Bologna, and lectured there on various astrological issues in 1463/64. As court astrologer of Cardinal Rodericus Borgia he visited Rome in 1464 and there met Johannes Regiomontanus, who had come to Rome at the invitation of Cardinal Bessarion. The dialogue written by Regiomontanus, ‘Dialogus inter Viennensem et Cracoviensem adversus Gerardum Cremonensem in planetarum theoricas deliramenta’, with a discussion between Johannes from Vienna and Martin from Cracow, immortalizes the meeting between these two astronomers.164

Regiomontanus and Bylica were invited to Hungary to take up posts at the newly founded University of Poszony, for which foundation Matthias Corvinus, King of Hungary from 1458–90, had received a papal charter on 19 May 1465 through the kind offices of Janus Pannonius, a nephew of archbishop of Gran, and Chancellor of Hungary János Vitéz (1408–72).165 Before moving to Poszony, Regiomontanus and Bylica stayed at the archbishop's palace at Esztergom where Regiomontanus produced with Bylica's help his Tabulae directionem profectionumque with tables for calculating the boundaries of the mundane houses and directions for their use.166 In July 1465 the two astronomers moved to Poszony. While in Hungary, Regiomontanus worked on the construction of instruments. He wrote a treatise on the torquetum, dedicated to Vitéz and a treatise on the regula ptolemaei (also called triquetum) which he dedicated to King Matthias.167 Regiomontanus left Hungary in 1471 when he went to Nuremberg to carry out his ideas to reform astronomy.

Bylica's astrological commitment is evident from the horoscope cast for the opening of the university of Poszony on 5 June 1467, his lectures on astrology, and, for example, from a dispute with Jan Stercze, court astrologer to János Rozgon, held in 1468 before the Hungarian Diet in Poszony.168 Bylica seems to have had the upper hand in the debate and was awarded 100 florins. After the decline of the University, Bylica (p.391) spent the best part of his life as an astrologer at the court of King Matthias who died on 6 April 1490. Thereafter Bylica remained in Hungary and died a few years later in 1493. He donated his instruments—a celestial globe, an astrolabe, and a torquetum—to his home town university in Cracow where they have been since 1494.169 For centuries these instruments were in the library of the Collegium Maius but in 1953 they were transferred to the Jagiellonian University Museum. The celestial globe of 1480 and the astrolabe of 1486 carry the coat of arms of Bylica showing Sagittarius above a rose with five petals in the centre of the field, with sunrays emanating from a starry symbol in the top right corner. On top of the field is a hat with double tasselled ropes characterizing the title of Protonotary Apostolic held by Bylica.170

All three instruments donated by Bylica to his alma mater have been attributed to Hans Dorn.171 This instrument maker was born in Austria between 1430 and 1440 and studied astronomy in Vienna between 1450 and 1461, first under Georg Peurbach and then under Regiomontanus. Dorn learned his skills in instrument making from Peurbach. According to Tanstetter Dorn was a capable instrument maker who made three globes:

Joannem Doren eorundem instrumentorum elaboratorem artificiosissimum. Hic postea ordinem fratrum predicatorum ingressus, ibidem varia instrumenta ex aere: noviter vero sphaeras solidas tres mirae magnitudinis diligenter elaboravit. Vixit hic frater Joannes in monasterio fratrum predicatorum usque in annum christi 1509 ubi magno confectus senio quievit in pace.’172

The precise whereabouts of Dorn in the 1560s are not known. It seems that he arrived in Buda before 1478 because from a record in the Nuremberg archives it follows that King Matthias sent him in that year to Nuremberg to buy the instruments and books of Regiomontanus. Dorn's efforts were in vain and he returned empty-handed to Buda.173 Back in Hungary Dorn made a number of instruments for Bylica. After King Matthias had died Dorn returned to his monastery in Vienna where he continued to make instruments, witness of which is a horizontal sundial in the British Museum, signed ‘DAS CHOMPAS IS GERECHT AVF ALLE LAND VND HAT GEMACHT PRVDER HANNS DORN PREDIGER ORDEN VON WIEN ANNO DOMINI 1491’.174 Letters of 1501 by Thomas Dainerius, a secretary of the nuncio in Buda, confirm that Hans Dorn also made instruments for King Laudislaus II, the successor of Hungarian King Matthias, in particular an astrolabe and a sundial.175 He died in 1493.

Let me now turn to Dorn's globe shown in Fig. 5.27. In basic outline it resembles the type of globe shown in the drawing in MS 5415 in Fig. 5.26 but it has a number of features that set it a apart from the Vienna globe. It consists of a sphere mounted in an adjustable meridian ring supported by a stand with a horizon plate (Fig. 5.28) but there the agreement stops as far as the construction is concerned. Conspicuous for the time of production is the hour circle (Fig. 5.29) which must be a later addition to judge by its modern lettering. The sundial in the south corner of the horizon plate is conspicuous for better reasons (Fig. 5.30). Its novel (p.392)

The Mathematical Tradition in Medieval Europe

Fig. 5.27 The celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

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Fig. 5.28 Horizon of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

The Mathematical Tradition in Medieval Europe

Fig. 5.29 Hour circle of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

design with a magnetic compass with the needle showing a variation of 10° is the invention of Peurbach, Dorn's Viennese teacher.176

In order to use the globe it has to be adjusted to local conditions. This involves three steps. First the meridian ring (Fig. 5.31) has to be aligned with the local meridian plane. This could have been done using the compass on the horizon ring. Other methods were known to find the local meridian line but the use of a compass for this is novel. When the meridian ring is in the local meridian plane the wind directions engraved on the horizon plate agree with the real directions of a place. Next one has to adjust the globe to the proper geographical latitude by turning the mobile meridian ring in its own plane until the elevation of the pole above the horizon ring agrees with the latitude of the place. The last step is to rotate the sphere around its own axis to make the stars on the sphere correspond to those in the sky overhead. In daytime this can be done with the help of the Sun, whereas at night the stars can be used. In globe treatises it is recommended to place a peg on the place of the Sun in the zodiac, and then turn the sphere until no shadow is seen. This method works of course only in daytime. With Dorn's globe the problem is easily solved for day and night with the astrolabe disc placed on top of the meridian ring. The mobile support of the disc consists of two quadrants which extend to the horizon plate and can rotate with the support in azimuthal direction. By turning the quadrants round the zenith and using the alidade of the astrolabe disc on top (Fig. 5.32) one can sight the Sun or a star and fix the azimuth of the celestial object. Next the celestial sphere is turned until (p.394)

The Mathematical Tradition in Medieval EuropeThe Mathematical Tradition in Medieval Europe

Fig. 5.30 a–b Sundial on the horizon of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

The Mathematical Tradition in Medieval Europe

Fig. 5.31 Meridian ring of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

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Fig. 5.32 The orthographic grid at the back of the astrolabe disc at on top of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

the Sun (whose position on the zodiac for a specific time of the year can be found on the horizon ring) or the star concerned is under the appropriate quadrant. Then the celestial configuration on the globe corresponds with that in the sky. This method, using the azimuth direction of the celestial object, cannot be applied with a common astrolabe because with this latter instrument only altitudes can be measured.

If the altitude of the Sun is measured using the umbra recta and versa scales on the astrolabe disc on top of the globe, one can determine simultaneously what time it is by using the zodiacal ring in combination with the equal and unequal hour lines on the one side (Fig. 5.33) or with the orthographic grid on the other side of the astrolabe disc (Fig. 5.32). To find the time at night, one can after having sighted a star read off where the ecliptic is intersected by the horizon plate and enter this

The Mathematical Tradition in Medieval Europe

Fig. 5.33 Mundane house on the astrolabe disc on top of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

into the side of the astrolabe disc with the zodiac ring.

The zodiacal ring and the unequal hour lines are traditional features of the common astrolabe.177 The grid in the orthographic projection is a later development. It is engraved on the back of an astrolabe made by Regiomontanus in 1462 and other astrolabes belonging to the same tradition.178 As an aside I note that in the fifteenth and sixteenth century the grid in the orthographic projection is sometimes labelled organum ptolemei.179 This label refers to the method of constructing a specific set of declination lines in the orthographic projection corresponding to certain moments that the Sun is in the zodiacal signs (p.396)

The Mathematical Tradition in Medieval Europe

Scheme 5.5 The boundaries of the mundane houses after the equatorial method are fixed by the intersections between the ecliptic and the circles of positions passing through 30º divisions of the Equator.

in the course of a year. In earlier medieval literature the label organum ptolemei was used for rectilinear dials, as for example the navicula and Regiomontanus's dial with straight parallel lines marking the hour lines.180 The grid in the orthographic projection differs conceptually from rectilinear dials, if only because the hour lines are sections of ellipses, not straight lines.

The main function of the astrolabe disc on top of the globe is, however, to find the mundane houses for making horoscopes. Various methods were available to determine the boundaries of the mundane houses. One, known as the prime vertical method, is commonly ascribed to Campanus, another was known as the equatorial method and the credit for it is often given to Regiomontanus.181 As north has shown, these two fixed methods were known long before in Arabic literature and used on Eastern astrolabes. In the equatorial method, the boundaries of the mundane houses are fixed by the intersections between the ecliptic and the ‘circles of positions’, passing through 30º divisions of the Equator (see Scheme 5.5). Fixed boundary methods have the advantage that they can be marked graphically, and thus greatly simplify the determination of the houses. The astrolabe disc on top of Dorn's celestial globe is engraved with a grid of lines of the boundaries of the mundane houses fixed by the equatorial method for a latitude of 47.5º (Fig. 5.33). The main boundaries of the 12 houses are marked by dots. Each house is subdivided by curves into 10 subsections. A series of construction dots on a straight line mark the centres of the circles of the mundane houses. On top of this pattern of boundaries is the already mentioned zodiacal ring with a ruler.

To make a horoscope an astrologer would have to know the time of birth. This is used to set the ecliptic on the astrological plate (Fig. 5.33) in the right position. Then the points of intersection of the ecliptic and the lines of the mundane houses can be determined. By using the point of intersection of the ecliptic and the horizon the celestial sphere can also be set to correspond to the celestial sky at the moment of birth. The astrological function of Dorn's globe is further emphasized by the planetary natures of the stars marked on it. The astrological characteristics of the fixed stars are expressed by means of the influences thought to be exerted by the planets. All this makes Dorn's globe a suitable aid for an astrologer.

Let us now consider in more detail the stars and the constellations engraved on the sphere. The longitudes of the stars on Dorn's globe differ with respect to the corresponding Ptolemaic values by 19° 56´ ± 12´, which averaged value and standard deviation were obtained by measuring the ecliptic longitudes of 24 stars located close to the ecliptic. How to interpret this value is not clear. Ameisenowa states that—following (p.397) the calculations of Birkenmajer—the stellar positions correspond to their actual positions in the sky in 1586, which is 106 years after the date of production of the globe. Even more mysterious is her remark that ‘from this result Birkenmajer concluded that the position of the stars on the globe was set for 1424 according to the Alfonsian Tables’.182 The Alfonsine precession correction for 1424 used in the Vienna catalogue is 18° 56’, which is 1° less than the precession correction of Dorn's globe.

There are in principle two ways to determine the precession correction: by calculation or by observation. If the stellar positions on Dorn's globe were corrected by calculation we may assume that the Alfonsine trepidation theory was used. Then the value of 19° 56´ would correspond to an epoch of about 1532.183 At face value there seems to be no good reason to calculate the precession correction for a date about 50 years ahead. However, it would be a feasible choice if the maker wanted to ensure the validity of his globe for the next 100 years. Thus this interpretation cannot be ruled out. If the precession correction was determined by observation one can predict what value applies for the year 1480. Since there is a systematic error in the Ptolemaic star catalogue of around 1° it is best to calculate the stellar positions in 1480 by precessing the accurate stellar longitudes in the star catalogue of Tycho Brahe (for the epoch 1601). Using an averaged modern rate of 1° in 72 years one arrives at a precession correction of 19° 40´ for 1480, which is 16´ less than the value 19° 56´ ± 12´obtained here. Since errors can easily amount to 10´ we cannot rule out this way of explaining the globe's precession correction either. In the absence of a definite explanation I am inclined to think that the globe maker found it convenient to adapt all 1025 stellar longitudes in a 1424 catalogue simply by increasing the longitudes by 1°, and thus validate his globe for the period of 1480–1580.

Whatever the precise interpretation of the globe's precession correction may be, it is certain that the catalogue used by Dorn belonged to the Vienna tradition. Since the stars on the globe are not numbered, it is not possible to compare the ordering of the stars in Andromeda and in Auriga with that in the star catalogue in Vienna MS 5415. However, the star in the right knee of Auriga (Aur 14) is missing on the globe as in the Vienna map and catalogue. Further, the stars in the tail of Aries (Ari 9 and Ari 10) are south of the ecliptic (Fig. 5.34) and star no. 45 in the rudder of Navis is south of star no. 44 (Fig. 5.35), as in the Vienna map and catalogue.

The nomenclature on Dorn's globe does not follow in all respects the Vienna tradition. All the names are engraved in capital letters. Some constellation names on Dorn's globe (AVRIGA,

The Mathematical Tradition in Medieval Europe

Fig. 5.34 Aries on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

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Fig. 5.35 Argo on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

SAGITTA, AQVLA, EQVVS PEGASVS, ERIDANVS, ARA, and PISCIS MERIDIANVS) replace the corresponding names on the Vienna maps (Agitator, ystius, vvlt(vr) volans, equus volans, fluuius, sacrum thuribulum, and piscis meridionalis). Most of these alternative names occur in the Vienna star catalogue. Whereas star names in the middle of the fifteen century are still determined by transliterations from the Arabic, Dorn's globe exhibits the trend for marking the stars by Roman or Latin labels, see Table 5A1 (p. 412). The stars which on the Vienna map are called alhayoth and denebkaytoz, are labelled on the globe respectively HEDVS and CAVDA. Indeed, of the 17 names there are six (ACARNAR (θ Eri), ALDEBORA (α Tau), DVBHE (α UMa), MARKEB (τ Pup), RIGEL (β Ori), and SVEL (α Car)) which still reflect the medieval Arabic nomenclature. A few names are unusual but typical for Dorn, since they occur also on his 1486 astrolabe. These are two names in Orion, IVGVLA A OR (α Ori) and IVGVLA B OR (γ Ori), and one name in Cetus, MENTVM (α Cet). Iugula and Jugulae are names used in Roman sources for Orion or his belt.184 On Dorn's globe IVGLA A OR and IVGVLA B OR are used for the stars on the shoulders of Orion (Fig. 5.36). The label MENTVM is on the globe in the same location as the name Menkar on the Vienna map. Menkar is a medieval Arabic name used for the first star in Cetus (α Cet). On Dorn's astrolabe of 1486 the position of the star labelled MENTVM agrees with the position of α Cet.
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Fig. 5.36 Orion on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

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Fig. 5.37 Cassiopeia on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

It seems therefore that MENTVM was meant as a replacement for Menkar, but according to Kunitzsch the name cannot have been derived from Menkar. A reference to mentum is used for the fourth star in the entry of Cetus, ‘Praecedens de tribus & est in mento’, in the Latin translation of Ptolemy's Almagest made about 1451, at the request of Pope Nicholas V, directly from the Greek by the humanist George of Trezibond, or Trapezuntius (1395–1484).185 This humanist version of the star catalogue differs from Gerard of Cremona's Latin translation from the Arabic by the use of what humanists considered ‘good’ Latin. In 1467 a copy was made for the library of King Matthias.186 It may be taken for granted that Trezibond's translation was known in Buda. Yet, there is no good reason why a label for the fourth, insignificant star should be transferred to the first star of Cetus (α Cet).

Finally a few words should be said about the iconography of the constellation images of Dorn's globe. Considering his Viennese background it is no surprise that the designs follow in the main the Vienna tradition as exemplified by the maps in Vienna MS 5415 discussed above. Yet there are a few significant deviations from the maps. For example, Bootes is engraved as a nude figure instead of being dressed. Cassiopeia is no longer nude but wears a long dress and a kerchief over her head which covers her face and extends to her shoulders and she holds no

The Mathematical Tradition in Medieval Europe

Fig. 5.38 Hercules on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

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Fig. 5.39 Perseus on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

attribute in her excessively large hands (Fig. 5.37). Hercules still holds a curved sword in his raised right hand but is now presented more explicitly as a warrior in a suit of armour and a lion's skin is added to his left hand (Fig. 5.38). Orion still has a club in his raised right hand and a sword in a scabbard but he too is dressed in a suit of armour. He has been given a Phrygian hat to wear and holds a cloth in his raised left hand instead of an animal skin (Fig. 5.36).187 Crater is a kettle with one handle instead of a wooden tub with two handles as on the Vienna maps.

Compared to the maps the most striking change on Dorn's globe for me is the image of Cassiopeia (Fig. 5.37). Can one see in it the woman who boasted that her beauty surpasses that of the Nereids? In the star catalogue Vienna MS 5415, f. 224v Cassiopeia is presented with certain elegance, which cannot be said of Dorn's image. Dorn's Cassiopeia with her awkward hands contrasts strongly with the other well engraved constellations. These latter images could have been inspired by the constellation cycle of the star catalogue Vienna MS 5415, the Vienna maps, or copies thereof.

The lion's skin in the image of Hercules seems to be a new element compared to the Vienna maps but this attribute is already part of the image of Hercules in the star catalogue in Vienna MS 5415, f. 222v. It is a central theme in the discussion of Ameisenowa who interprets it as a correction of ‘the change introduced by the Arabs’.188 The mythological Hercules is not part of the Ptolemaic iconography proper. The theme of the reintegration of classical form developed by Saxl is, within the context of the present study, one of introducing myths in the mathematical tradition in map and globe making. This process may have been helped by the fact that the artists of constellation cycles in illustrated Ptolemaic star catalogues seem to have borrowed, among others, from those belonging to the descriptive tradition. On Dorn's globe Hercules does not yet have the classical shape with which he is presented in the early fourteenth century on Cusanus's globe (Fig. 5.9) discussed above in Section 5.1 and on the Nuremberg maps (Fig. 5.23). The constellations Perseus and Lyra are more telling about the trend to rectify Arabic iconography: Perseus still carries the head of (p.401) Ghūl, the desert demon, in keeping with the Ṣūfī Latinus tradition (Fig. 5.39) and Lyra is still drawn as Vultur volans.189

A prominent element in the iconography of Dorn's globe seems to be that Hercules and Orion are dressed in suits of armour. Their armour may have been borrowed from the images in the star catalogue in Vienna MS 5415, f. 222v and f. 243r, respectively. However, on the globe Orion wears a Phrygian hat, not a proper helm. In the illustrated manuscript in Florence, Biblioteca Nazionale Centrale Angeli MS 1147 A.6, dating from the second half of the fifteenth century, four constellations are dressed in armour and all wear a helmet: Hercules (without a lion's head), Perseus (without sword but with a proper Medusa head), Auriga (with goat and harness), and Orion (with club, sword and a pelt). This cycle must stem from a globe because the east–west orientations of the constellations are as seen on a globe and all human figures are in rear view.190 In this connection it is also worth mentioning the celestial hemisphere of the Old Sacristy in Florence. This fresco presents half of the celestial sky, which at a certain time, July 1442, was above the horizon in Florence, and all constellations are consistently facing the viewer in keeping with Hipparchus's rule.191 Two of the visible figures on the fresco, Perseus and Orion, are also dressed in armour. The trend to present constellation figures as warriors, as seen in the Vienna maps and star catalogue and on Dorn's globe, seems to be a characteristic trend in constellation design in the second half of the fifteenth century which does not yet foreshadow a return to classical form seen on the later Nuremberg maps.

The second extant fifteenth-century globe, now in the Landesmuseum Württemberg Stuttgart, was made by the astronomer Johann Stöffler (1452–1531) in 1493 for Bishop Daniel Zehender of Konstanz. Stöffler is said to have made another globe in 1499 for Bishop Johann Dalberg of Worms but this one is now lost.

Stöffler was born in Justingen, a small town near Blaubeuren. On 21 April 1472 he entered the University of Ingolstadt, where he obtained his bachelor's degree in September 1473 and his master's in January 1476. After completing his studies he obtained the parish of Justingen where next to his duties as a priest he worked on astronomical and astrological issues. His most important publication during this stay in Justingen was the Almanach nova plurimis annis venturis inserentia published in 1499 in collaboration with the astronomer Jakob Pflaum of Ulm for the years 1499–1531.192 This almanac was a continuation of the Ephemerides astronomicae ab anno 1475 ad annum 1506, published by Regiomontanus in 1474.193 Stöffler's Almanach reproduces Regiomontanus's instruction for the use of the tables and includes additional material. Among the additions is a list of the names, the ecliptic and equatorial coordinates for the epoch 1499, the magnitudes and the astrological natures of 52 stars (Tabula Stellarum fixarum Insigniorum).194 Next is a list of the locations of the 28 lunar mansions, their names, and their astrological significance. Other astrological topics follow, such as the best time for bloodletting, and so on and tables for determining the (p.402) boundaries of the mundane houses for latitudes 42º, 45º, 48º, 51º, and 54º using the equatorial method, then known as that of Regiomontanus. In the period 1499–1551 13 editions were published of Stöffler's Almanach.

The publication of the Almanach created a great deal of sensation. Stöffler had predicted for the year 1524 20 planetary conjunctions of which 16 would take place in a watery sign (such as Pisces). Such a configuration was doomed to bring about great changes. Stöffler's prognostication was linked to others that predicted a deluge, a popular theme throughout the Middle Ages. In Europe, more than 100 different pamphlets were published on the 1524 prognostication.195 In response to a publication by Tanstetter, who argued against a great flood, Stöffler justified himself by saying that he never predicted a deluge, only great changes, and moreover that he believed that only God himself could cause the end of the world.196

In 1507 Stöffler became professor of mathematics at the University of Tübingen, where he lectured on various topics such as Ptolemy's Geography. In 1522 he became rector there. In Tübingen Stöffler continued to produce important astronomical works. In 1512 he published a book on the construction and use of the astrolabe, Elucidatio fabricae ususque astrolabii, which appeared in 16 editions. In this manual his astrological interests are expressed again by his description of the construction of the boundaries of the mundane houses after the equatorial or Regiomontanus's method. How to draw a horoscope is extensively discussed in the second part of the treatise on the use of the astrolabe. A work on astronomical tables, his Tabulae astronomicae, followed in 1514. Not long thereafter his Calendarium romanum magnum (Oppenheim: Jakob Koebel, 24 March 1518) appeared, which in addition to extensive astronomical information contains proposals for calendar reform. Astrology also left its trace in this work. There is, for example, a section on blood-letting accompanied by a full-page woodcut of an anatomical man showing the points for bloodletting for the various circumstances described in the text. Stöffler's most famous pupil was Philipp Melanchthon (1497–1560).197 Under Stöffler's influence Melanchthon acquired, next to knowledge of astronomy, mathematics, and geography, a strong belief in astrology—as he acknowledged on several occasions. Between 1535 and 1545 Melanchthon lectured about the Tetrabiblos, and he prepared a Latin translation of it which was published in 1553 alongside the second Greek edition by Joachim Camerarius.

Against this backdrop it does not come as a surprise that Stöffler's celestial globe for Bishop Daniel of Konstanz, described in detail in Appendix 5.2 (WG3) and shown in Fig. 5.40, also bears the mark of his astrological interests. The design of the globe made in Justingen follows in most respects the Vienna model shown in Fig. 5.26. Stöffler added, however, two new construction features. The first is a set of semicircles which serve to determine the boundaries of the 12 mundane houses by the equatorial or Regiomontanus's method. The same astrological structure for determining the mundane houses is seen on top of a planetary clock made in 1555 by Philipp Immser (1500–70), another pupil of Stöffler, in cooperation with Emmoser.198 Another unique feature of his globe is the hour (p.403)

The Mathematical Tradition in Medieval Europe

Fig. 5.40 The celestial globe of Johannes Stöffler. (Landesmuseum Württemberg, Stuttgart; Photo: Peter Frankenstein, Hendrik Zwietachs.)

(p.404) circle on top of the meridian ring. Stöffler's celestial globe is the oldest surviving globe with this accessory. The hour circle serves as an easy mechanical way to find the time of certain events, such as the rising and setting of the Sun and the stars. When correctly adjusted it can also be used for easily finding the configuration in the sky at the moment of birth, and so on. Earlier Arabic treatises on the use of globes provided trigonometric methods for solving time-related problems. Since calculations are usually cumbersome, astrolabes were often used for solving these problems graphically. Stöffler's hour circle still shows the influence of the astrolabe, since its dial plate is engraved with the same set of unequal hours lines commonly found on an astrolabe such as that shown in Stöffler's Elucidatio (Fig. 5.41). It has the advantage that equal and unequal hours can be used simultaneously for expressing the time. Stöffler's hour circle and the set of semicircles make it easy to solve astrological problems, such as casting a horoscope for a particular moment and place. Additional astrological information, such as the planetary natures of the stars, which Dorn engraved on his globe, could be found in Stöffler's Almanach.

The longitudes of the stars on Stöffler's globe differ with respect to the corresponding Ptolemaic values on average by 19° 38´ ± 11´, which value was determined by measuring the ecliptic longitude of 16 stars located close to the ecliptic. Stöffler also used this value of 19° 38´ in his star tables for the epochs 1499 and 1500, in respectively his Almanac and Elucidatio, consistent with the prediction of the Alfonsine trepidation theory. The epoch of Stöffler's globe may therefore be reliably set to 1500.

The nomenclature on Stöffler's globe follows in the main that on the Vienna maps. Often Stöffler gives additional names for the constellations.

The Mathematical Tradition in Medieval Europe

Fig. 5.41 The unequal hour lines on an astrolabe plate from Johannes Stöffler's Elucidatio. (Photo: Elly Dekker.)

For example, the names OLOR and ANGVITENENS are added to the corresponding names on the Vienna maps (Gallina and Serpentarius). The star names marked on Stöffler's globe are listed in Table 5A.1 (p. 412) in Appendix 5.1 together with those on the Vienna maps and Dorn's globe. Most but not all of the names on Stöffler's globe occur in the Vienna star catalogue. Stöffler's star names are also found in the star catalogue in the second edition of the Alfonsine Tables of 1492, the history of which has been discussed extensively by Kunitzsch.199 It is plausible that Stöffler used for his 1493 globe this particular 1492 star catalogue, properly adapted for precession, because two labels occurring on Stöffler's globe: Icalurus and Suhel ponderosus Canopius occur exclusively in the editions of the Alfonsine Tables of 1492 and 1518 (1521). Icalurus is (p.405) a misreading or miswriting of the Latin ‘et est incalurus’. Stöffler may also have used this 1492 catalogue of the Alfonsine Tables for the star tables published in his Almanac of 1499 and in his treatise of the astrolabe Elucidatio fabricae ususque astrolabii of 1512.200

The constellation designs on Stöffler's globe recall only in some respects the Vienna tradition. For example, all constellations are drawn in rear view as on the Vienna maps and on Dorn's globe. On Stöffler's globe, Crater is represented by the typical wooden tub seen on the Vienna maps but apart from this one finds quite a number of iconographic differences. Important changes are seen in the way some constellations are dressed. Auriga and Ophiuchus, who are nude on the Vienna maps, have been painted in nicely coloured suits, narrowed at their middle. In addition to changes in dress, other deviant characteristics—some substantial and others minor—are introduced with respect to the iconography of the Vienna maps.

A number of conspicuous attributes of especially Bootes, Cassiopeia, Andromeda, and Virgo recall the aforementioned medieval constellation cycle connected with Michael Scot whose descriptive star catalogue Liber de signis includes many astrological predictions. Scot's iconography was used in the editio princeps of Germanicus's Latin translation of Aratus's poem The Phaenomena published in Bologna in 1474.201 The woodcuts of the Scot illustrations were also used in the 1482 and 1485 editions of Hyginus's De Astronomia, published by Erhard Ratdolt in Venice, and in many other astronomical works printed during the Renaissance.202 Erhard Ratdolt used the woodcuts again with a few additional images when he published a German translation of Scot's Liber de signis in 1491 with the confusing title Hyginus von den XII zaichen und XXXVI pilden des hymels mit yedes stern.203 Scot's iconography was readily available at the end of the fifteenth century.

Scot describes Bootes as a farmer wearing a hat with long hair, and holding a sickle in his right and a lance in the left hand, attributes that are easily recognized in the picture of Bootes on Stöffler's globe, albeit that the left and right hand are exchanged.204 The sheaf of corn on his left side underlines his role as a farmer. It is not explicitly mentioned in Scot's text but it is certainly part of Scot's iconography and occurs in the constellation cycle in Vienna MS 2352, f. 13v and in the woodcuts of the Scot illustrations.

The impact of Scot's iconography is also seen in Virgo who holds a sceptre in her right hand (Fig. 5.42). Scot says that Virgo is in the house of Mercury, who gave her the sceptre.205 Ackermann suggests that this attribute may derive from the image of Virgo in Madrid, Biblioteca Nacional MS 19, ff. 57v.

Andromeda and Cassiopeia on Stöffler's globe partly recall Scot's iconography. The myth around Andromeda, the daughter of Cepheus and Cassiopeia, is well known. It starts with the impiety of Cassiopeia challenging the beauty of the Nereids, the daughters of Poseidon. For this act Andromeda is punished and exposed to the sea monster Cetus. Just in time Perseus rescues her and presumably marries her. To commemorate this story all five participants in the drama were placed among the stars. On Stöffler's globe, Andromeda is chained at her wrists to the (p.406)

The Mathematical Tradition in Medieval Europe

Fig. 5.42 Virgo on the celestial globe of Johannes Stöffler. (Landesmuseum Württemberg, Stuttgart; Photo: Peter Frankenstein, Hendrik Zwietachs.)

branches of two trees at her sides and Cassiopeia looks in a mirror held in her left hand and her other hand is tied to the ornament at the back of the throne (Fig. 5.43). Scot describes Andromeda, tied to trees between mountain rocks, as being above her middle a woman and below it a man, partly dressed and partly nude.206 The manner in which Andromeda is tied to the trees agrees with Scot's description but she is not the hermaphrodite that Scot outlines. In the printed version of Scot's iconography Cassiopeia is also fastened to her throne although it is not clear why this is so. Scot describes Cassiopeia as a beautiful well dressed woman with outstretched arms, as was common in the descriptive tradition, but this attitude does not fit the Ptolemaic stellar configuration.207 On Stöffler's globe both Andromeda and her mother are presented as nude figures as on the Vienna maps. Perseus wears a loincloth and holds a slightly curved sword in his right hand above his head. In his lowered left hand he carries a cut-off head from which blood spatters which pictures vividly the beheading of Medusa as described by Scot and other authors. The wings at his feet are mentioned by Hyginus in Book II.12.

As discussed above in connection with the later Nuremberg maps (see Fig. 5.24) the ox hide held by its head in Orion's raised left hand (Fig. 5.44) may come from Scot. There is an interesting difference though, because whereas in the Nuremberg maps the ox hide is held by the tail and the head hangs down, on Stöffler's globe the head is held in Orion's hand. This same orientation is seen in a constellation cycle connected with Michael Scot's treatise in Vienna MS 3394, f. 227 where Scot's text is missing and the name Hyginus is mentioned instead at the end of the text preceding the image.208 This manuscript is dated around 1470 and was written in a north Italian scriptorium, possibly in Padua. The myth explaining the ox hide is given in Hyginus Book II.34:

‘Aristomachus, however, says there was at Thebes a certain Hyrieus (Pindar says he lived on the island of Chios), who received Jupiter and Mercury as his guests, and sought from them the gift of becoming a father. Further, in order to obtain his request (p.407)

The Mathematical Tradition in Medieval Europe

Fig. 5.43 Andromeda and Cassiopeia on the celestial globe of Johannes Stöffler. (Landesmuseum Württemberg, Stuttgart; Photo: Peter Frankenstein, Hendrik Zwietachs.)

more easily, he sacrificed an ox and placed it before them at a banquet. When Hyrieus had done this, Jupiter and Mercury ordered that the hide of the ox be removed and that the oxhide, into which they urinated, should be buried. From the oxhide was later born a lad whom Hyrieus called Urion [“urine born”], because of his origin, but long-standing custom calls him Orion’.209

Other iconographic adaptations are seen in the image of Cepheus, who on Stöffler's globe is painted like a king, with a crown on his head, a sceptre in his right hand, and a sword attached to a belt around his middle. Scot mentions only the sword. The crown and sceptre do occur in some constellation cycles, for example in Munich Clm 595, f. 40r and on the Dyffenbach map M1a (Fig. 5.13) although less convincingly than on the globe. Auriga's role as a charioteer is underlined by the harness in his right hand and, less commonly, a wheel at his side.

The Mathematical Tradition in Medieval Europe

Fig. 5.44 Orion on the celestial globe of Johannes Stöffler. (Landesmuseum Württemberg, Stuttgart; Photo: Peter Frankenstein, Hendrik Zwietachs.)

(p.408) The most interesting feature of Hercules's outfit is not his colourful attire or the lion's skin but the branch with fruits in front of his right lower leg which may represent the golden apples of the Hesperides. The golden apples are not exclusively mentioned by Scot and since Scot described Hercules as a naked man with sword, it may well be that the inspiration for this image did not come from Scot.

A last feature that certainly does not originate from Scot's iconography is that of two dogs connected by leads to the wrist of the same hand that holds the lance (see the dogs in the right lower corner of Fig. 5.42). Bootes's dogs are part of the image of Bootes as a young man in the fifteenth-century illustrated manuscript in Florence, Biblioteca Nazionale Centrale Angeli MS 1147 A.6, f. 7v.210 This image is part of a cycle that, as mentioned above, must stem from a globe. This may support the suggestion that Bootes's two dogs emerged from an attempt to make sense of a difficult phrase in Gerard of Cremona's Ptolemaic star catalogue of Boo 8 (μ Boo).211

There can be no doubt that the globe's artist borrowed from Scot's iconography, but he also borrowed from other sources and seems to have combined a good knowledge of mythology with great imagination. The colourful way in which many figures are dressed, including even Ophiuchus who as a rule is nude, may point to an artist from northern Italy. This anonymous designer left his monogram, a sword with a letter N, on the constellation Centaurus.212 His cooperation with Stöffler resulted in a globe that combines elements of a medieval descriptive iconographic tradition and the Western mathematical tradition, and in this way highlights the astronomical, astrological and mythological interests in Renaissance celestial cartography.

Appendix 5.1 European Celestial Maps Made before 1500

M1. VATICAN CITY, BIBLIOTECA APOSTOLICA VATICANA, MS Plate. lat. 1368, ff. 63r–64v

Heidelberg or vicinity, first half of the fifteenth century.

FOLIO SIZE: 29.3 × 39.4 cm.

AUTHOR: Conrad of Dyffenbach.

f. 45r: ‘Et sic finitur centilogium Ptolomei scriptum per me Conradum/de Dyffenbach Anno domini 1426 festo epiphanie domini etc’.

There are four celestial maps divided over four pages which are ordered after their projection.

M1a. ff. 63V–64r: Map of the northern hemisphere (Figs 5.135.14).

CARTOGRAPHY: Language Latin. Polar equidistant projection from the north ecliptic pole to the ecliptic. Great circles through the ecliptic pole are drawn every 5º; circles parallel to the ecliptic are drawn every 5º. The ecliptic is graduated (12 times 0º–30º; numbered every 5º, division 1º); the (sometimes abbreviated) names of the 12 zodiacal signs are placed at the beginning of each sign and their symbols in the middle of it. (The symbols of Aries and Taurus have been exchanged.) The great circles through the beginning of Aries, Gemini, and Libra are numbered every 5º. At the end of the great circle through the beginning of Cancer is the label: colurus.

(p.409) ASTRONOMICAL NOTES: A few northern Ptolemaic constellations are drawn and labelled: ursa minor, ursa maior, draco, cepheus, boetes/teguius/lanceator, corona, agitator [?]. The stars within a constellation are marked by the numbers of their magnitudes, presumably from the Ptolemaic star catalogue. Some stars of Perseus and Ophiuchus are marked but these constellations are neither finished nor drawn. A few stars are labelled: alfeta (α CrB), alhaiot (α Aur), alramech/artophilax (α Boo), cauda (α UMi), alioze (ε UMa), and edub (α UMa). The constellations are drawn in a primitive way. Ursa Minor is hardly recognizable as a bear. Bootes is presented with a lance in his right hand and a bow in his raised left hand. Cepheus wears a crown and carries in his left hand a sceptre and in his right hand a globus cruciger, an orb with a cross.

M1b: f. 63r: Map of the zodiac (Fig. 5.15), [lon 25º–150º, lat N 30º–S 55º]

CARTOGRAPHY: Language Latin. Dyffenbach projection from the north and south ecliptic poles to the ecliptic. Great circles through the ecliptic pole are drawn as straight lines for latitudes N 10°–30° and S 10°–55° for every 5°, and for latitudes 6° N and S, marking the boundaries of the ecliptic. The ecliptic is labelled eclipticus; it is graduated (from Ari 25° to Leo 30°; numbered every 5°, division 5°); the beginning of the scale at Ari 25° is labelled arietis and the names of next four zodiacal signs are placed at the beginning of each sign: Thaurus, Gemini, Cancer, and Leo.  The great circles at the boundaries through Ari 25° and Leo 30° are numbered every 5° for latitudes N 10°–30° and S 10°–55° and at 6° N and 6° S of the ecliptic. The northern and southern part of the map are labelled: septentrio and meridies.

ASTRONOMICAL NOTES: The stars are marked on the map by the numbers of their magnitudes (2–6), presumably taken from the Ptolemaic star catalogue. The brightest stars of the first magnitude are indicated by a starry symbol (*). Nebulous object are sometimes presented by a point in a dotted circle, or by labels oc and ne. The texts around stars indicate their position within the constellation. The stellar configurations have been surrounded by the contours of the constellations. External stars, often labelled ‘ex [. . .]’, are also in most cases enclosed by a line. The astrological natures are added to some of the brighter stars. The following zodiacal constellations are drawn: Aries, Taurus, Gemini, Cancer, and the western part of Leo. North of the zodiac one finds Triangulum and south of it the eastern part of Cetus, Eridanus, Orion, Lepus, Canis Maior, and Canis Minor. There are a number of stars east of Canis Maior that belong to Navis but the contours of the ship are not drawn. Two stars that belong to the constellation Navis (nos 44 and 45) and which should actually lie below Canis Maior, lie north of Canis Maior. One is labelled: ‘canap[. . .] in navi/in remo/saturni [et] jouis’ and the other, below Canis Minor: ‘sequens canap[. . .]’. Their positions in the present map are based on erroneous latitudes (respectively -29° and -21° 50´) recorded in some star catalogues. The constellations are labelled (in red?): ymago arietis, y[ma]go thauri, gem ante[. .]s, gem seq[. .]s, y[ma]go cancri, y[ma]go ceti, and Cetus, ymago orionis and Orion, y[ma]go leporis, y[ma]go canis, twice y[ma]go flu[. . .]s. There are names for the brighter stars: aldabaram (α Tau), alfeta (α CrB), rigil (β Ori), algomesa (α CMi), alhabor (α CMa), canap[. . .] (α Car), cor leonis (α Leo), and for some nebula: P[re]sepe and Pleyades.

Mlc. f. 64r: Map of the zodiac (Fig. 5.14), [lon 150º–270º, lat N 30º–S 30º].

CARTOGRAPHY: Language Latin. Dyffenbach projection from the north and south ecliptic poles to the ecliptic. Great circles through the ecliptic pole are drawn as straight lines for the range of longitudes 150º–270º for every 5º; parallels to the ecliptic are drawn as straight lines for latitudes N 10°–30° and S 10°–30° for every 5°, and for latitudes 6° N and S, (p.410) marking the boundaries of the ecliptic. The ecliptic is graduated (from Vir 0° to Sgr 30°; numbered every 5°, division 5°); the names of four zodiacal signs are at the beginning of each sign: virgo, libra, Scorpio, and Sagit[arius]. The great circles at the boundaries through Vir 0° and Sgr 30° are numbered every 5° for latitudes N 10°–30° and S 10°–55° and at 6° N and 6° S of the ecliptic

ASTRONOMICAL NOTES: The stars are marked as on M1b. The following zodiacal constellations are drawn: the eastern part of Leo, Virgo, Libra, and Scorpio. North of the zodiac one finds the three stars of Coma Berenices (Leo 6e–8e), marked oc, oc, and ne, with a note saying that they lie between the tail of Leo and Ursa Maior. One more star plotted north of Virgo is probably the northernmost of the three stars in the leg of Bootes (Boo 20). South of the zodiac one finds Crater, Corvus, and two stars that belong to Lupus (Lup1–2). The constellations are labelled (in red?): ymago leonis, y[ma]go virginis, y[ma]go librae, y[ma]go scorpionis, y[ma]go vasis, and corui. There are names for the brighter stars: cauda (β Leo), Praevindemiatorem? (ε Vir), Spica (α Vir), and cor scorpionis (α Sco).

M1d. f. 64v: Map of the zodiac (Figs 5.16). [lon 270º–30º, lat N 30º–S 30º]

CARTOGRAPHY: Language Latin. Dyffenbach projection from the north and south ecliptic poles to the ecliptic. Great circles through the ecliptic pole are drawn as straight lines for the range of longitudes 270º–30º for every 5º; circles parallel to the ecliptic drawn as straight lines for latitudes N 10°–30° and S 10°–30° for every 5°, and for latitudes 6° N and S, marking the boundaries of the ecliptic. The ecliptic is graduated (from Cap 0° to Ari 30°; numbered every 5°, division 5°); the names of four zodiacal signs are at the beginning of each sign: Capricornus, Aqua[rius], pisces, and Aries. The great circle at The great circle the boundary through Cap 0° is numbered every 5° for latitudes N 10°–30° and S 10°–55° and at 6° N and 6° S of the ecliptic.

ASTRONOMICAL NOTES: The stars are marked as on M1b. The following zodiacal constellations are drawn: Sagittarius, Capricornus, Aquarius, and Pisces. North of the zodiac are four stars of Pegasus, the identification of which is troublesome. At first sight they seem to represent the bright stars of magnitude 2 in the square of Pegasus (Peg 1–4) but these stars ought to lie more to the east. South of the zodiac one finds Piscis Austrinus and Cetus. The star Sgr 25 in the front right hock of Sagittarius is off by 20°, thus creating the curious shape of the constellation. The constellations are labelled (in red?): ymago sagitarii,y[ma]go capricorni, y[ma]go aquarii, y[ma]go piscum, y[ma]go ceti [. . .]. There are no stars named.

COMMENTS: The projection referred to here as the Dyffenbach projection is described in detail in Section 5.3. It has commonly been described as trapezoidal and for that reason has been confused with the Donis projection. The bow held by Bootes is also part of the drawing of this constellation in Vienna MS 5415 (f. 221r). In this constellation cycle Cepheus also holds a globus cruciger, an orb with a cross (f. 220r). Literature: Durand 1952, pp. 114–17; Saxl I 1915, pp. 10–15, Tafel XI, Fig. 24; for the inscription on f. 45r see p. 13. See also Saxl II 1927, pp. 22–5 and Uhden 1937.

M2. VIENNA, ÖSTERREICHISCHE NATIONALBIBLIOTHEK, MS 5415, f. 168r and f. 170r

Vienna or Klosterneuburg or Salzburg, ca. 1434/1435.

FOLIO SIZE: 29.0 ×21.6 cm/ folded parchment.

AUTHOR: Reinhardus Gensfelder.

The codex was acquired in 1780 by the Österreichische Nationalbibliothek as part of the old municipal library in Vienna.

(p.411) M2a. f. 168r: Map of the northern hemisphere, from the north ecliptic pole to south of the ecliptic to include the zodiacal constellations (Fig. 5.18).

CARTOGRAPHY: Language Latin. Great circles presented as straight lines through the ecliptic pole have been drawn in black ink for every 30°, marking the boundaries of the zodiacal signs. The ecliptic has a radius of 13.5 cm; it is graduated (12 times 0°–30°; each sign is divided into five parts of 6°, which are in turn subdivided into parts of 1°; each sign is numbered at 12°, 18°, 24°, and 30°). The numbers of the signs themselves (1,…,12) are added in the first section of 6° of each sign; these numbers are drawn in black ink. The degrees/numbers of the zodiacal scale are drawn alternatively in red and black ink (sign 1: black/red, sign 2: red/black,…, 11 black/red, sign 12: red/black). In addition four other circles have been drawn. Two of these are drawn in black ink and are centred on the north equatorial pole which is located on the solstitial colure, at a distance of 3.6 cm from the north ecliptic pole. The largest of these two circles passes though the north ecliptic pole and presumably is meant to represent the north polar circle. The smallest circle has a radius of 0.7 cm. Two other circles are drawn in red ink; both pass through the first points of Aries and Libra and extend beyond the ecliptic circle. One of them is centred on the north equatorial pole and has a radius of 14.0 cm and presumably is meant to represent the part of the Equator north of the ecliptic. The centre of the other circle is also located on the solstitial colure, but at a distance of 2.9 cm from the ecliptic pole; it has radius of 13.8 cm. Its centre coincides with the northernmost intersection of the small circle (of 1.4 cm in diameter centred on the north equatorial pole) with the solstitial colure, where a dot is clearly visible. When expressed as fractions of the radius of the ecliptic, the distance of the north equatorial pole from the centre of the northern map amounts to 0.267 and the radius of the small circle inside the north polar circle is 0.052. The radii of the two large circles amount to 1.022 and 1.037. When assuming that the equidistant projection was used in constructing the map, the distance of the north equatorial pole from the centre of the map amounts to 24°, and the radius of the small circle inside the south polar circle is to 4.7°. The radii of the other two circles would correspond to 92° and 93.3°, respectively.

ASTRONOMICAL NOTES: Epoch 1424 (α Leo in Leo 21° 20´). All stars are marked by a hole in the parchment. Stars located within a constellation figure are marked in red ink and numbered in black ink. The brightest stars are marked by a starry symbol, the others by dots of varying sizes. Unformed or external stars, located outside constellation figures, are marked in black ink; they are not numbered. One unformed star below the tail of the great Bear has been crossed over by red ink. The Milky Way is drawn, but it is not labelled. The names of the stars, listed in Table 5A.1 below, are in red ink.

CONSTELLATIONS: Of the 48 Ptolemaic constellations 33 are presented. These include all the constellations of the zodiac and north of it. Three constellations are not named: Ursa Maior, Serpens, and Triangulum. All constellation names are written in red ink.

DESCRIPTIONS: URSA MINOR, labelled Ursa minor, is a small bear with a long tail. His back is turned to Ursa Maior. URSA MAIOR, not labelled, is a great bear with a long tail. DRACO, labelled draco, is a snake with four curls; his tongue sticks out his mouth. Draco's head is below the left foot of Hercules. CEPHEUS, labelled Cepheus, is seen from the rear, dressed in a tunic, has curly hair and wears a Phrygian hat. He is kneeling on his right leg and his arms are stretched out. BOOTES, labelled Bootes, is seen from the rear; he is dressed in a tunic and has curly hair. His left arm is raised and in his right hand is a straight stick which touches the right foot of Hercules. CORONA BOREALIS, labelled Corona, is an open crown with petals. HERCULES, labelled hercules vel saltator, is seen from the rear; he has curly hair and he is dressed in some kind of armour with gloves covered by a tunic. His head is (p.412)

Table 5a.1 A Star names on the Vienna maps, and the globes of Hans Dorn and Johannes Stöffler

BPK

Identification

Vienna maps

Dorn's globe

Stöffler's globe

1

α

UMi

alrucaba

CAVDA

Alrucaba Stella polaris

24

α

UMa

dubhe

DVBHE

dubhe

33

ε

UMa

Alioth

35

η

UMa

bennenatz

48

γ

Dra

razdaben

Rasaben

78

α

Cep

Alderaimim

92

γ

Boo

Teginus

Teginus

95

μ

Boo

Icalurus

110

α

Boo

alramech

Ascimech Arramech

111

α

CrB

alfeta

Alpheta

119

α

Her

Rasalheti

149

α

Lyr

vvega

Wega

163

α

Cyg

addigege ariof

Deneb adigege [vel] Arided

179

α

Cas

Scheder

Scheder

197

α

Per

algenib

Algenib

202

β

Per

razd algola

Caput Algol

222

α

Aur

alhayoth

HEDVS

Hircus

234

α

Oph

razdalhaue

240

δ

Oph

yed

yed

271

α

Ser

razdalagueb

288

α

Aql

alkair

Alkaÿr

317

β

Peg

scheat

Scheat

318

α

Peg

mankar

Markab

331

ε

Peg

Enifalferaz

346

β

And

mirach

Mirach

393

α

Tau

ALDEBORA

Aldebran

424

α

Gem

razdalgeuze

Rasalgenze

469

α

Leo

cor leonis

COR LEONIS

Cor

488

β

Leo

cauda leonis

CAVDA LEONES[!]

Cauda

510

α

Vir

Spica azime[ch]

SPICA

Spica

553

α

Sco

cor scorpionis

Cor

565

λ

Sco

cauda scorpionis

Cauda

624

δ

Cap

algedi

Cauda

646

δ

Aqr

Scheat

Sceath

670

α

PsA

Fomahaut

713

α

Cet

menkar

MENTVM

Menckar

725

ζ

Cet

pentakaiton

VENTER

Venter ceti

733

β

Cet

denebkaytoz

CAVDA

Denebcaÿton

735

α

Ori

bedelgeuze

IVGLA(!) A OR

736

γ

Ori

bellatrix

IVGVLA B OR

768

β

Ori

rigil

RIGEL

790

τ2

Eri

augetenar

Angetenar

805

θ

Eri

acarnar

ACARNAR

Acarnar

818

α

CMa

alhabor

SIRIVS

Alhabor Sirius

848

α

CMi

algomeisa

Algomeÿsa

855

p

Pup

markeb

MARKEB

Markeb

892

α

Car

Suel

SVEL

Suhel ponderosus Canopius

905

α

Hya

alphart

Alphart Serpente idra

921

α

Crt

Alhes

931

γ

Crv

algorab et coruus

Algorab

a On the Vienna map there is in addition a label ‘caput algol’ which I presume is not a star name but a label for the head of Medusa.

b For this name, see Kunitzsch 1986b, p. 97, note 22.

(p.413) west of that of Ophiuchus. He is kneeling on his right knee and his left foot is above the head of Draco. His left arm is stretched out in the direction of Lyra and he holds a curved sword in his raised right hand. LYRA, labelled vvltvr cade(n)s, is presented as a bird, with a crooked beak. CYGNUS, labelled gallina, is a bird with an outstretched neck and outstretched wings, as if flying. CASSIOPEIA, labelled Cassiepea, is turned in her chair and thus seen from the rear. She is nude and her right arm is stretched. In her left hand she holds a long feather. PERSEUS, labelled P[e]rseus, is a naked figure with curly hair, seen from the rear. He holds a curved sword in his right hand above his head and he carries a head with devil's ears in his lowered left hand. The four stars in the head of Medusa are labelled: caput algol. AURIGA, labelled Agitator, is a nude figure with curly hair, seen from the rear. His head is turned west and his knees are slightly bent but he is not kneeling. Both arms are lowered. On his left shoulder stands a goat and around his right wrist is a harness. His right foot touches the northern horn of Taurus. OPHIUCHUS, labelled Serpentarius, is a naked figure with curly hair, seen from the rear. His head is turned east away from the nearby head of Hercules. He holds the body of Serpens in his hands. One of his feet rests on the body of Scorpius. SERPENS, not labelled, is a snake with an open mouth. Its body, which encircles the wrists and middle of Ophiuchus, has four coils. SAGITTA, labelled ystius?, is a simple arrow north of Aquila. AQUILA, labelled vvlt(vr) volans, is drawn as a bird with outstretched wings, flying in a south-eastern direction. DELPHINUS, labelled delphin, is drawn as a dolphin. EQUULEUS, labelled Equus p(ri)or, is drawn as the head of a horse. PEGASUS, labelled Equus volans, is drawn as half a horse with wings. ANDROMEDA, labelled Andromeda, is a nude female figure with her hair in tresses around her head, seen from the rear. She holds a band or cord in her hand which encircles her middle. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her left arm is raised above the northern one of the Pisces. The other, right arm is stretched towards the north. TRIANGULUM, not labelled, is drawn as a triangle. ARIES, labelled Aries, is drawn as a ram with two horns and a curly fleece. He lies with his forefeet bent. He is looking backwards to Taurus. The ecliptic cuts through his body and passes above his tail. TAURUS, labelled thaurus, is a half bull with a bent head, two front legs, and two horns. The ecliptic passes through his body and his head. The northern horn extends to the left foot of Auriga. The Pleiades are labelled: Pliades. GEMINI, labelled Gemini, consist of two nude figures with curly hair, both seen from the rear. Their heads are turned to each other and their legs stretch westwards. They are without attributes. The right arm of the western twin rests on the shoulder of the eastern twin. CANCER, labelled Cancer, is a crawfish with two claws facing Leo and three legs on either side. The ecliptic passes through the main body. LEO, labelled leo, is a lion is standing on its hindlegs with his forefeet as if jumping. He has his mouth open and is looking forward to Cancer. (p.414) The lion's tail makes a loop. The ecliptic passes through the chest and the hindlegs. VIRGO, labelled virgo, is a female figure with curly hair and with wings, seen from the rear. She wears a long dress with a belt. Her head is turned in profile to the north. The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. She points with her right hand to her head. On her lowered left hand is a bright star, presumably Spica, close to the ecliptic. LIBRA, labelled libra, is presented by a pair of scales. SCORPIUS, labelled Scorpio, is drawn as a scorpion with two short claws, three legs on both sides, and a segmented tail. SAGITTARIUS, labelled Sagittarius, is a horse with a nude figure on top, seen from the rear. The male figure has curly hair and a head band with bands of cloth fluttering behind him. He looks forward in the direction of Scorpius. In his left hand he carries a bow and in his (invisible) right hand he holds the arrow. The ecliptic intersects his head. CAPRICORNUS, labelled Capricornus, has two short horns and a fish tail. The ecliptic intersects him just below the neck and through the tail. AQUARIUS, labelled Aquarius, is a nude figure with curly hair, seen from the rear. His slightly bent left arm is stretched westwards and holds a folded piece of cloth. The ecliptic intersects his body at the hips. His right arm rests on an urn from which water streams. The stream is cut-off by the ecliptic. PISCES, labelled pisces, consists of two fishes. The southern of the two is located below the wing of Pegasus. The other, northern fish is located below the raised arm of Andromeda. There is band with a knot which connects the tails of the fishes.

M2b. f. 170r: Map of the southern hemisphere, from the south ecliptic pole to the ecliptic (Fig. 5.19).

CARTOGRAPHY: Same as map M2a, but here the ecliptic is slightly differently graduated: (12 times 0°–30°; each sign is divided into five parts of 6°; only the first of these five parts is subdivided in parts of 1°; each sign is numbered at 12°, 18°, 24°, and 30°). The numbers of the zodiacal scale are drawn alternately in red and black ink starting with black in the first sign. The signs themselves are not numbered on this map. In addition two other circles have been drawn. One of these is drawn in black ink; it is centred on the south equatorial pole which is located on the solstitial colure, at a distance of 3.6 cm from the south ecliptic pole. This circle passes though the ecliptic pole and presumably is meant to represent the south polar circle. The other circle is drawn in red ink and passes through the first points of Aries and Libra; it is centred on the south equatorial pole; it has a radius of 14.0 cm and presumably represents the part of the Equator south of the ecliptic. There is another point indicated on the solstitial colure at a distance of 2.9 cm from the south ecliptic pole around which a small circle has been traced, presumably with a pair of dividers, because this circle is not drawn in ink; it does not pass through the south equatorial pole and it has diameter of about 1 cm. When expressed as fractions of the radius of the ecliptic, the distance of the equatorial pole from the centre of the southern map amounts to 0.267 and the radius of the vague compass tracing inside the south polar circle is 0.037. The radius of the largest circle centred on the south equatorial pole is 1.037. When it is assumed that the equidistant projection was used in constructing the map, the distance of the north equatorial pole from the centre of the map amounts to 24°, and the radius of the vague compass tracing inside the south polar circle 3.3°. The radius of the largest circle would correspond 93.3°.

ASTRONOMICAL NOTES: All stars are marked by a hole in the parchment. Stars located within a constellation figure are marked in red ink and numbered in black ink. The brightest stars are marked by a starry symbol, the others by dots of varying sizes. Most of the unformed or field stars, located outside constellation figures, are marked in black ink and a few in red ink; they are not numbered. Two unformed (p.415) stars below Lepus have been crossed over by red ink. The Milky Way is drawn, but it is not labelled. The names of the stars, listed in Table 5A.1 below, are in black.

CONSTELLATIONS: Of the 48 Ptolemaic constellations 15 are presented. These include all the constellations south of the zodiac. One constellation, Canis Minor, is not named. All names are all written in red ink.

DESCRIPTIONS: CETUS, labelled Cetus, is presented as a whale. ORION, labelled Orion, is seen from the rear. He has curly hair and he is dressed in some kind of armour with gloves covered by a tunic. He holds his head backwards to show his face. He holds an animal skin in his raised left hand and carries a club in his raised right hand. He kneels on his left knee and his right leg is slightly bent. He has a belt around his middle to which a sword in a scabbard is attached. ERIDANUS, labelled fluuius, is a river presented by a band which starts at the left foot of Orion, and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). LEPUS, labelled lepus, is a hare with long ears south of Orion. CANIS MAIOR, labelled canicula, is a dog with an open mouth. CANIS MINOR, not labelled, is a walking dog with a collar. NAVIS, labelled navis ut archa noe, is a ship with a mast, a crow's nest, and three ropes, but no sails. There are two steering oars which seem to emerge from behind the ship. At the western end of the ship is a balustrade and at the eastern end a dog's head. HYDRA, labelled ydra, is a snake with two coils. The mouth is open and his tongue is shown. The end of the tail is above the head of Centaurus. CRATER, labelled vas ut c(ra)t(er), is a tub with two handles, standing behind on the body of Hydra. CORVUS, labelled coruus, is a bird standing with its feet on the body of Hydra. It is picking the snake. CENTAURUS, labelled Ce(n)taurus, is a horse with a nude figure with curly hair on top, seen from the rear. On his right arm rests a shield and in his right hand he holds a lance which pierces the head of Lupus. LUPUS, labelled lupus, is an animal with its mouth open, held by Centaurus. ARA, labelled Sacrum thuribulu(m) vel lar, is a square altar with flames on top. It is upside-down. CORONA AUSTRALIS, labelled corona, is an open crown with petals. PISCIS AUSTRINUS, labelled piscis meridio(na)lis, is a fish with its head turned towards its tail, mouth open showing its teeth.

COMMENTS: The maps are part of the treatise on the construction and use of a celestial globe, Vienna MS 5415, ff. 161r–191r, Tractatus de sphaera solida, the explicit of which gives the date of the copy: ‘Explicit tractatus…finitus anno 1435 currente’. This is presumably also the date of the maps. The codex has on f. 33v the coats of arms of Vienna, Austria, and Klosterneuburg. Literature: Saxl II 1927, pp. 24–31, pp. 34–38, and pp. 150–55; Roland 2012, Kat. no. 77, pp. 19–28; Blume et al. to be published.

M3. MUNICH, BAYERISCHE STAATSBIBLIOTHEK, Clm 14583, ff. 70v–73r

St Emmeran, between 1447–55.

AUTHOR: Fredericus (Friedrich Gerhart).

There are three celestial maps divided over six pages.

M3a: ff. 70v–71r: Map of the zodiacal and three northern constellations Ursa Minor, Ursa Maior, and Draco (Fig. 5.20).

CARTOGRAPHY: Language Latin. The map is bounded by the zodiac presented by three concentric circles. Great circles presented as straight lines have been drawn (in red ink) through the ecliptic north pole. The signs (not to be confused with the zodiacal constellations) are labelled in red ink: Aries; Thaurus; Gemini; Cancer; Leo; Virgo; Libra; Scorpio; [Sag]ittarius; Capricornus; Aquarius; Pisces.

ASTRONOMICAL NOTES: Neither stars nor the Milky Way are marked. The zodiacal constellations and three (p.416) northern ones, Ursa Minor, Ursa Maior, and Draco, are drawn but not labelled.

M3b: ff. 71v–72r: Map of the constellations north of the zodiac (Fig. 5.21).

CARTOGRAPHY: Language Latin. The map is bounded by the zodiac presented by three concentric circles. Great circles presented as straight lines have been drawn (in red ink) through the ecliptic north pole. The signs are labelled in red ink: Aries; Thaurus; Gemini; Cancer; Leo; Virgo; Libra; Scorpio; Sagittarius; Capricornus; Aquarius; Pisces.

ASTRONOMICAL NOTES: Neither stars nor the Milky Way are marked. All 21 Ptolemaic constellations north of the zodiac are drawn but none labelled: Ursa Minor, Ursa Maior, Draco, Cepheus, Bootes, Corona Borealis, Hercules, Lyra, Cygnus, Cassiopeia, Perseus, Auriga, Ophiuchus, Serpens, Sagitta, Aquila, Delphinus, Equuleus, Pegasus, Andromeda, and Triangulum.

M3c: ff. 72v–73r: Map of the constellations south of the zodiac (Fig. 5.22).

CARTOGRAPHY: Language Latin. The map is bounded by the zodiac presented by three concentric circles. Great circles presented as straight lines have been drawn (in red ink) through the ecliptic south pole. The signs are labelled in black and red ink: Aries; Thaurus; Gemini; Cancer; Leo; Virgo; Libra; Scorpio; Sagittarius; Capricornus; Aquarius; Pisces. Names in black seem to be a correction of other names in red which have been wiped out (though not completely). There are also names below the zodiac in another hand.

ASTRONOMICAL NOTES: Neither stars nor the Milky Way are marked. All 15 Ptolemaic constellations south of the zodiac are drawn but not labelled: Cetus, Orion, Eridanus, Lepus, Canis Maior, Canis Minor, Navis, Hydra, Crater, Corvus, Centaurus, Lupus, Ara, Corona Australis, Piscis Austrinus.

COMMENTS: Although primitively drawn, the present maps shares most iconographic characteristics with those described above (M2). Literature: Durand 1952, p. 174.

M4. NUREMBERG, GERMANISCHES NATIONALMUSEUM, Inv. Nr. Hz 5576/5577.

Nuremberg, 1503.

FOLIO SIZE: 66.5 × 66.5 cm.

AUTHORS/CONTRIBUTORS: Konrad Heinfogel, Theodericus Ulsenius, Sebastian Sperancius

M4a. Inv. Nr. Hz 5576: Map of the northern hemisphere (Fig. 5.23).

In the corners of the map are the images and the names (in red ink) of the four elements and the gods associated with them. In the top left corner one finds images and names of IGNIS, APOLLO, and MARS; in the top right corner are images and names of AER, SATVRNVS, and VENVS; in the bottom left corner are images and names of TERRA, IVPPITER [sic], the goddesses of vengeance ALLECTO, MEGAERA, TESIPHONE, as well of PLVTO and CERBERVS; in the bottom right corner one finds images and names of AQVA, MERCVRIVS, and LVNA.

CARTOGRAPHY: Language Latin. The map is in stereographic projection from the north ecliptic pole to south of the ecliptic to include the zodiacal constellations. Great circles presented as straight lines through the ecliptic pole have been drawn for every 30°, marking the boundaries of the zodiacal signs. The ecliptic has a radius of 24 cm; it is graduated (12 times 0°–30°; each sign is divided into parts of 1°, a division marked by dots); the signs are neither labelled nor numbered. In addition to the ecliptic five other circles have been drawn. Three of these with a radius of 21.7, 26.4, and 32.4 cm respectively, are centred on the north ecliptic pole and mark the boundaries of the (p.417) zodiacal band and the boundary of the map. Two others are centred on the north equatorial pole, labelled POLVS ARCTIKVS, which is located on the solstitial colure, at a distance of 5.0 cm from the north ecliptic pole. The largest of these two circles passes though the north ecliptic pole and represent the north polar circle. The smallest circle has a radius of 0.9 cm. When expressed as fractions of the radius of the ecliptic, the distance of the north equatorial pole from the centre of the northern map amounts to 0.267, and the radii of the three circles centred on the ecliptic pole amount to 0.9, 1.1, and 1.35. Assuming that the stereographic projection was used in constructing the map, the distance of the north equatorial pole from the centre of the map amounts to 23.4°, and the radii of the three circles parallel to the ecliptic would correspond to 84°, 95.5°, and 107°, respectively. The radius of the small circle around the north polar pole is then 4.3°.

ASTRONOMICAL NOTES: Stars inside constellation figures are numbered in black and many of the external stars are NUMBERED in red ink, following the order of the Ptolemaic star catalogue. The brightest stars are marked in gold by starry symbols, the weaker ones by a dot surrounded by a circle filled with gold. Unformed or external stars, located outside constellation figures, are marked by black dots of varying sizes. Only one star name in Ursa Maior, possibly dubhe, is vaguely visible.

CONSTELLATIONS: Of the 48 Ptolemaic constellations 33 are presented. These include all the constellations of the zodiac and north of it. One constellation is drawn but not named: Serpens. The other constellations are labelled in red ink.

DESCRIPTIONS: URSA MINOR, labelled VRSA MINOR, is a small bear with a long tail. His back is turned to Ursa Maior. URSA MAIOR, labelled VRSA MAIOR, is a great bear with a long tail. DRACO, labelled DRACO, is a snake with four curls; his tongue sticks out his mouth. CEPHEUS, labelled CEPHEVS, is a nude figure seen from the rear, with curly hair and a beard. His head is turned east. He wears a Phrygian hat. He is standing with his arms stretched out. BOOTES, labelled BOOTES, is a nude figure seen from the rear, with curly hair and a beard. His head is turned east. His left arm is raised and in his right hand is a lance which ends above the right foot of Hercules.

CORONA BOREALIS, labelled CORONA, is an open crown with petals. HERCULES, labelled HERCVLES, is a nude figure seen from the rear, with curly hair and a beard. His head, which is turned east, is west of that of Ophiuchus. He is kneeling on his right knee and his left foot is above the head of Draco. His left arm is stretched out in the direction of Lyra and his wrist is covered by a lion's skin. He holds a club in his raised right hand. LYRA, labelled VVLTVR CADE(N)S, is presented as a bird. CYGNUS, labelled GALLINA, is a bird with outstretched wings, as if flying. The bird has a long outstretched neck. CASSIOPEIA, labelled CASSIOPEIA, is turned in her chair and seen from the rear. She is nude but wears a crown and her right arm is stretched. In her left hand she holds a long feather. PERSEUS, labelled PERSEVS, is a naked figure seen from the rear, with curly hair, a beard, and wings on his feet. He looks upwards and holds a curved sword in his right hand above his head and he carries the head of Medusa, labelled: CAPVT ALGOL, in his lowered left hand. AURIGA, labelled AGITATOR, is a nude figure seen from the rear, with curly hair and a beard. His head is turned west and his knees are slightly bent but he is not kneeling. Both arms are lowered. On his left shoulder stands a goat and around his right wrist is a harness. His right foot touches the northern horn of Taurus. OPHIUCHUS, labelled OPHIVLCVS [sic], is a naked figure seen from the rear, with curly hair and a beard. His head is turned east away from the nearby head of Hercules. He holds the body of Serpens in his hands. One of his feet rests on the body of Scorpius. SERPENS, not labelled, is a snake with an open mouth. Its body, which encircles the wrists and middle of Ophiuchus, has two coils. SAGITTA, labelled SAGITTA, is drawn as a simple arrow north of Aquila. AQUILA, labelled VVLTVR VOLA(N)S, is drawn as a bird with outstretched (p.418) wings, flying in a southeastern direction. DELPHINUS, labelled DELPHIN, is drawn as a dolphin. Equuleus, labelled EQVVS PRIOR, is drawn as the head of a horse. PEGASUS, labelled EQVVS PEGASVS, is drawn as half a horse with wings. ANDROMEDA, labelled ANDROMEDA, is a nude female figure seen from the rear with her head facing north. Her hair is laid in tresses around her head. She holds a chain in her hand which passes behind her. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her left arm is raised above the northern one of the Pisces. The other right arm is stretched towards the north. TRIANGULUM, labelled DELTON, is drawn as a triangle. ARIES, labelled ARIES, is drawn as a ram with two horns. He lies with his forefeet bent. He is looking backwards to Taurus. The ecliptic cuts through his body and passes above his tail. TAURUS, labelled TAURVS, is a half bull with a bent head, two front legs, and two horns. The ecliptic passes through his body and his head. The northern horn extends to the left foot of Auriga. GEMINI, labelled GEMINI, consist of two nude figures with curly hair, both seen from the rear. Their heads are turned to each other and their legs stretch westwards. They are without attributes. The right arm of the western twin rests on the shoulder of the eastern twin. CANCER, labelled CANCER, is a crawfish with two claws facing Leo and four legs on either side. The ecliptic passes through the main body. LEO, labelled LEO, is a lion standing on its hindlegs with his forefeet as if jumping. He has his mouth open and is looking forward to Cancer. The lion's tail makes a loop. The ecliptic passes through the chest and the hindlegs. VIRGO, labelled VIRGO, is a female figure seen from the rear, with wings and with her hair laid in tresses around her head. She wears a long dress with a belt. Her head is turned in profile to the north. The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. She points with her right hand to her head. In her lowered left hand she holds an ear of wheat with the bright star Spica. LIBRA, labelled LIBRA, is presented by a pair of scales. SCORPIUS, labelled SCORPIO, is drawn as a scorpion with two short claws, four legs on either side, and a segmented tail. SAGITTARIUS, labelled SAGITTARIVS, is a horse with a nude figure on top, seen from the rear. The bearded male figure seems bold. He has a head band with garments attached to it which flutter behind him. In his left hand he carries a bow and in his (invisible) right hand he holds the arrow. The ecliptic intersects his head. CAPRICORNUS, labelled CAPRICORNVS, has two short horns and a fish tail. The ecliptic intersects him just below the neck and through the tail. AQUARIUS, labelled AQVARIVS, is a nude figure with curly hair, seen from the rear. His head is turned west and his slightly bent left arm is stretched westwards and holds a folded piece of cloth. The ecliptic intersects his body at the hips. His right arm rests on an urn from which water streams all the way below his feet. PISCES, labelled PISCES, consists of two fishes. The southern of the two is located below the wing of Pegasus. The other, northern fish is located below the raised arm of Andromeda. There is band with a knot which connects the tails of the fishes.

M4b. Inv. Nr. Hz 5377: Map of the southern hemisphere (Fig. 5.24).

On top of the name is the date: ANNO DO MDIII. In the top left corner one finds images and names of the three fates: CLOTHO, LACHESIS, and ATROPOS. To the right is a figure carrying the coat of arms of Nuremberg.

In the right top corner: ‘CLARA TVIS RVTILANT ARMIS CEV LVMINABINA/SEC DECVS EXIMIAE FVLGES VIRTVTIS HONOSQVE/TOCIVS GENERIS HEIMFOGEL MORIBVS APTVM/NOMEN HABENS CVNCTIS GRATVS BONVSQVE BENIGNVS’.

Below this text is the coat of arms of Heinfogel and the figure and name of VANITAS. The female figure (p.419) has a text in a band around her body: ‘MECVM SVNT FORTITVDO ET AGILITAS/MECVM EST IVVENTVS ET SPECIOSITAS/MECVM SVNT DIVICIE ET GLORIA/MECVM SVNT LETICIE ET DELICIE’ and below it: ‘HEC OMNIA VANITAS’.

In the bottom left corner is the figure and name of BACHVS. Below him is a poem by Theodorius Ulsenius: (in red) ‘VENTORVM DESCRIPCIO/THEORICI VLSENII’(in black, except the first letters): ‘VENTORVM BOREAS PRINCEPS ZEPHIR EVRVS ET AVSTER/EX ISTIS MEDII CONSTITVVNTVR ITEM/COLLATERANT EVRVM VVLTVRNVS SVBQVE SOLANVS/SVNT NOTVS AVSTRALIS AFFRICVS ET SOCII/CIRCIVS VT ZEPHIRVM SEMPERQVE FAVONIVS ORNANT/VVLTAQVILO BOREE CHORVS ET ESSE COMES/PRIMVS ERIT DEXTER QVOCIENS HUNC EVRE VEL AVSTER/PRAESTITERIS. RELIQVIS PRIME SINISTER ERIS’.

In the bottom right corner are two figures. One sits on a celestial sphere and represents Urania. The other figure is a man holding an armillary sphere and represents Sebastianus Sperancius, as explained in the text below him: (in red): ‘SEBASTIANVS SPERANCIVS’ (in black, except the first letters): ‘QVAE REGIS IGNIVOMOS O DIVA VRANIA COELOS/LEGIBVS AETERNIS VASTVM QVI ORBEM MODERANTVR/CALLEAT ILLORVM SPERANCIVS ABDITA QVAEQVE/DA PRECOR ET FAVSTVM TRIBVASPER TE[M]PORAFATV[M]’.

CARTOGRAPHY: Language Latin. The map is in stereographic projection from the south ecliptic pole to the ecliptic. Great circles are presented as straight lines through the ecliptic pole, labelled POLVS ZODIACI, have been drawn for every 30°, marking the boundaries of the zodiacal signs. The ecliptic has a radius of 24 cm; it is graduated (12 times 0°–30°; each sign is divided into parts of 1°, a division marked by dots); the signs are neither labelled nor numbered. In addition to the ecliptic three other circles have been drawn. One of these with a radius of 27 cm is centred on the south ecliptic pole and marks the boundary of the map. Two others are centred on the south equatorial pole, labelled POLVS ANTARTIKVS, which is located on the solstitial colure, at a distance of 4.9 cm from the north ecliptic pole. The largest circle passes though the north ecliptic pole and represents the south polar circle. The smallest circle has a radius of 0.9 cm. When expressed as fractions of the radius of the ecliptic, the distance of the north equatorial pole from the centre of the northern map amounts to 0.267, and the radius of the boundary circle centred on the ecliptic pole amounts to 1.13. Assuming that stereographic projection was used in constructing the map, the distance of the north equatorial pole from the centre of the map amounts to 23.4°, and the radius of the boundary circle corresponds to 97°. The radius of the small circle around the north polar pole is then 4.3°.

Across the map are four compass directions in red ink: MERIDIES, OCCIDENS, SEPTENTRIO, ORIENS. At the border of the map are wind heads and the corresponding names of the winds: AVSTER, AFFRICVS, ZEPHIROAVSTER, PAVONIVS, ZEPHIRVS, CIRCIVS, ZEPHIROBOREAS, CHORVS, BOREAS, AQVILO, EVRO-BOREAS, VVLTVRNVS, EVRVS, SVBSOLANVS, EVROAVSTER, NOTVS.

ASTRONOMICAL NOTES: Stars inside constellation figures are numbered in black and external stars are numbered in red ink, following the order of the Ptolemaic star catalogue. The brightest stars are marked in gold by starry symbols, the weaker ones by a dot surrounded by a circle filled with gold. Unformed or external stars, located outside constellation figures, are marked by black dots of varying sizes.

CONSTELLATIONS: Of the 48 Ptolemaic constellations 15 are presented. These include all the constellations (p.420) south of the zodiac. All names are written in red ink.

DESCRIPTIONS: CETUS, labelled CETVS, is presented as a whale. ORION, labelled ORION, is a nude figure seen from the rear, with curly hair and a beard. His head is backwards to show his face. He holds an ox hide in his raised left hand and carries a club in his raised right hand. He kneels on his left knee and his right leg is slightly bent. He has a belt around his middle to which a sword in a scabbard is attached. ERIDANUS, labelled ERIDANVS, is a river presented by a band with a wavy pattern which starts at the left foot of Orion, and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). LEPUS, labelled LEPVS, is a hare with long ears south of Orion. CANIS MAIOR, labelled CANIS MAIOR, is a dog with a collar. CANIS MINOR, labelled CANIS MINOR, is a walking dog with a collar. NAVIS, labelled ARGONAVIS, is half a ship with a mast but no sails. There are two steering oars on one side of the ship. HYDRA, labelled HIDRA, is a snake with two coils. The mouth is open and his tongue is shown. The end of the tail is in front of the head of Centaurus. CRATER, labelled VAS, is a tub with two handles standing on the body of Hydra. CORVUS, labelled CORVVS, is a bird standing on the body of Hydra. It is picking the snake. CENTAURUS, labelled CENTAURVS, is a horse with a nude figure with a bold head and a beard on top, seen from the rear. He holds a lance in his hands which pierces the head of Lupus. A shield is attached to a belt around his shoulder. LUPUS, labelled LVPVS, is an animal with its mouth is open, held by Centaurus. ARA, labelled ARA, is a square altar with flames on top. It is upside-down. CORONA AUSTRALIS, labelled CORONA MERI:, is an open crown with petals. PISCIS AUSTRINUS, labelled PISCIS NOTVS, is a fish with its head turned towards its tail, mouth open showing its teeth.

COMMENTS: The artist of these maps is unknown. Literature: Voss 1943.

Appendix 5.2 European Celestial Globes Made before 1500

WG1. Bernkastel-Kues, St. Nikolaus Hospital (Cusanusstift)

Ø sphere 27.2 cm.

DATE: 1320–40.

Acquired in 1444 in Nuremberg by Cardinal Nicolaus Cusanus.

CONSTRUCTION: The hollow sphere of birch wood is 20 mm thick, and 27.2 cm in diameter. The sphere is closed by a circular disc of 11.8 cm in diameter and covered with plaster and cloth. Next layers of white oil paint have been added to smooth the surface. At the north and south ecliptic poles a messing circular disc (diameter 3.1 cm) is fixed by four nails. A messing ring is attached to these discs such that it can rotate around the sphere. Half of the ring is 8 mm thick, but the size of the other half is cut out such that one side of the ring coincides precisely with a great circle through the poles (see Fig. 5.6). This part of the ring through the ecliptic poles is divided into units of 5° and subdivided into 1°, but not numbered. At a distance of around 23.5° is a provision to attach a meridian ring.

CARTOGRAPHY: The ecliptic is graduated (not numbered, division into 1° by dots). Perpendicular to the ecliptic is a circle (not graduated) passing through the ecliptic poles and the star Sirius (α CMa). Along a circle at a distance of about 24° from the north and south ecliptic poles one finds several holes, presumably indicating the equatorial poles for a number of epochs. Following Hartmann 1919, p. 30, the positions of these holes, labelled A, B, and C, are schematically summarized in Scheme 5.1. One of the holes (A in Scheme 5.1) lies 12.4° east (i.e. in advance) of the great circle through Sirius. Two other holes (B and C in Scheme 5.1.) are shifted with respect to the great circle through Sirius 20.5° east and 3.3° west, respectively. Around the points A and C are traces of a (p.421) small circle and a series of points which were caused by the nails with which a circular disc was fixed to the sphere at the equatorial poles at A and C. Hartmann 1919, p. 32 also recorded a number of circles specific to each of the equatorial poles A, B, and C: the Equator corresponding to pole A; a part of the Equator corresponding to pole C; the tropics corresponding to pole B; two parallel circles around the north and south pole at a distance of 35º from pole B; a circle of 36º around the star α UMi (Hartmann 1919, p. 32 says ‘α Ursae majoris, unsern jetzigen Polarstern’ which shows that α UMi is intended here).

ASTRONOMICAL NOTES: The stellar positions are marked by small holes drilled into the sphere and filled with red wax. The sizes of the holes vary with the brightness of the star from ½ to 2 mm. All 48 Ptolemaic constellations have been drawn in brownish ink. In Taurus is a group of seven stars representing the Pleiades.

CONSTELLATIONS: All 48 Ptolemaic constellations are drawn and none are labelled.

DESCRIPTIONS: URSA MINOR is a small bear with a short tail. His belly is turned to Ursa Major. URSA MAIOR is drawn as a great bear with a long tail. DRACO is a snake with two bends; his tongue sticks out his mouth. CEPHEUS is a naked figure with curly hair and a hunter's hat. He is kneeling on his left leg and his arms are stretched. The right hand points to Cassiopeia. BOOTES is a naked figure with curly hair and a hunter's hat, walking westwards. He has a girdle on his waist. His right arm is raised and intersects at his elbow with a specific ever-visible circle. In his left (eastern) hand is a straight stick which ends on the left foot of Hercules. CORONA BOREALIS is a crown with six petals, three of which are drawn on the outside and the other three inside the ring. HERCULES is a naked figure with curly hair, a moustache, and a beard. His slightly bent head is west of that of Ophiuchus. He is kneeling on his left leg and his right leg is above the head of Draco. His right arm is stretched out in the direction of Lyra and his left arm is raised. He holds a lion's skin with a long tail in his right hand, and he carries a club in his left hand. LYRA is presented as a lyre. CYGNUS is a bird with outstretched wings, as if flying. The bird has a long beak at the end of an outstretched neck. CASSIOPEIA is drawn in profile as a naked figure, presumably female, sitting in a simple square chair. Her left arm is stretched out in the direction of Perseus and her bent right arm is raised. Her legs seem to be drawn between the legs of her chair but her feet are in front of it. PERSEUS is a naked figure with a warrior's helm on his head. His right arm is lowered and he carries a female head with long hair in his right hand. In his left hand raised above his head he holds a sickle with teeth. AURIGA is a naked figure with curly hair. His head is turned west and his knees are slightly bent but he is not kneeling. Both arms are lowered. On his right shoulder sits the head of a goat and on his right wrist is a smaller goat. His left foot touches the northern horn of Taurus. OPHIUCHUS is a naked figure with curly hair. His head is turned west to face the nearby head of Hercules. He holds Serpens in his hands. One of his legs is on the body of Scorpius. SERPENS is a snake with a two-forked tongue, passing in front of the thighs of Ophiuchus. SAGITTA is drawn as a simple arrow north of Aquila. AQUILA is drawn as a bird with outstretched wings, flying in a south-eastern direction. DELPHINUS is drawn as a dolphin with a beard and a fin, showing his teeth. EQUULEUS is drawn as the head of a horse. PEGASUS is drawn as half a horse with wings. ANDROMEDA is a female figure with long hair. She wears a long dress with a belt around her middle. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her right arm is raised above the northern one of the Pisces. The other left arm is stretched towards the north. TRIANGULUM is drawn as a triangle. ARIES is drawn as a ram with two horns and a curly fleece. He is standing on his hindlegs with forefeet as if jumping. He is looking backwards to Taurus. The ecliptic cuts through his right foreleg and passes under his tail. TAURUS is a half bull with a bent head, two front legs, and two horns. The ecliptic passes through his body and neck. The northern (p.422) horn extends to the left foot of Auriga. GEMINI consists of two nude figures with curly hair. Their heads are turned to each other. They are without attributes. The right arm of the western twin is stretched towards Auriga; the right arm of the eastern twin rests on the shoulder of the western twin. The left arms of both twins are bent. CANCER is a crab with two claws facing Leo and three legs on either side. The ecliptic intersects the body lengthways. LEO is a lion is standing on its hindlegs with his forefeet as if jumping. He has his mouth open and shows his tongue. The lion's tail makes a loop. The ecliptic passes through the chest and the hindlegs. VIRGO is a female figure with long hair and with wings, and wears a long dress with a girded top. Her head is turned in profile to the north. The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. The left hand is on her breast. Her lowered right hand with a bright star, presumably Spica, is close to the ecliptic. LIBRA is presented by the segmented claws of Scorpius. SCORPIUS is drawn as a scorpion with two claws, three legs, and a segmented tail of seven parts. SAGITTARIUS is a horse with a nude figure on top. The male figure has curly hair. In his right hand he carries a bow and in his left hand he holds the arrow. The ecliptic intersects him in the neck, just below his head. CAPRICORNUS has two horns and a fish tail. The ecliptic intersects him just below the neck and through the tail. AQUARIUS is a nude figure with curly hair. His slightly bent left arm is stretched westwards. The ecliptic intersects his body at the middle. His left arm holds an urn from which water streams. The stream runs down but does not connect to the flow of water that streams south from the ecliptic and below the feet of Aquarius to the mouth of Piscis Austrinus. PISCES consists of two fishes. The southern of the two fishes is located below the wing of Pegasus. The other, northern fish is located below the raised arm of Andromeda. There is a barely visible ‘cord’ which connects the tails of the fishes. CETUS is presented as a whale, the head of which is south of Aries. The mouth is wide open and the teeth are shown. ORION is a naked figure with curly hair. His head is turned towards Taurus. He holds a shield in his raised right arm. He carries a club in his raised left hand. He kneels on his left knee and his right leg is bent. He has a belt around his middle to which a sword in a scabbard is attached. ERIDANUS is a river presented by a band with wave-like borders. It starts at the western lower leg of Orion and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). LEPUS is a hare with long ears. CANIS Maior is a dog with a collar around his neck. CANIS MINOR is a walking dog. NAVIS is the rear part of a sailing ship with a mast and a triangular sail. There are two steering oars, the southern one of which emerges from behind the ship. HYDRA is a snake with a head that is drawn twice. The mouth is wide open and his teeth are shown. The head is below the southern claw of Cancer. The end of the tail is above the head of Centaurus. CRATER is a cup with handles standing on the body of Hydra. CORVUS is a bird standing on the body of Hydra. It is picking the snake. CENTAURUS is a horse with a nude figure with curly hair on top. His arms are stretched out in front of him. His left hand holds the right foreleg of Lupus, his right hand touches the belly of Lupus. LUPUS is an animal with its mouth is open, held by Centaurus. His teeth and tongue are shown. ARA is a square altar with flames on top. It is upside-down. CORONA AUSTRALIS is, like the northern crown, a crown with six petals, three of which are drawn on the outside and the other three on the inside the ring. It is located in front of the left leg of Sagittarius. PISCIS AUSTRINUS is a fish with an open mouth, with its head turned east.

COMMENTS: For illustrations, see Figs 5.25.12. This globe is unfortunately not in GOOD condition. Although I examined the globe personally in 1992, my description depends greatly on Hartmann's excellent study of it. Literature: Hartmann 1919 and my description in Bott 1992, pp. 508–9, no. 1.8.

(p.423) WG2. Cracow, Jagiellonian University Museum, Inv. no. 4039–37/V

Ø sphere 40 cm, height 132 cm; made in Hungary, Buda.

DATE: 1480.

MAKER: Attributed to Hans Dorn.

Made for Martin Bylica who donated the globe after his death in 1493 to the University of Cracow.

CONSTRUCTION: The brass sphere consists of two hemispheres fixed to each other at the Equator. There are holes at the north and south ecliptic poles. The sphere is mounted at the north and south equatorial pole in a graduated brass meridian ring (clockwise from N: 0°–90°; 90°–0°; S: 90°–0°; 0°–90°; numbered every 5°, division 1°). On top of the meridian ring is an hour circle (twice 0–12 hours; marked every hour, divided into ¼ hours) and a pointer, which is firmly attached to a handle that helps to rotate and tilt the sphere. All numbers are gothic except those on the hour circle. The meridian ring fits into a brass stand consisting of four quarter-circles, which rise to support a square horizon plate (51.5 × 51.5 cm). The quarter circles are joined around the support for the meridian ring. From the support curved legs divert downwards and end in feet made of claws around balls.

Around the circular cut in the horizon plate are a number of scales (from inside to outside):for the ecliptic (12 times 0°–30°; numbered every 5°, division 1°) with the Latin names of the zodiacal signs: ARIES, THAVRVS, GEMINI, CANCER, LEO, VIRGO, LIBRA, SCORPIO, SAGITARIVS (sic), CAPRICORNVS, AQVARIVS, PISCES; for the Julian calendar (numbered every five days from 5–25, and the last day of month (for July, August, September, and October this last day (30/31) is missing), division 1 day) with the Latin names of the months: IANVARIVS, FEBRVARIVS, MARCIVS, APRILIS, MAIVS, IVNIVS, IVLIVS, AVGVSTVS, SEPTEBER (sic), OCTOBER, NOVEMBER, DECEMBER. The zodiac is aligned with respect to the calendar such that the first point of Aries is at 11 March, that of Cancer at 13 June, that of Libra at 14 September, and that of Capricorn at 12 December. In the outermost ring is a wind rose, starting from north anti-clockwise: (no name for north), CHORVS, CIRCIVS, ƷEPHIRVS, FAVONVIS, AFRISVS, (no name for south), NOTHVS, EVRVS, SVBSOLĀN(VS), VVLT(VR)NVS, BOREAS. The name at the south is possibly hidden under the accessory to fix the meridian ring. On the horizon plate the last capital letter S is often, but not always, elongated. In the south corner of the horizon plate is a sundial with string-gnomon and a compass having a magnetic variation of around 10°. In the northern corner is the coat of arms of Martin Bylica, showing Sagittarius with sunrays in the top behind him around a starry symbol and a rose with five petals below the centaur. On top of the field is a hat with double tasselled ropes characterizing the title of Protonotary Apostolic held by Martin Bylica.

ASTROLABE DISC: On top of the meridian ring is a vertical rod attached to a mobile support for a disc with a diameter of 28 cm. From this support two quadrants extend to the horizon plate which can rotate with the support in azimuthal direction. The limb of the mater of the astrolabe disc is graduated for degrees (0°–360°; numbered every 5°, division 1°). The inside of the mater is engraved just below the rim with a scale for equal hours (numbered every hour: 1–24) and two sets of curves in stereographic projection: the twelve unequal hour lines (numbered every hour: 1–12) and a grid of lines marking the boundaries of mundane houses and their divisions for latitude 47.5º. The twelve houses are labelled in Latin: PRIMA, SECVNDA, TERTIA, QVARTA, QVINTA, SEXTA, SEPTIMA, OCTAVA, NONA, DECIMA, VNDECIMA, DVODECIMA. The main boundaries are marked by dots. Each house is subdivided by curves into 10 subsections. A series of dots on a straight line marks the centres of the circles of the mundane houses. On top of this is a zodiacal ring sustained by (p.424) bars in the north–south and east–west directions with a ruler on top, attached by way of a 6-petal rose such that both ring and ruler can rotate independently around the north pole. The ecliptic is graduated (12 times 0°–30°; numbered every 5°, division 5°) with the Latin names of the zodiacal signs: ARIFS [sic], THAVRVS, GEMINI, CANCER, LEO, VIRGO, LIBRA, SCORPIO, SAGITARIVS [sic], CAPRICORNVS, AQVARIVS, PISCES. On the back of the astrolabe disc the limb is graduated for degrees (clockwise from the zenith: 90°–0°; 0°–90°; 90°–0°; 0°–90°; numbered every 5°, division 1°). In the lower half are two quadrants each with scales for the VMBRA VERSA (0–12; numbered every unit, divided into 24 units) and the VMBRA RECTA (12–0; numbered every unit, divided into 24 units). Inside these graduated scales is a grid (sometimes labelled organum ptolemei) consisting of two sets of lines in the orthographic projection: the parallels between the tropics corresponding to specific positions of the Sun in the ecliptic and 12 equal hour lines (numbered 1–11 along the tropics). North and south of the Equator, along the hour lines 1 and 11, is a scale (numbered 10, 20, 30) expressing which parallels correspond to locations 10, 20, 30 degrees in the zodiacal signs indicated at the sides. The signs are labelled: from the Tropic of Cancer to that of Capricorn around the autumnal equinox: CA, LEO, VIRGO, LIBRA, SCORP, SA; from the Tropic of Capricorn to that of Cancer around the vernal equinox: CA, AQVA, PISCES, ARIES, TAVRVS, GE. Along a semicircle north of the Equator is a graduated scale for declination (clockwise and anti-clockwise from the Equator: 0°–90°; numbered every 5°, division 1°). An alidade with sights is attached to the centre of the astrolabe disc such that the alhidade can rotate around the north pole. The empty area north of the Tropic of Cancer is filled with a band with the following text: ‘HORA(M)·SOLE·LVCENTE·VIDEBIS·SI·AB·ELEVACIONE·SOLIS·REGVLA·

CVM·FILO·SECVNDVM·NVMERVM·RESIDVI·LATITV-DINIS·REGIONIS·DEMISSA·FILVM·SVPER·COLLECTVM.

The empty area south of the Tropic of Capricorn is filled with a band with the following text: ‘EX·ELEVATIONE·SOLIS·ET·IPSO·RESIDVO·IN·INTERIORI·CIRCVLO*

PROTRAXERIS·QVOD·PARALELVM·SOLIS·INTER· SECANDO·HORAM·OSTENDET 1480.

CARTOGRAPHY: Language Latin. There are great circles through the ecliptic pole and the boundaries of the zodiacal signs. The Equator is graduated (0º–360º; numbered every 5º, division 1º). The ecliptic is graduated (12 times 0º–30º; numbered every 5º from 5º–25º, division 1º). The numbers of the zodiacal signs (1,…, 12) are added in the last section of 5º. The polar circles, the tropics, and the colures are drawn but not labelled.

ASTRONOMICAL NOTES: (α Leo is in Leo 22.5°). The longitudes of the stars plotted on the globe exceed on the average the Ptolemaic longitudes by 19° 56´±12´. The brightness is indicated by four different symbols (starry symbols with respectively 8, 7, 6, 5, and 4 rays). For some but not all stars, the planetary symbols are engraved. The Milky Way is drawn but not labelled. The star names are listed in Table 5A.1 in Appendix 5.1 above.

CONSTELLATIONS: All 48 Ptolemaic constellations are engraved and most are labelled.

DESCRIPTIONS: URSA MINOR, labelled VRSA MINOR, is a small bear with a long tail. His back is turned to Ursa Maior. URSA MAIOR, labelled VRSA MAIOR, is a great bear with a long tail. DRACO, labelled DRACO, is a snake with four curls; his tongue sticks out his mouth. CEPHEUS, labelled CEPHEVS, is seen from the rear, dressed in a tunic, with hair emerging from a Phrygian hat. He is kneeling on his right leg and his arms are stretched out. BOOTES, labelled BOETES, is a naked figure with curly hair, seen from the rear. His left arm is raised and in his right hand is a straight stick which ends on the right foot of Hercules. CORONA BOREALIS, labelled CORANA (sic), is an open crown with petals. HERCULES, labelled HERCVLES, is seen from the rear; he is dressed in a suit of armour and has mid-length curly hair. His head is west of that of Ophiuchus. He is kneeling on his right knee and his left foot is above the head of Draco. His left (p.425) arm is stretched out in the direction of Lyra. He holds a lion's skin by his left hand and a curved sword in his raised right hand. LYRA, labelled VVLTVR CADENS, is presented as a bird with a short crooked beak. CYGNUS, labelled GALINA, is a bird with outstretched wings, as if flying. The bird has a short beak. CASSIOPEIA, labelled CASSFPIA (sic), is turned in a simple square chair and thus seen from the rear. She wears a long dress and a long kerchief over her head which covers her face and extends to her shoulders. Her right arm is stretched out. She has no attributes. PERSEUS, labelled PERSEVS, is a naked figure with mid-length curly hair, seen from the rear. He holds a curved sword in his right hand above his head and he carries a head with devil's ears in his lowered left hand. AURIGA, labelled AVRIGA, is a nude figure seen from the rear, with a long pointed cap extending in a kind of short cape over his shoulders. His left knee is bent. Both arms are lowered. On his left shoulder stands a goat and in his right hand is a harness. His right foot touches the northern horn of Taurus. OPHIUCHUS, labelled SERPNTARIVS (sic), is a naked figure with curly hair seen from the rear. His head is turned west towards the nearby head of Hercules. He holds Serpens in his hands. One of his feet rests on the body of Scorpius. SERPENS is a snake with an open mouth. Its body, which encircles the lower arms and middle of Ophiuchus, has four coils. SAGITTA, labelled SAGITTA, is drawn as a simple arrow. AQUILA, labelled AQVILA, is drawn as a bird with outstretched wings, flying in a southeastern direction. DELPHINUS, labelled DELPHINVS, is drawn as a dolphin with sharp teeth. EQUULEUS, labelled EQVVS PRIOR, is drawn as the head of a horse. PEGASUS, labelled EQVVS PEGASVS, is drawn as half a horse with wings. ANDROMEDA, labelled ANDROMADA (sic), is a nude female figure with her hair in tresses around her head, seen from the rear. She holds a chain in her hands which encircles her middle. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her left arm is raised above the northern one of the Pisces. The other right arm is stretched towards the north. TRIANGULUM, labelled TRIANGVLVS, is drawn as a triangle. ARIES, labelled ARIES, is drawn as a ram with two horns and a curly fleece. He lies with his forefeet bent. He is looking backwards to Taurus. The ecliptic cuts through his body and passes above his tail. TAURUS, labelled TAVRVS, is a half bull with a bent head, two front legs, and two horns. The ecliptic passes through his body and his head. The northern horn extends to the left foot of Auriga. GEMINI, labelled GEMINI, consist of two nude figures with curly hair, both seen from the rear. Their heads are turned to each other and their legs stretch westwards. They are without attributes. The right arm of the western twin rests on the shoulder of the eastern twin. CANCER, labelled CANCER, is a crawfish with two claws facing Leo and three legs on either side. The ecliptic passes through the main body. LEO, labelled LEO, is a lion standing on its hindlegs with his forefeet as if jumping. He has his mouth open. The lion's tail makes a loop. The ecliptic passes through the chest and the hindlegs. VIRGO, labelled VIRGO, is a female figure with her hair in tresses around her head and with wings, seen from the rear. She wears a long dress with a belt. Her head is turned in profile to the north. The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. She points with her right hand to her head. In her lowered left hand she holds an ear of wheat with the bright star Spica. LIBRA, labelled LIBRA, is presented by a pair of scales. SCORPIUS, labelled SCORPIVS, is drawn as a scorpion with short claws, five northern and four southern legs, and a segmented tail. SAGITTARIUS, labelled SAGITARIVS (sic), is a horse with a nude figure on top, seen from the rear. The male figure has a cloak attachments and an ornamental belt. In his left hand he carries a bow and in his (invisible) right hand he holds the arrow. The ecliptic intersects his head. CAPRICORNUS, labelled CAPRICOR(NVS), has two long horns and a fish tail. The ecliptic intersects him through the mouth, just below the neck and through the tail. AQUARIUS, labelled AQVARIVS, is a nude figure with curly hair, seen from the rear. His slightly bent left arm is stretched westwards and holds a folded piece of cloth. The ecliptic intersects his body at the hips. His (p.426) right arm passes through the handle of an urn from which water runs, which streams to the mouth of Piscis Austrinus. PISCES, labelled PISCES, consists of two fishes. The southern of the two is located below the wing of Pegasus. The other northern fish is located below the raised arm of Andromeda. There is band with a knot which connects the tails of the fishes. CETUS, labelled CETVS, is presented as a whale. ORION, labelled ORION, is dressed in a suit of armour, with hair emerging from a Phrygian hat. He has curly hair and is seen from the rear. He holds a cloth in his raised left hand and carries a club in his raised right hand. He kneels on his left knee and his right leg is slightly bent. He carries a sword in a scabbard. ERIDANUS, labelled ERIDANVS, is a river presented by a band which starts at the left foot of Orion, and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). LEPUS, labelled LEPVS, is a hare with long ears. CANIS MAIOR, labelled CANIS MAIOR, is a wolf-like animal with wide open mouth, erect ears, and hair in its neck. CANIS MINOR, labelled PROCHION, is a running dog with a collar. NAVIS, labelled NAVIS, is a galleon with a mast, a crow's nest, and a sail. There are two steering oars which emerge from both sides of the ship. At the western end of the ship is a chair with a shield attached to it. HYDRA, labelled IDRA, is a snake with long ears. Its open mouth shows his teeth and tongue. The end of the tail is above the head of Centaurus. CRATER, labelled CRATER, is a kettle with one handle standing on the body of Hydra. CORVUS, labelled CORVVS, is a bird standing on the body of Hydra. It is picking the snake. CENTAURUS, labelled CENTAVRVS, is a horse with a nude figure on top, seen from the rear. He has long curly hair held together by a band. On his middle is an ornamental belt. On his right arm rests a shield which is attached to a strap around his neck. With his right hand he holds the left legs of Lupus. In his (invisible) left hand he holds a stick which ends at the head of Lupus. LUPUS, labelled LVPVS, is an animal with its mouth is open, held by Centaurus. ARA, labelled ARA, is a square pedestal with flames on top. It is upside-down. CORONA AUSTRALIS, labelled CORONA AVSTIALIS (sic), is a domed crown with petals on the border and one on top. PISCIS AUSTRINUS, labelled PISCIS MERIDIANVS, is a fish with mouth open, showing its teeth.

COMMENTS: I acknowledge with pleasure the assistance of Marcin Banas of the Jagiellonian University Museum in making the description of this globe.

The precessions correction of 19° 56´ ± 12´ was determined by measuring the ecliptic longitudes of 24 stars. The data on sizes are from Ameisenowa 1959, p. 12 who also mentions the circumference of the sphere as 125.4 cm. Zinner 1967, reprint 1979, mentions a circumference of 124 cm, that is a diameter of 39.5 cm. Pilz 1977, p. 63 quotes a height of 1.32 m and a diameter of 1.24 m, confusing the diameter with the circumference of the globe. Chlench 2007, p. 76, mentions a diameter of 1.32 m, confusing the diameter with the height of the globe. Zinner 1967, reprint 1979, p. 295 mentions the diameter of the astrolabe disc of 28 cm and the size of the horizon plate. Ameisenowa 1959, p. 12 says that the sphere is made out of one piece of brass. Excess material was removed from a hole in the south polar area by a tightly fitting plate. Her source is Birkenmajer whose text I have not been able to consult. King and Turner 1994, p. 194, say that the elongated last capital letter S in some names of the months on the horizon plate is typical for Dorn. Bartha 1990/1991 p. 39, and Bartha 2000, p. 49, mentions a scale for azimuth on the horizon plate from 0°–360° with a division into 1° which is not there. Literature: Ameisenowa 1959; Zinner 1967/1979, pp. 292–7.

WG3. STUTTGART, WURTTEMBERGISCHES LANDESMUSEUM, Inv. no. WLM 2000–120

Ø sphere 49 cm, height 107 cm; made in Justingen.

DATE: 1493.

AUTHOR: Johannes Stöffler; an artist's monogram consisting of a sword with the letter N is marked on the hindquarters of the constellation Centaurus.

(p.427) In the seventeenth century the globe was the property of the Dom School in Konstanz; in 1825 it is mentioned in a description of the Dom; thereafter the globe was placed in the library of the Gymnasium in Konstanz. In 1895 it was given on loan to the Germanisches Nationalmuseum, GNM Inv. Nr. WI 1261 and it is now in the Wurttembergisches Landesmuseum.

There are two inscriptions on the stand (Figs 5.45a–b). On the left side is the image of a man pointing to the sphere. Below him is the inscription from Ovid, Metamorphoses, I. lines 78–79, 84–86: ‘NAT(VS) HOMO EST QVEM DIVINO SEMINE FECIT/ILLE OPIFEX RERVM MVNDI MELIORIS ORIGO/PRONAQ(VE) QVOM SPECTENT ANIMALIA CETERA/TERRAM OS HOMINI SVBLINE DEDIT CAELVMQ(VE) VI-/DERE IVSSIT ET ERECTOS AD SYDERA TOLLERE VVLT(VS)’.

On the right side is a coat of arms with a lion on a white field. Left of it is the other inscription: ‘SPHAERAM HANC SOLIDAM/IOANNES STÖFFLER IVSTING-/ENSIS ANNO CHRISTI MAXIMI/1493 FOELICISSIMO SYDERE FA-/BREFECIT’.

CONSTRUCTION: The sphere is made of wood and around 5 cm thick. It is mounted on an axis through

The Mathematical Tradition in Medieval EuropeThe Mathematical Tradition in Medieval Europe

Figs 5.45 a–b Inscriptions on the stand of the celestial globe of Johannes Stöffler. (Photo: Elly Dekker.)

(p.428) the north and south equatorial poles in a metal meridian ring, 10 mm thick and 39 mm wide. The meridian ring is graduated for declination (clockwise and anti-clockwise from N: 90°–0; 0°–90°; numbered every 5°, division 1°) and its complement (clockwise and anti-clockwise from N: 0°–90°; 90°–0°; numbered every 5°, division 1°) and fits into a wooden stand on four legs, which are connected to each other by wooden strengthening. On top of the meridian ring is a brass hour circle with pointer by which the sphere can be set to equal or unequal time with the help of a handle connected to the polar axis. The stand supports a wooden horizon ring. On its outer boundary is a series of nails and the four main compass directions: ‘ORIENS, MERIDIES, OCCIDENS, SEPTENTRIO’.
The Mathematical Tradition in Medieval Europe

Fig. 5.46 Coat of arms on the horizon ring of the celestial globe of Johannes Stöffler. (Photo: Elly Dekker.)

On top of the horizon ring are a number of scales (from inside to outside): for azimuth (clockwise and anti-clockwise from N: 90°–0°; 0°–90°; numbered every 5°, division 1°); for the ecliptic (12 times 0°–30°; numbered every 5°, division 1°) with the Latin names of the zodiacal signs; for a calendar with the names of the saints, dominical letters and the Latin names of the months. The zodiac is aligned with respect to the calendar such that the first point of Aries is between 10 and 11 March. In the outermost ring are compass directions marked by 12 wind heads (Fig. 5.47). At the month October is the coat of arms of Daniel of Konstanz, his mitre and crosier (Fig. 5.46). Above the coat of arms is the inscription: ‘Danielis Dei gratia Pontificis Bellinensis foelicia hec sunt Arma’.
The Mathematical Tradition in Medieval Europe

Fig. 5.47 Wind head on the horizon ring of the celestial globe of Johannes Stöffler. (Photo: Elly Dekker.)

Around (p.429) the sphere, close to its surface, are two sets of four brass semicircles passing through the north and south points of the horizon. These semicircles are connected in the middle by a brass arc. The points of intersection of these semicircles with the ecliptic on the sphere determine the boundaries of the mundane houses.

CARTOGRAPHY: Language Latin. There are great circles through the ecliptic poles and the boundaries of the zodiacal signs. The ecliptic is labelled ZODIAC(VS); it is graduated (12 times 0º–30º; numbered every 5º, division 1º). The zodiacal band is defined by two parallels 12º north and south of the ecliptic. The ecliptic poles are labelled ‘P:Z:S:’ and ‘POL(VS) ZODIACI MERI:’. The Equator is labelled EQVINOCCIALIS; it is graduated (0º–360º; numbered every 5º, division 1º). The equatorial poles are labelled: ‘POLVS SEPTENTRIO/NALIS ARCTICVS VEL/BOREALIS and [POLVS] ANTARCTICVS’. The polar circles are labelled ‘CIRCVL(VS) ARCTICVS’ and ‘CIRCVLVS ANTARCTICVS’. The tropics are labelled ‘TROPIC(VS) CANCRI VEL ESTIVALIS’ and ‘TROPICVSHVEMALIS/CAPRICORNI’. The colures are drawn and labelled: ‘COLVRVS EQVINOCIALIS and COLVR(VS) SOLSTI[. . .]’. The solstitial colures are graduated (N and S from the Equator 0°–90°; numbered every 5°, division 5°).

ASTRONOMICAL NOTES: (α Leo is in Leo 22°). The longitudes of the stars plotted on the globe exceed on the average the Ptolemaic longitudes by 19° 38’ ± 11’. The stars are marked by brass nails with a starry head consisting of six rays. Different brightnesses are indicated by different sizes. The Milky Way is drawn and labelled: GALAXIA. The star names are listed in Table 5A.1 in Appendix 5.1 above.

CONSTELLATIONS: All 48 Ptolemaic constellations are drawn and most are labelled.

DESCRIPTIONS: URSA MINOR, labelled VRSA MINOR AVT CINOSVRA, is a small bear with a long tail. Ursa MAIOR, labelled ARCTOS M[. . .] VRSA MAIOR [VE]L ARCTVR, is a great bear with a long tail. DRACO, labelled DRACO, is a snake with his tongue sticking out his mouth. CEPHEUS, labelled CEPHEVS, is seen from the rear. He is dressed in a tunic, wears a crown, holds a sceptre in his right hand and has a sword attached to a belt around his middle. BOOTES, labelled ARCTOPHILAX [VE]L BOETES, is seen from the rear. He wears a hat, a tunic and boots, and holds in his right hand a lance which ends on the right foot of Hercules. In his raised left hand he has a sickle. On his left side is a sheaf of corn. In his right side are two dogs connected by leads to the wrist of the same hand that holds the lance. CORONA BOREALIS, labelled CORONA BOREALIS, is an open crown with petals. HERCULES, labelled HERCVLES AVT GENVFLEXVS, is seen from the rear; he is dressed in a colourful garment. He is kneeling on his right knee and his left foot is above the head of Draco. His left arm is stretched out in the direction of Lyra. He holds a lion's skin in his left hand and a stick or club in his raised right hand. In front of his right lower leg is a bunch of branches, possibly the golden apples of the Hesperides. LYRA, labelled VVLTVR CADENS, is presented as a bird with a short crooked beak. CYGNUS, labelled OLOR AVT GALLINA, is a bird with outstretched wings. The bird has a winding neck. CASSIOPEIA, labelled CASSIOPEIA, is turned in a throne with a high square back and an ornament on top and thus seen from the rear. She is nude and looks in a mirror held in her left hand. Her raised right hand is tied to the ornament at the back of the throne. PERSEUS, labelled PERSEVS, is seen from the rear. He has long curly hair, wears a loincloth and has wings at his feet. He holds a slightly curved sword in his right hand above his head. In his lowered left hand he carries a cut-off head from which blood spatters. AURIGA, labelled AVRIGA AVT AGITATOR, is seen from the rear. He wears a hat, a tunic, and boots. On his left shoulder stands a goat. His head is turned west and he is on his knees. Both arms are lowered. In his right hand is a harness and his left hand seems to rest on a carriage wheel. His right foot touches the northern horn of Taurus. OPHIUCHUS, labelled SERPENTARIVS [VE]L (p.430) ANGVITENENS, is seen from the rear; he is dressed in a colourful garment. His head is turned west towards the nearby head of Hercules. He holds the body of Serpens in his hands. One of his feet rests on the body of Scorpius. SERPENS, labelled SERPENS is a snake with an open mouth. Its body, which encircles the lower arms and middle of Ophiuchus, has four coils. SAGITTA, labelled SAGICTA (sic), is drawn as a simple arrow. AQUILA, labelled AQVILA, is a bird but it is hardly visible. DELPHINUS, labelled DELPHIN, is drawn as a dolphin with sharp teeth. EQUULEUS, labelled EQVVS PRIOR, is drawn as the head of a horse. PEGASUS, labelled EQV(VS) Z[. . .] ALAT(VS), is drawn as half a horse with wings. ANDROMEDA, labelled ANDROMADA (sic), is a nude female figure with her hair held together by a tress around her head, and seen from the rear. She is chained at her wrists to the branches of two trees at her sides. The chain passes behind her back. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her left arm is raised above the northern one of the Pisces. The other right arm is stretched towards the north. TRIANGULUM, labelled TRIANGVLVS, is drawn as a triangle. ARIES, labelled ARIES, is drawn as a ram with two horns and a curly fleece. He lies with his forefeet bent. He is looking backwards to Taurus. The ecliptic cuts through his body and passes above his tail. TAURUS, labelled THAVRVS, is half a bull with a bent head, two front legs, and two horns. The ecliptic passes through his body and his head. The northern horn extends to the right foot of Auriga. The Pleiades are marked by seven stars which are labelled: Plijades. GEMINI, labelled GEMINI, consist of two nude figures, both seen from the rear. Their heads are turned to each other and their legs stretch westwards. They are without attributes. The right arm of the western twin rests on the shoulder of the eastern twin and the left arm of the eastern twin is around the middle of the western twin. CANCER, labelled CANCER, is a crawfish with two claws facing Leo and three legs on either side. The ecliptic passes through the main body. The two Asses are labelled: Due asini. LEO, labelled LEO, is a lion standing on its hindlegs with his forefeet as if jumping. His mouth is slightly open. The lion's tail makes a loop. The ecliptic passes through his forefeet. VIRGO, labelled VIRGO, is a female figure seen from the rear with her hair held together by a tress around her head and with wings. She wears a long dress with a belt loosely around her middle. Her head is turned in profile to the north. The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. She points with her right hand to her head. In her lowered left hand she holds an ear of wheat with the bright star Spica. In her other right hand she holds a sceptre. A banner with the text ‘Justitia terras reliquit, quia victa jacet pietas’, is connected to the hand holding the sceptre. LIBRA, labelled LIBRA, is presented by a pair of scales. SCORPIUS, labelled SCORPIO, is drawn as a scorpion with short claws and a segmented tail. SAGITTARIUS, labelled SAGICTARI(VS) (sic), is a horse with a nude figure on top, seen from the rear. The male figure wears a hat and from it emerges very long hair that flies behind him. In his left hand he carries a bow and in his (invisible) right hand he holds the arrow. The ecliptic intersects his head. CAPRICORNUS, labelled CAP[RI]CORN(VS), has two long horns and a fish tail. The ecliptic intersects him through the mouth, below the neck and through the tail. AQUARIUS, labelled AQRI(VS), is seen from the rear. All he wears is a loincloth. His slightly bent left arm is stretched westwards and holds a folded piece of cloth. The ecliptic intersects his body at the hips. His right lower arm is on top of an urn from which water runs, which streams to the mouth of Piscis Austrinus. PISCES, labelled PISCES, consists of two fishes. The southern of the two is located below the wing of Pegasus. The other, northern fish is located below the raised arm of Andromeda. There is band with a knot which connects the tails of the fishes. CETUS, labelled CETVS MAGNVS AVT PISTRIX, is presented as a whale. ORION, labelled ORION, is dressed as a knight, seen from the rear. His head is backwards to show his face. He holds an ox hide by its head in his raised left hand and carries a club in his raised right hand. He kneels on his left knee and his right leg is slightly bent. (p.431) He carries a sword in a scabbard. ERIDANUS, labelled FLVVIVS GYON SIVE NILVS, is a river presented by a band with a wavy pattern which starts at the left foot of Orion, and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). LEPUS, labelled LEPVS, is a hare with erect ears. CANIS MAIOR, labelled CANIS MAIOR, is a dog with a collar, as if jumping. CANIS MINOR, labelled CANIS MINOR PROCION, is a walking dog with a collar. NAVIS, labelled NAVIS [VE]L ARGVS, is half a ship with a mast, a crow's nest, and a lowered sail. There are two steering oars which emerge from both sides of the ship. At the western end of the ship is a small building and at the cut-off side there is a cloud. HYDRA, labelled HYDRA, is a snake with its mouth open, showing its teeth. The end of the tail is above the head of Centaurus. CRATER, labelled VAS [VE]L CRATER, is a tub with two handles standing on the body of Hydra. CORVUS, labelled CORV(VS) APPOLLINE(VS), is a bird standing on the body of Hydra. It is picking the snake.CENTAURUS, labelled CENTAVRVS AVT CHYRON, is a horse with a figure on top, seen from the rear. He has long curly hair and his middle is marked by a hairy belt. Above his right arm is a hard to identify object which is attached to a belt around his shoulder. He holds with both hands a lance which pierces the head of Lupus. LUPUS, labelled LVPVS, is an animal with its mouth is open, held by Centaurus. ARA, labelled ARA, is a square pedestal with flames on top. It is upside-down. CORONA AUSTRALIS, labelled CORONA MERIDIONALIS [VE]L AVSTRALE SERVM, is an open crown with petals. PISCIS AUSTRINUS, labelled PISCIS MERIDIONALIS, is a fish with its head turned towards its tail, mouth open showing its teeth.

COMMENTS: The precessions correction of 19° 38’ ± 11’ was determined by measuring the ecliptic longitude of 16 stars located close to the ecliptic. Literature: Moll 1877; Zinner 1967/1979, pp. 543–5; my description in Bott 1992, Kat. 1.16, pp. 516–18; Oestmann 1993; Oestmann 1995/6.

Notes:

(1) Bubnov 1899; Millás Vallicrosa 1931; Bergmann 1985; Kunitzsch 1997; Borrelli 2008.

(2) Kunitzsch 1987a.

(3) Stevens et al. 1995.

(4) Dekker 2000.

(5) Gunther 1931/1976, pp. 252–6.

(6) For the Arabic-Latin tradition of the Ptolemaic star catalogue, see Kunitzsch 1974. A modern scholarly edition has been published in Kunitzsch II 1990.

(7) Samsó 1987; Chabás and Goldstein 2003, pp. 1–8.

(8) Chabás and Goldstein 2003, pp. 19–94.

(9) Rico y Sinobas 1863; Samsó 2007.

(10) Kunitzsch 1986a, pp. 65–6; Samsó and Comes 1988; Chabás and Goldstein 2003, pp. 234–6.

(11) Chabás and Goldstein 2003, p. 235.

(12) Kunitzsch 1965; Kunitzsch 1986a, pp. 66–77.

(13) See for example Strohmaier 1984.

(14) Kunitzsch 1986b. On the Alfonsine Tables see Poulle 1988 and Chabás and Goldstein 2003, pp. 243–90.

(15) Chabás and Goldstein 2003.

(16) Chabás and Goldstein 2003, pp. 89–90 and 217–21.

(17) Mercier 1976; Mercier 1977; Chabás and Goldstein 2003, pp. 89–90 and 256–66.

(18) Samsó and Castelló 1988, p. 116.

(19) Poulle 1988; Samsó and Castelló 1988.

(20) Chabás and Goldstein 2003, pp. 234–5.

(21) Chabás and Goldstein 2003, pp. 260–2.

(22) Lippincott 1985, pp. 67–70.

(23) Saxl 1927, p. 151.

(24) Kremer 1980, p. 189, note 28, suggests that the value 19° 40´ used by Regiomontanus in his star catalogue for 1500 is not based on the Alfonsine trepidation theory, but this is not necessarily so. Regiomontanus's value could have been obtained by counting from 1252 and adding to the Alfonsine value 17° 8´.

(25) Millás Vallicrosa 1931, pp. 288–90; Lorch 1980b, p. 161, note added in proof; Samsó 2005, p. 64.

(26) Samsó 2005, pp. 66–79.

(27) Savage-Smith 1985, pp. 80–1.

(28) Samsó 2005, p. 74.

(29) North 1986, pp. 4 and 9.

(30) The text is edited in Lorch and Martínez Gázquez 2005.

(31) Lorch and Martínez Gázquez 2005, pp. 14–15.

(32) Lorch 1980b; Chlench 2007.

(33) Chlench 2007, p. 60.

(34) Chlench 2007, pp. 59–60.

(35)   Varenbergh 1888/1889.

(36) Lorch 1980b, p. 155.

(37) Chlench 2007, pp. 53–7, lists 28 manuscripts.

(38)  Two editions were published in 1518 and a third in 1531, see Chlench 2007, p. 51.

(39) Chlench 2007, pp. 51–180.

(40) Lorch 1980b, pp. 155–6.

(41) Savage-Smith 1985, pp. 19–21.

(42) See for example Samhaber 2000, p. 28 who reproduced the illustration in Linz, Oberöstereichisches Landesmuseum, MS 3.

(43) Chlench 2007, p. 112 and pp. 151–2.

(44) Stahl 1952, pp. 208–12; Obrist 2004, pp. 183–4.

(45) Chlench 2007, p. 98.

(46) King 1995a, p. 376.

(47) Bernkastel-Kues, Cusanus-Stift MS 211, f. 1r. The citation is taken from Krchňák 1964, p. 109. See also Hartmann 1919, p. 8.

(48) Hartmann 1919, pp. 42–50.

(49) Toomer 1984, p. 404.

(50) Ptolemy's precession globe is discussed in detail by Neugebauer 1975, pp. 890–2 and Savage-Smith 1985, pp. 8–10.

(51) Toomer 1984, p. 404.

(52) Toomer 1984, p. 405.

(53) Neugebauer 1975, p. 890.

(54) Toomer 1984, p. 405, and his note 181.

(55) Toomer 1984, pp. 405–6.

(56) Toomer 1984, p. 406.

(57) This is the case when the required time is the Ptolemaic epoch.

(58) Toomer 1984, p. 406.

(59) Hartmann 1919, p. 30.

(60) Hartmann 1919, p. 11.

(61) Private communication Thom Richardson, Keeper of Armour and Oriental Collections. For the current thinking on this, with lots of illustrations of objects and art, see Southwick 2006.

(62) Hartmann 1919, p. 33 gives a date of 1293. I calculated the date with the formula in Mercier 1977, pp. 58–9.

(63) Hartmann 1919, p. 33.

(64) Hartmann 1919, p. 34. Zinner 1967/1979, p. 383 concludes that the globe is based on the Alfonsine star catalogue and dates the globe for different reasons to ca. 1400.

(65) Hartmann 1919, pp. 32–3.

(66) In the translation of Toomer 1984, p. 406, the word ‘connecting’ is used instead of ‘surrounding’. This latter word is used by Manitius 1963, Band II, p. 74 and in my opinion is preferable in order to avoid confusion with modern usage to connect the stars inside a constellation by lines.

(67) Toomer 1984, p. 406.

(68) The hunting hat occurs in the Liederbuch Heidelberg (1300–44), f. 228, and in Bernkastel-Kues MS 207, f. 115v, see Krchňák 1964, p. 121, Fig. 1.

(69) Krchňák 1964, p. 179.

(70) Blume et al. in preparation, suggest alternatively ‘Mittelrhein (böhmisch?)’.

(71) Kunitzsch 1986a, pp. 70–1.

(72) Krchňák 1964, p. 121, Fig. 1.

(73) On these tables see Goldstein and Chabás 2008.

(74) Hartmann 1919, pp. 11–14.

(75) Zinner 1967/1979, p. 383 has taken over this attribution to Nicolaus of Heybreck.

(76) Krchňák 1964, pp. 165–6.

(77) Krchňák 1964, p. 135. He believes that the artistic style of the constellations cycle in this codex compares well with the Welislaw bible (Prague, Nationalbibliothek, MS XXIIIc 24).

(78) Krchňák 1964, pp. 136–44. For the rejection of Alvaro de Oviedo, see Yamamoto and Burnett 2000, p. xxvi.

(79) Hartmann 1919, p. 36. For an example of a Spanish map,  see Addendum.

(80) Durand 1952, p. 107.

(81) Saxl 1915, pp. 10–15, esp. p. 15.

(82) Uhden 1937; Durand 1952, pp. 114–17.

(83) Saxl 1915, p. 10.

(84) Saxl 1915, pp. 14–15.

(85) Kennedy et al. 1999.

(86) Berggren 1982, p. 52.

(87) Uhden 1937, p. 8.

(88) Durand 1952, p. 116.

(89) Durand 1952, p. 151, incorrectly claims that the author of the Dyffenbach maps used the trapezoidal projection for which Nicolaus Germanus is credited.

(90) Kunitzsch III 1991, p. 163.

(91) Kunitzsch II 1990. Kunitzsch assures me that these erroneous latitudes occur exclusively in Gerard's translation (Letter 3 July 2010). In the printed edition of the Almagest of 1515 and the Alfonsine catalogue of 1524 the latitudes of nos 44 and 45 are corrected to respectively -69° and -61° 50´.

(92) Durand 1952, p. 115.

(93) See the Warburg Institute Iconographic Database http://warburg.sas.ac.uk/photographic-collection/iconographic-database/.

(94) Durand 1952, pp. 44–8.

(95) Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland).

(96) Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland).

(97) Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland).

(98) Durand 1952, pp. 45 and 116.

(99) Durand 1952, p. 45, note 1.

(100) I acknowledge with pleasure the information given by Martin Roland and Dieter Blume.

(101) Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland).

(102) Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland) proposes Vienna and Blume et al. in preparation, Klosterneuburg.

(103) Uiblein 1988; Simek and Chlench 2006.

(104) Uiblein 1988, p. 61.

(105) Durand 1952, p. 232; Wawrik 2006, pp. 58 and 60–2.

(106) These features were found already by Rosenfeld 1980, pp. 151–72 in her study of Dürer's maps of 1515. See also Warner 1979, pp. 74–5.

(107) Kunitzsch 1986b.

(108) Dekker 1992.

(109) Saxl 1927, pp. 25 and 38: ‘ein genaues Abbild einer orientalischer Vorlage’.

(110) Kunitzsch 1961, p. 87, no. 195a; Kunitzsch 1974, p. 177; Kunitzsch 1986c, pp. 45–50.

(111) On vultur cadens in star tables, see Kunitzsch 1966, the Types mentioned in the index on p. 127 and the additional types VIII.35, XI.22, and XIII.10.

(112) Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland).

(113) Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland). Saxl 1927, p. 30, believed that the drawings on the maps and in the catalogue were by the same hand.

(114) Klosterneuburg, Augustiner Chorherrenstiftes MS 125, ff. 6r–16r, see Haidinger 1991, pp. 33–34. I thank Martin Roland for bringing this codex to my attention.

(115) Bauer 1983; Burnett 1994; Ackermann 2009.

(116) Ackermann 2009, pp. 146–251.

(117) Bauer 1983, pp. 44–46, Hercules; pp. 49–50, Auriga; pp. 53–55, Andromeda; pp. 61–63, Eridanus; pp. 72–74, Ara; pp. 74–76, Centaurus.

(118) Haidinger 1980, pp. 101–9.

(119) Zinner 1990, p. 250, no. 257.

(120) Zinner 1990, p. 202, lists two copies of the 1424 catalogue in Nuremberg MS Cent. V 53 und V 61.

(121) Zinner 1990, p. 252, no. 291a.

(122) Voss 1943, pp. 90–1.

(123) Grössing 1983, p. 150, mentions a pair of maps in Vienna MS 5268 f. 30v, a codex in the hand of Johannes von Gmunden. This turns out to be a ghost map. According to Kunitzsch (private communication), there is on f. 30v a star table of 44 stars computed for the year 1436, not a star map. On the next page, f. 31r, is another star table of 41 stars computed for the year 1432 with the remark ‘Et recepta ex Spera solida’.

(124) Durand 1952, pp. 71–6. See also Meurer 2007, pp. 1177–8.

(125) Zinner 1990, p. 44.

(126) Meurer 2007, p. 1178.

(127) Durand 1952, p. 116.

(128) Voss 1943. The relation with Dürer's maps is discussed on pp. 119–22.

(129) Apian's planisphere of 1536 is described in Warner 1979, p. 10, and reproduced in Kunitzsch 1986c.

(130) For Vopel's globe, see Dekker 2010a; Gemma Frisius's globe is described in Dekker 1999, pp. 87–91 and 341–2. For Praetorius's globe, see my description in Bott 1992, vol. 2, pp. 637–8.

(131) Heinfogel (Brévart 1981), p. II.

(132) On Walther, see Zinner 1990, pp. 138–42, 144–7, and 157–61. Kremer 1980; Kremer 1981.

(133) Santing 1992.

(134) Santing 1992, pp. 130–5.

(135) Zinner 1967/1979, p. 539.

(136) Oberhummer 1926. Chet Van Duzer informed me (February 2009) that the Brixen pair of globes is now at the Department of Rare Books and Manuscripts, Yale Center for British Art.

(137) Voss 1943, p. 113.

(138) Voss 1943, p. 128.

(139) Zinner 1990, p. 252, no. 291a. Voss 1943, p. 116. See also Exhibition catalogue 1973, p. 21, Kat. 71.

(140) Ackermann 2009, pp. 218–19 and 390–1.

(141) Haidinger 1991, pp. 33–4.

(142) Voss 1943, p. 128.

(143) Saxl 1927, p. 35; Panofsky and Saxl 1933, pp. 240–1.

(144) Warner 1979, pp. 32–3.

(145) ‘Theft of Instruments in Rome’, Bulletin of the Scientific Instrument Society, no. 4, 1984, p. 18.

(146) The picture is from Turner (G) 1991, p. 70.

(147) North 1976.

(148) North 1976, p. 274.

(149) Hadrava and Hadravová 2006.

(150) Uiblein 1988, p. 61; Durand 1952, p. 334.

(151) Poulle 1980, p. 406.

(152) The positions of CMa 9 and CMa 10 in the Alfonsine star catalogue for the epoch 1252 are respectively 88º 8’ and 91º 48’.

(153) Saxl and Meier 1953, pp. 341–4. Image available in Iconographic Database of The Warburg Institute, see the drawing in MS Can. Misc. 554, f. 161v of Serpens.

(154) McGurk 1966, pp. 26–7. Image available in Iconographic Database of The Warburg Institute, see the drawing in Biblioteca Laurenziana, Plut 89, sup 43, f. 43r of Cetus.

(155) Poulle 1963, pp. 86–8.

(156) Uiblein 1988, p. 61.

(157) Chlench 2007, p. 98. King 1995a, p. 376.

(158) Graf-Stuhlhofer 1996, p. 158.

(159) The Latin text of these bills is in Ruysschaert 1985, p. 95. For a translation in English, see Babicz 1987, pp. 161–2.

(160) Durand 1952, pp. 80–3.

(161) Ruysschaert 1985, pp. 97–8.

(162) I do not count here the unfinished globe described by Hartmann 1919, pp. 42–50.

(163) Birkenmajer 1972; Vargha and Both 1987; Hayton 2007.

(164) Hayton 2007, pp. 187–8.

(165) Gabriel 1969, pp. 38–9.

(166) Zinner 1990, p. 92.

(167) Zinner 1990, pp. 98–100.

(168) Zinner 1990, pp. 91–2; Hayton 2007, pp. 185–6.

(169) All three instruments are shown in Levenson 1991, pp. 221–4, nos 120–22.

(170) Ameisenowa 1959, Fig. 2.

(171) Zinner 1967/1979, pp. 292–7.

(172) Graf-Stuhlhofer 1996, p. 164.

(173) Zinner 1990, p. 157.

(174) Details can be found on www.mhs.ox.ac.uk/epact/ [accessed 21 March 2012].

(175) Zinner 1967/1979, p. 293 and Ameisenowa 1959, p. 46.

(176) Zinner 1967/1979, p. 464.

(177) Proctor 2005.

(178) King and Turner 1994.

(179) Zinner 1967/1979, pp. 130–4.

(180) Eagleton 2010, pp. 93–119.

(181) North 1986, pp. 27–30.

(182) Ameisenowa 1959, p. 15. I cannot verify her statement because the paper she refers to is written in Polish and not accessible to me.

(183) As an aside I note that the precession correction of the stars on Dorn's astrolabe of 1486 is 19° 23’ ± 8’. In terms of the Alfonsine trepidation theory this would correspond to an epoch of 1472, which is not bad at all for an astrolabe made in 1486.

(184) Le Boeuffle 1977, pp. 129–33.

(185) The first printed edition of Trapezuntius's translation appeared in 1528, see Trapezuntius 1528.

(186) Monfasani 1976, p. 194.

(187) Ameisenowa 1959, p. 27 sees this as ‘a torch flame downwards’.

(188) Ameisenowa 1959, p. 39.

(189) Ameisenowa 1959, Fig. 13.

(190) McGurk 1966, p. 33 and Plate IVd; Lippincott 1985, p. 70.

(191) Forti et al.1987; Lapi Ballerini 1987.

(192) Oestmann 1993, pp. 8–9 and cat. 24, pp. 55–6. Stöffler 1499.

(193) Zinner 1990, pp. 117–30, esp. p. 124.

(194) Stöffler 1499, pp. 9v–10v.

(195) Oestmann 1993, p. 9.

(196) Graf-Stuhlhofer 1996, pp.135–40.

(197) On Melanchthon, see Stupperich 1990.

(198) Oestmann 1993, pp. 31–4.

(199) Kunitzsch 1986b. Kunitzsch's study is based on the catalogues in the editions of Venice 1483, 1492, 1518 (dated 1521 at the end of the book), 1524; Paris 1545,1553; and Madrid 1641.

(200) Stöffler 1512, f. XX.

(201) Bauer 1983, p. 12.

(202) The Scot illustrations have been reprinted in Condos 1997.

(203) Blume et al. in preparation. I thank Dieter Blume for this information.

(204) Ackermann 2009, pp. 182–3 and 362–3.

(205) Ackermann 2009, pp. 158–9 and 347.

(206) Ackermann 2009, pp. 190–1 and 368.

(207) Ackermann 2009, pp. 187–8 and 366.

(208) Ackermann 2009, pp. 546–9, esp. p. 549.

(209) The translation is from Condos 1997, p. 148.

(210) McGurk 1966, p. 33 and Plate IVd.

(211) Dekker 2010a, p. 173.

(212) Oestmann 1995/6, p. 64.