This chapter introduces Euclidean geometry, which provides the mathematical framework in which the laws of Newtonian physics are formulated. It first discusses how the concepts of ‘space’ and ‘relative, apparent, and common’ place are represented by a mathematical ensemble of points—the ‘absolute’ space ε3. A Cartesian frame of absolute space is materialized in ‘relative, apparent, and common’ space by a reference frame. Specifically, this reference frame is a solid trihedral—that is, an ensemble of physical objects whose relative distances are invariable in time and for which an orientation of the axes has been chosen. This chapter postulates that if the labeling of the points of ε3 is changed, the distance between two points remains unchanged. It then goes on to explain further the various associated formulas associated with Cartesian coordinates.
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