Graphical Choices and Geometrical Thought in the Transmission of Theodosius' Spherics from Antiquity to the Renaissance (2010)
Spherical geometry studies the sphere not simply as a solid object in itself, but chiefly as the spatial context of the elements which interact on it in a complex three-dimensional arrangement. This compels to establish graphical conventions appropriate for rendering on the same plane---the plane of the diagram itself---the spatial arrangement of the objects under consideration. We will investigate such graphical choices made in the Theodosius' Spherics from antiquity to the Renaissance. Rather than undertaking a minute analysis of every particular element or single variant, we will try to uncover the more general message each author attempted to convey through his particular graphical choices. From this analysis, it emerges that the different kinds of representation are not the result of merely formal requirements but mirror substantial geometrical requirements expressing different ways of interpreting the sphere and testify to different ways of reasoning about the elements that interact on it.
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