In 1454 Georg Peurbach taught astronomy at the Collegium Civium in Vienna by reading a work of his own: the Theoricae novae planetarum. In 1483 Albert of Brudzewo, teaching astronomy at Cracow University, adopted Peurbach’s text together with a commentariolum of his own. Among the numerous commentaries preserved both in manuscript and in printed form, Brudzewo’s stands out because it submits Peurbach’s work to a subtle analysis that, while recognising the merits for which it was widely accepted, also focuses on (...) the limitations of the celestial spheres described in it. Budzewo’s commentary is of interest, in itself both for its criticism of Peurbach’s descriptions of solar, lunar and planetary theory and also for its importance to Copernicus’s own planetary theory. For Copernicus makes clear in the Commentariolus that his concern was the very same issue, violation of uniform circular motion by the rotation of spheres, that Brudzewo criticises in detail. In this way, Brudzewo’s commentary stands as the original motivation for the investigation of the motion of the planets that was eventually to lead Copernicus to a planetary theory based strictly upon uniform rotation of spheres, and through that investigation to the motion of the Earth and the heliocentric theory. (shrink)

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. (shrink)