An analysis of the text and tables in Georg Joachim Rheticus' Canon doctrinae triangulorum

Georg Rheticus' Canon doctrinae triangulorum (1551) challenges traditional approaches to trigonometry in Europe by offering the first conceptualization of the subject which examines the relationships between the side lengths of a right triangle. Rheticus' 14-page trigonometric table, built around three "species" of triangles, contains all six of the modern trigonometric functions laid out in semi-quadrantal arrangement for arguments of every 10'. Analysis of this table reveals underlying computational methods to be based in mathematics pertaining to similar planar triangles, consistent with the hypotheses of previous scholars. The first complete Latin to English translation of the 6-page dialogue following the table clarifies Rheticus' intention for this work, putting it in conversation with previous scholarship by Ptolemy, Geber, and Copernicus. The content of the dialogue also offers insight into the development of Rheticus' triangles, the structure of his table, and possible precedence claims regarding the 10 modern identities of spherical trigonometry.