Excerpt:
Although certainly not the first trigonometric table, Ptolemy's On the Size of Chords Inscribed in a Circle (2nd Century AD) is by far the most famous. Based largely on an earlier work by Hipparchus (ca. 140 BC) it was included in Ptolemy's definitive Syntaxis Mathematica, better known by its Arabic name Almagest. In this paper I will describe the geometric theorems used in the construction of this table and attempt to relate them to their contemporary trigonometric counterparts.