
 Ptolemy's Table of Chords 
  Ptolemy began his discourse by calculating the chord lengths for the central angles corresponding to the sides of a regular inscribed decagon, hexagon, pentagon, square, and triangle. 
  With this theorem, Ptolemy produced three corollaries from which more chord lengths could be calculated: the chord of the difference of two arcs, the chord of half of an arc, and the chord of the sum of two arcs. 
  Given the wellknown impossibility of this trisection, Ptolemy decided instead to approximate the value of crd 1° by means of "a little lemma which, even if it may not suffice for determining chords in general, can yet in the case of very small ones, keep them indistinguishable from chords rigorously determined" (Ptolemy 28). 
 hypertextbook.com /eworld/chords.shtml (1804 words) 
