SEQUEL TO THE EPOCH OF HIPPARCHUS. 221 



doctrine of the sphere, or that of epicycles, is the 

 calculation of its numerical results in particular 

 cases. With regard to the latter theory, this was 

 done in the construction of Solar and Lunar Tables, 

 as we have already seen ; and this process required 

 the formation of a Trigonometry, or system of 

 rules for calculating the relations between the sides 

 and angles of triangles. Such a science had been 

 formed by Hipparchus, who appears to be the 

 author of every great step in ancient astronomy 21 . 

 He wrote a work in twelve books, "On the Con- 

 struction of the Tables of Chords of Arcs ;" such 

 a table being the means by which the Greeks 

 solved their triangles. The Doctrine of the Sphere 

 required, in like manner, a Spherical Trigono- 

 metry, in order to enable mathematicians to cal- 

 culate its results ; and this branch of science also 

 appears to have been formed by Hipparchus 22 , who 

 gives results that imply the possession of such a 

 method. Hypsicles, who was a contemporary of 

 Ptolemy, also made some attempts at the solution 

 of such problems : but it is extraordinary that the 

 writers whom we have mentioned as coming after 

 Hipparchus, namely, Theodosius, Cleomedes, and 

 Menelaus, do not even mention the calculation of 

 triangles 23 , either plane or spherical; though the 

 latter writer 24 is said to have written on "the 

 Table of Chords," a work which is now lost. 



21 Delamb. A. A. ii. 37. 22 A. A. i. 117. 



83 A. A. i. 249. a4 A. A. ii. 37. 



