XVII 
TRIGONOMETRY: HIPPARCHUS, MENELAUS, 
PTOLEMY 
We have seen that Sphaeric, the geometry of the sphere, 
was very early studied, because it was required so soon as 
astronomy became mathematical ; with the Pythagoreans the 
word Sphaeric, applied to one of the subjects of the quadrivium, 
actually meant astronomy. The subject was so far advanced 
before Euclid’s time that there was in existence a regular 
textbook containing the principal propositions about great 
and small circles on the sphere, from which both Autolycus 
aiid Euclid quoted the propositions as generally known. 
These propositions, with others of purely astronomical in 
terest, were collected afterwards in a work entitled Sphaerica, 
in three Books, by Theodosius. 
Suidas has a notice, s. v. @eoS6<nos, which evidently con 
fuses the author of the Sphaerica with another Theodosius, 
a Sceptic philosopher, since it calls him ‘ Theodosius, a philoso 
pher ’, and attributes to him, besides the mathematical works, 
‘ Sceptic chapters ’ and a commentary on the chaptei’s of 
Then das. Now the commentator on Theudas must have 
belonged, at the earliest, to the second half of the second 
century a.d., whereas our Theodosius was earlier than Mene 
laus (fl. about A.D. 100), who quotes him by name. The next 
notice by Suidas is of yet another Theodosius, a poet, who 
came from Tripolis. Hence it was at one time supposed that 
our Theodosius was of Tripolis. But Vitruvius 1 mentions a 
Theodosius who invented a sundial £ for any climate ’ ; and 
Strabo, in speaking of certain Bithynians distinguished in 
their particular sciences, refers to ‘ Hipparchus, Theodosius 
and his sons, mathematicians’ 2 . We conclude that our Theo- 
2 Strabo, xii. 4, 9, p. 566. 
De architectura ix. 9.