246 
TRIGONOMETRY 
dosius was of Bithynia and not later in date than Vitruvius 
(say 20 b.c.) ; but the order in which Strabo gives the 
names makes it not unlikely that he was contemporary with 
Hipparchus, while the character of his Sphaerica suggests a 
date even earlier rather than later. 
Works by Theodosius. 
Two other works of Theodosius besides the Sphaerica, 
namely On habitations and On Days and Nights, seem to 
have been included in the ‘Little Astronomy 5 (/uKpos darpo- 
rofMovyevos, sc. tottos). These two treatises need not detain us 
long. They are extant in Greek (in the great MS. Vaticanus 
Graecus 204 and others), but the Greek text has not appar 
ently yet been published. In the first, On habitations, in 12 
propositions, Theodosius explains the different phenomena due 
to the daily rotation of the earth, and the particular portions 
of the whole system which are visible to inhabitants of the 
different zones. In the second, On Days and Nights, contain 
ing 13 and 19 propositions in the two Books respectively, 
Theodosius considers the arc of the ecliptic described by the 
sun each day, with a view to determining the conditions to be 
satisfied in order that the solstice may occur in the meridian 
at a given place, and in order that the day and the night may 
really be equal at the equinoxes; he shows also that the 
variations in the day and night must recur exactly after 
a certain time, if the length of the solar year is commen 
surable with that of the day, while on the contrary assump 
tion they will not recur so exactly. 
In addition to the works bearing on astronomy, Theodosius 
is said 1 to have written a commentary, now lost, on the ecpoSiov 
or Method of Archimedes (see above, pp. 27-34). 
Contents of the Sphaerica. 
We come now to the Sphaerica, which deserves a short 
description from the point of view of this chapter. A text 
book on the geometry of the sphere was Avanted as a supple 
ment to the Elements of Euclid. In the Elements themselves 
1 Suidas, loe. cit.