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.