A history of Greek mathematics - Wilbourhall.org

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
date even earlier
rather than later.
his Sphaerica suggests a
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' [jxiKpos d&Tpovofjiovfj.ei'os,
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 apparently
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, containing
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 commensurable
with that of the day, while on the contrary assumption
they will not recur so exactly.
In addition to the works bearing on astronomy, Theodosius
is said l to have written a commentary, now lost, on the e