A history of Greek mathematics - Wilbourhall.org

218 SUCCESSORS OF THE GREAT GEOMETERS
and from these and the common difference 0* O'lS'^O'" all
the times corresponding to all the degrees in the circle can be
found.
The procedure was probably, as Tannery thinks, taken
direct from the Babylonians, who would no doubt use it for
the purpose of enabling the time to be determined at any
hour of the night. Another view is that the object was
astrological rather than astronomical (Manitius). In either
case the method was exceedingly rough, and the assumed
increases and decreases in the times of the risings of the signs
in arithmetical progression are not in accordance with the
facts. The book could only have been written before the invention
of trigonometry by Hipparchus, for the problem of
finding the times of rising of the signs is really one of
spherical trigonometry, and these times were actually calculated
by Hipparchus and Ptolemy by means of tables of
chords.
Dionysodorus is known in the first place as the author of
a solution of the cubic equation subsidiary to the problem of
Archimedes, On the Sjrfiere and Cylinder, II.
4, To cut a given
sphere by a plane so that the volumes of the segments have to
one another a given ratio (see above, p. 46). Up to recently
this Dionysodorus was supposed to be Dionysodorus of Amisene
in Pontus, whom Suidas describes as a mathematician worthy
'
of mention in the field of education '. But we now learn from
a fragment of the Herculaneum Roll, No. 1044, that ' Philonides
was a pupil, first of Eudemus, and afterwards of Dionysodorus,
the son of Dionysodorus the Caunian'. Now Eudemus is
evidently Eudemus of Pergamum to whom Apollonius dedicated
the first two Books of his Conies, and Apollonius actually
asks him to show Book II to Philonides. In another fragment
Philonides is said to have published some lectures by
Dionysodorus. Hence our Dionysodorus may be Dionysodorus
of Caunus and a contemporary of Apollonius, or very little
later. 1 A Dionysodorus is also mentioned by Heron 2 as the
author of a tract On the ^ire (or tore) in which he proved
that, if d be the diameter of the revolving circle which
1
W. Schmidt in Bibliotheca mathematica, iv 3 , pp. 321-5.
2
Heron, Metrica, ii. 13, p. 128. 3.