A history of Greek mathematics - Wilbourhall.org

THEON OF SMYRNA 239
edited by E. Hiller (Teubner, 1878) and finally, with a French
translation, by J. Dupuis (Paris, 1892).
Theon's date is
approximately fixed by two considerations.
He is clearly the person whom Theon of Alexandria called
'the old Theon', top' iraXaibv Qecova} and there is no reason
to doubt that he is the ' Theon the mathematician '
(6 fiaOr)-
fianKos) who is credited by Ptolemy with four observations
of the planets Mercury and Venus made in a.d. 127, 129, 130
and 132. 2 The latest writers whom Theon himself mentions
are Thrasyllus, who lived in the reign of Tiberius, and
Adrastus the Peripatetic, who belongs to the middle of the
second century a.d.
Theon's work itself is a curious medley,
valuable, not intrinsically, but for the numerous historical
notices which it contains. The title, which claims that the
book contains things useful for the study of Plato, must not
be taken too seriously. It was no doubt an elementary
introduction or vade-mecum for students of philosophy, but
there is little in it which has special reference to the mathematical
questions raised in Plato. The connexion consists
mostly in the long proem quoting the views of Plato on the
paramount importance of mathematics in the training of
the philosopher, and the mutual relation of the five different
branches, arithmetic, geometry, stereometry, astronomy and
music. The want of care shown by Theon in the quotations
from particular dialogues of Plato prepares us for the patchwork
character of the whole book.
In the first chapter he promises to give the mathematical
theorems most necessary for the student of Plato to know,
in arithmetic, music, and geometry, with its application to
stereometry and astronomy. 3 But the promise is by no means
kept as regards geometry and stereometry : indeed, in a
later passage Theon seems to excuse himself from including
theoretical geometry in his plan, on the ground that all those
who are likely to read his work or the writings of Plato may
be assumed to have gone through an elementary course of
theoretical geometry. 4 But he writes at length on figured
1
Theon of Alexandria, Comm. on Ptolemy s Syntaxis, Basel edition,
pp. 390, 395, 396.
2
Ptolemy, Syntaxis, ix. 9, x. 1, 2.
3
Theon of Smyrna, ed. Hiller, p. 1. 10-17.
4
lb., p. 16. 17-20.