A history of Greek mathematics - Wilbourhall.org

THEON OF ALEXANDRIA 527
pp. 58-63). Of the historical notices we may mention the
following. (1) Theon mentions the treatise of Menelaus On
Chords in a Circle, i. e. Menelaus's Table of Chords, which came
between the similar Tables of Hipparchus and Ptolemy. (2) A
quotation from Diophantus furnishes incidentally a lower limit
for the date of the Arithmetica. (3) It is in the commentary
on Ptolemy that Theon tells us that the second part of Euclid
VI. 33 relating to sectors in equal circles was inserted by himself
in his edition of the Elements, a notice which is of capital
importance in that it enables the Theonine manuscripts of
Euclid to be distinguished from the ante-Theonine, and is
therefore the key to the question how far the genuine text
of Euclid was altered in Theon's edition. (4) As we have
207 sq.), Theon, a propos of an allusion of Ptolemy
seen (pp.
to the theory of isoperimetric figures, has preserved for us
several propositions from the treatise by Zenodorus on that
subject.
Theon's edition of Euclid's Elements.
We are able to judge of the character of Theon's edition of
Euclid by a comparison between the Theonine manuscripts
and the famous Vatican MS. 190, which contains an earlier
edition than Theon's, together with certain fragments of
ancient papyri. It appears that, while Theon took some
trouble to follow older manuscripts, it was not so much his
object to get the most authoritative text as to make what he
considered improvements of one sort or other, (l) He made
alterations where he found, or thought he found, mistakes in
the original; while he tried to remove some real blots, he
altered other passages too hastily when a little more consideration
would have shown that Euclid's words are right or could
be excused, and offer no difficulty to an intelligent reader.
(2) He made emendations intended to improve the form or
diction of Euclid ;
in general they were prompted by a desire
to eliminate anything which was out of the common in expression
or in form, in order to reduce the language to one and the
same standard or norm. (3) He bestowed, however, most
attention upon additions designed to supplement or explain
the original ;
(a) he interpolated whole propositions where he
thought them necessary or useful, e.g. the addition to VI. 33