A history of Greek mathematics Vol.II from Aristarchus to Diophantus by Heath, Thomas Little, Sir, 1921

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
528 COMMENTATORS AND BYZANTINES
already referred to, a second case to VI. 27, a porism or corollary
to II. 4, a second porism to III. 16, the proposition VII. 22,
a lemma after X. 12, besides alternative proofs here and there
(b) he added words for the purpose of making smoother and
clearer, or more precise, things which Euclid had expressed
with unusual brevity, harshness, or carelessness ;
(c) he supplied
intermediate steps where Euclid's argument seemed too
difficult to follow. In short, while making only inconsiderable
additions to the content of the Elements, he endeavoured
to remove difficulties that might be felt b}^ learners in studying
the book, as a modern editor might do in editing a classical
text-book for use in schools ; and there is no doubt that his
edition was approved by his pupils at Alexandria for whom it
was written, as well as by later Greeks, who used it almost
exclusively, with the result that the more ancient text is only
preserved complete in one manuscript.
Edition of the Optics of Euclid.
In addition to the Elements, Theon edited the Optics of
Euclid ; Theon's recension as well as the genuine work is
included by Heiberg in his edition. It is possible that the
Catoptrica included by Heiberg in the same volume is also by
Theon.
Next to Theon should be mentioned his daughter Hypatia,
who is mentioned by Theon himself as having assisted in the
revision of the commentary on Ptolemy.
This learned lady
is said to have been mistress of the whole of pagan science,
especially of philosophy and medicine, and by her eloquence
and authority to have attained such influence that Christianity
considered itself threatened, and she was put to death by
a fanatical mob in March 415. According to Suidas she wrote
commentaries on Diophantus, on the Astronomical Canon (of
Ptolemy) and on the Conies of Apollonius. These works
have not survived, but it has been conjectured (by Tannery)
that the remarks of
Psellus (eleventh century) at the beginning
of his letter about Diophantus, Anatolius, and the
Egyptian method of arithmetical reckoning were taken bodily
from some manuscript of Diophantus containing an ancient
and systematic commentary which may very well have been
that of Hypatia.
Possibly her commentary may have extended