A history of Greek mathematics - Wilbourhall.org

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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
preserved complete in one manuscript.
Edition of the Optics of Euclid.
only
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,
philosophy and medicine, and by her eloquence
especially of
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