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

HYPATIA. PORPHYRY 529
only to the first six Books, in which case the fact that Hypatia
wrote a commentary on them may account for the survival of
these Books while the rest of the thirteen were first forgotten
and then lost.
It will be convenient to take next the series of Neo-
Platonist commentators. It does not appear that Ammonius
Saccas (about a.d. 175-250), the founder of. Neo-Platonism, or
his pupil Plotinus (a.d. 204-69), who first expounded the
doctrines in systematic form, had any special connexion with
mathematics, but Porphyry (about 232-304), the disciple of
Plotinus and the reviser and editor of his works, appears to
have written a commentary on the Elements. This we gather
from Proclus, who quotes from Porphyry comments on Eucl.
I. 14 and 26 and alternative proofs of I. 18, 20. It is possible
that Porphyry's work may have been used later by Pappus in
writing his own commentary, and Proclus may have got his
references from Pappus, but the form of these references suggests
that he had direct access to the original commentary of
Porphyry.
Iamblichus (died about a.d. 330) was the author of a commentary
on the Introductio arithmetica of Nicomachus, and
of other works which have already been mentioned. He was
a pupil of Porphyry as well as of Anatolius, also a disciple of
Porphyry.
But the most important of the Neo-Platonists to the historian
of mathematics is Proclus (a.d. 410-85). Proclus
received his early training at Alexandria, where Olympiodorus
was his instructor in the works of Aristotle, and
mathematics was taught him by one Heron (of course a
different Heron from the '
mechanicus Hero' of the Metrica,
&c). He afterwards went to Athens, where he learnt the
Neo-Platonic philosophy from Plutarch, the grandson of
•
Nestorius,
and from his pupil Syrianus, and became one of its
most prominent exponents. He speaks everywhere with the
highest respect of his masters, and was in turn regarded with
extravagant veneration by his contemporaries, as we learn
from Marinus, his pupil and biographer. On the death of
Syrianus he was put at the head of the Neo-Platonic school.
He was a man of untiring industry, as is shown by the
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530 COMMENTATORS AND BYZANTINES
number of books which he wrote, including a large number of
commentaries, mostly on the dialogues of PJato (e.g. the
Timaeus, the Republic, the Parmenides, the Cratylus). He
was an acute dialectician and pre-eminent among his contemporaries
in the range of his learning; he was a competent
mathematician ; he was even a poet. At the same time he
was a believer in all sorts of myths and mysteries, and
a devout worshipper of divinities both Greek and Oriental.
He was much more a philosopher than a mathematician. In
his commentary on the Timaeus, when referring to the question
whether the sun occupies a middle place among the
planets, he speaks as no real mathematician could have
spoken, rejecting the view of Hipparchus and Ptolemy because
6 Qzovpyos (sc. the Chaldean, says Zeller) thinks otherwise,
whom it is not lawful to disbelieve '. Martin observes too,
'
rather neatly, that for ' Proclus the Elements of Euclid had
the good fortune not to be contradicted either by the Chaldean
Oracles or by the speculations of Pythagoreans old and new '.
Commentary on Euclid, Book I.
For us the most important work of Proclus is his
commentary
on Euclid, Book I, because it is one of the main sources
of our information as to the history of elementary geometry.
Its great value arises mainly from the fact * that Proclus had
access to a number of historical and critical works which are
now lost except for fragments preserved by Proclus and
others.
(a) Sources of the Commentary.
The historical work the loss of which is most deeply to be
deplored is the History of Geometry by Eudemus. There
appears to be no reason to doubt that the work of Eudemus
was accessible to Proclus at first hand. For the later writers
Simplicius and Eutocius refer to it in terms such as leave no
doubt that they had it before them. Simplicius, quoting
Eudemus as the best authority on Hippocrates's quadratures
of lunes, says he will set out what Eudemus says * word for
word ', adding only a little explanation in the shape of references
to Euclid's Elements 'owing to the memorandum-like
style of Eudemus, who sets out his explanations in the abbre-