Born: 8 Feb 411 in Constantinople (now Istanbul),
Byzantium (now Turkey)
Died: 17 April 485 in Athens, Greece
Proclus's father, Particius, and his mother, Marcella,
were citizens of high social position in Lycia. Particius was a senior law
official in the courts at Byzantium. Proclus was brought up at Xanthus, on the
south coast of Lycia, where he attended school.
It was intended that Proclus should follow his father
and enter the legal profession. With this aim in mind he was sent to Alexandria
but, while in the middle of his studies, he visited Byzantium and he became
convinced that his calling in life was the study of philosophy. He returned to
Alexandria where now he studied philosophy under Olympiodorus the Elder, in
particular making a deep study of the works of Aristotle. He also learnt
mathematics in Alexandria and in this subject his teacher was Heron (not the famous
mathematician, Heron was a common name at this time).
Proclus was not entirely satisfied with the education
he was receiving in philosophy in Alexandria so, while still a teenager, he
moved from Alexandria to Athens where he studied at Plato's Academy under the
philosophers Plutarch and Syrianus (a pupil of Plutarch). He progressed from
being a student at the Academy to teaching there then, on the death of
Syrianus, Proclus became head of the Academy. The title Diadochus was given to
him at this time, the meaning of the word being successor.
At the Academy Proclus appears to have been well off
and to have helped his friends and relations financially. He never married and
lived a life which was, in certain respects, not unlike that proposed by
Pythagoras. He did not eat meat and tried to live a religious life, composing
hymns to the gods. His hymns were clearly highly thought of since seven of them
have been preserved and are seen today as having considerable literary merit.
Proclus was to remain as head of the Academy until his death.
A man of great learning, Proclus was regarded with
great veneration by his contemporaries. He followed the neoplatonist philosophy
which Plotinus founded, and Porphyry and Iamblichus developed around 300 AD.
Other developers of these ideas were Plutarch and Syrianus, the teachers of
Proclus. Heath writes:-
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.
Of course, as one might expect, his belief in many
religious sayings meant that he was highly biased in his views on many issues
of science. For example he mentions the hypothesis that the sun is at the
centre of the planets as proposed by Hipparchus but rejects it immediately
since it contradicted the views of a Chaldean whom he says that it is unlawful
not to believe.
Proclus wrote Commentary on Euclid which is our
principal source about the early history of Greek geometry. The book is
certainly the product of his teaching at the Academy. This work is not coloured
by his religious beliefs and Martin, writing in the middle of the 19th century,
says (see for example):-
... 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.
Proclus had access to books which are now lost and
others, already lost in Proclus's time, were described based on extracts in
other books available to Proclus. In particular he certainly used the History
of Geometry by Eudemus, which is now lost, as is the works of Geminus which he
also used. Heath, describing Proclus's Commentary on Euclid writes:-
Proclus deals historically and critically with all the
definitions, postulates and axioms in order. The notes on the postulates and
axioms are preceded by a general discussion of the principles of geometry,
hypotheses, postulates and axioms, and their relation to one another; here as
usual Proclus quotes the opinions of all the important authorities.
Another interesting part of Proclus's commentary is
his discussion of the critics of geometry. He writes:-
... it is against [the principles of geometry] that
most critics of geometry have raised objections, endeavouring to show that
these parts are not firmly established. Of those in this group whose arguments
have become notorious some, such as the Sceptics, would do away with all
knowledge ... whereas others, like the Epicureans, propose only to discredit
the principles of geometry. Another group of critics, however, admit the
principles but deny that the propositions coming after the principles can be
demonstrated unless they grant something that is not contained in the
principles. This method of controversy was followed by Zeno of Sidon, who
belonged to the school of Epicurus and against whom Posidonius has written a
whole book and shown that his views are thoroughly unsound.
Morrow in confirms the great debt that we owe to
Proclus, and in particular his Commentary on Euclid when he writes in:-
Proclus was not a creative mathematician; but he was
an acute expositor and critic, with a thorough grasp of mathematical method and
a detailed knowledge of the thousand years of Greek mathematics from Thales to
his own time.
The recent book gives a good description of the
writings of Proclus found in his commentary on Book I of Euclid's Elements. The
book  is an important contribution to the study of the philosophy of Proclus
and in particular his philosophy of mathematics.
Proclus also wrote Hypotyposis, an introduction to the
astronomical theories of Hipparchus and Ptolemy in which he described the
mathematical theory of the planets based on epicycles and on eccentrics. He
combined his geometrical skills and his knowledge of astronomy to give a
geometrical proof that the epicycle theory for the planets is equivalent to the
eccentric theory. In the epicycle theory the Earth is in the centre of a circle
which has smaller circles rotating round its circumference. In the eccentric
theory the planets move round in circles whose centres do not coincide with the
Nothing here is original and Proclus is proving
results first given by Hipparchus and Ptolemy. However, although Proclus
believed that this theory should be studied by his students at the Academy, he
was not uncritical, suggesting that the theory was overly complicated and also
that it was an ad hoc theory with no reason to explain its various parts.
In his astronomical writings, Proclus described how
the water clock invented by Heron could be used to measure the apparent
diameter of the Sun. Proclus's method can be used at the equinox. Water is
collected from the clock in a container while the sun rises. As soon as the Sun
has risen the water is collected in another container and this measurement
continues until sunrise the following day. Then the ratio of the weights of
water in the two containers gives the apparent diameter of the Sun.
Among Proclus's many works are Liber de causis (Book
of Causes), Institutio theologica (Elements of Theology), a concise exposition
of metaphysics, Elements of Physics, largely giving Aristotle's views, and In
Platonis theologiam (Platonic Theology) giving Plato's metaphysics. His
contribution is well summarised in as follows:-
Proclus deserves to be remembered ... for the
qualities he possessed that are exceedingly rare in any age and were almost
unique in his: the logical clarity and firmness of his thought, the acuteness
of his analyses, his eagerness to understand and readiness to present the views
of his predecessors on controversial issues, the sustained coherence of his
lengthy expositions, and the large horizon, as broad as the whole of being,
within which his thinking moved.
J J O'Connor and E F Robertson
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