*Proclus Diadochus, AD 410-485.*

(From his book: *Commentary on Euclid's Elements I*)

We must next speak of the origin of geometry in the present world cycle. For,
as the remarkable Aristotle tells us, the same ideas have repeatedly come to men
at various periods of the universe. It is not, he goes on to say, in our time or
in the time of those known to us that the sciences have first arisen, but they
have appeared and again disappeared, and will continue to appear and disappear,
in various cycles, of which the number both past and future is countless. But
since we must speak of the origin of the arts and sciences with reference to the
present world cycle, it was, we say, among the Egyptians that geometry is
generally held to have been discovered. It owed its discovery to the practice of
land measurement. For the Egyptians had to perform such measurements because the
overflow of the Nile would cause the boundary of each person's land to
disappear. Furthermore, it should occasion no surprise that the discovery both
of this science and of the other sciences proceeded from utility, since
everything that is in the process of becoming advances from the imperfect to the
perfect. The progress, then, from sense perception to reason and from reason to
understanding is a natural one. And so, just as the accurate knowledge of
numbers originated with the Phoenicians through their commerce and their
business transactions, so geometry was discovered by the Egyptians for the
reason we have indicated.

It was Thales, who, after a visit to Egypt, first brought this study to
Greece. Not only did he make numerous discoveries himself, but laid the
foundation for many other discoveries on the part of his successors, attacking
some problems with greater generality and others more empirically. After him
Mamercus the brother of the poet Stesichorus, is said to have embraced the study
of geometry, and in fact Hippias of Elis writes that he achieved fame in that
study.

After these Pythagoras changed the study of geometry, giving it the form of a
liberal discipline, seeking its first principles in ultimate ideas, and
investigating its theorems abstractly and in a purely intellectual way.

[He then mentions several who developed this abstract approach further:
Anaxagoras, Hippocrates, Theodorus, etc.]

Plato, who lived after Hippocrates and Theodorus, stimulated to a very high
degree the study of mathematics and of geometry in particular because of his
zealous interest in these subjects. For he filled his works with mathematical
discussions, as is well known, and everywhere sought to awaken admiration for
mathematics in students of philosophy.

[He then lists several mathematicians, including Eudoxus and Theatetus, who
discovered many new geometric theorems, and began to arrange them in logical
sequences-this process culminated in the work of Euclid, called his
*Elements* (of geometry) about 300 BC. ]

Euclid composed *Elements*, putting in order many of the theorems of
Eudoxus, perfecting many that had been worked out by Theatetus, and furnishing
with rigorous proofs propositions that had been demonstrated less rigorously by
his predecessors … the *Elements *contain the complete and irrefutable
guide to the scientific study of the subject of geometry.