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.