THE EARLIEST GREEK GEOMETRY. THALES 
The ‘Summary’ of Proclus. 
We shall often, in the course of this history, have occasion 
to quote from the so-called ‘ Summary ’ of Proclus, which has 
already been cited in the preceding chapter. Occupying a 
few pages (65-70) of Proclus’s Commentary on Euclid, Book I, 
it reviews, in the briefest possible outline, the course of Greek 
geometry from the earliest times to Euclid, with special refer 
ence to the evolution of the Elements. At one time it was 
often called the ‘ Eudemian summary ’, on the assumption 
that it was an extract from the great History of Geometry in 
four Books by Eudemus, the pupil of Aristotle. But a perusal 
of the summary itself is sufficient to show that it cannot 
have been written by Eudemus; the most that can be said is 
that, down to a certain sentence, it was probably based, more 
or less directly, upon data appearing in Eudemus’s History. 
At the sentence in question there is a break in the narrative, 
as follows: 
‘ Those who have compiled histories bring the development 
of this science up to this point. Not much younger than 
these is Euclid, who put together the Elements, collecting 
many of the theorems of Eudoxus, perfecting many others by 
Theaetetus, and bringing to irrefragable demonstration the 
propositions which had only been somewhat loosely proved by 
his predecessors.’ 
Since Euclid was later than Eudemus, it is impossible that 
Eudemus can have written this; while the description ‘ those 
who have compiled histories’, and who by implication were 
a little older than Euclid, suits Eudemus excellently. Yet the 
style of the summary after the break does not show any 
such change from that of the earlier portion as to suggest