VI 
PROGRESS IN THE ELEMENTS DOWN TO 
PLATO’S TIME 
In tracing the further progress in the Elements which took 
place down to the time of Plato, we do not get much assistance 
from the summary of Proclus. The passage in which he 
states the succession of geometers from Pythagoras to Plato 
and his contemporaries runs as follows : 
‘ After him [Pythagoras] Anaxagoras of Clazomenae dealt 
with many questions in geometry, and so did Oenopides of 
Chios, who was a little younger than Anaxagoras; Plato 
himself alludes, in the Rivals, to both of them as having- 
acquired a reputation for mathematics. After them came 
Hippocraffes of Chios, the discoverer of the quadrature of 
the lune, and Theodorus of Cyrene, both of whom became 
distinguished geometers; Hippocrates indeed was the first 
of whom it is recorded that he actually compiled Elements. 
Plato, who came next to them, caused mathematics in general 
and geometry in particular to make a very great advance, 
owing to his own zeal for these studies ; for every one knows 
that he even filled his writings with mathematical discourses 
and strove on every occasion to arouse enthusiasm for mathe 
matics in those who took up philosophy. At this time too 
lived Leodamas of Thasos, Archytas of Taras, ami Theaetetus 
of Athens, by whom the number of theorems was increased 
and a further advance was made towards a more scientific 
grouping of them.’ 1 
It will be seen that we have here little more than a list of 
names of persons who advanced, or were distinguished in, 
geometry. There is no mention of specific discoveries made 
by particular geometers, except that the work of Hippocrates 
on the squaring of certain lunes is incidentally alluded to, 
rather as a means of identifying Hippocrates than as a de 
tail relevant to the subject in hand. It would appear that 
1 Proclus on Eucl. I, p. 65. 21-66. 18.