XI 
EUCLID 
Date and traditions. 
We have very few particulars of the lives of the great 
mathematicians of Greece. Even Euclid is no exception. 
Practically all that is known about him is contained in a few 
sentences of Proclus’s summary : 
‘ Not much younger than these (sc. Hermotimus of Colophon 
and Philippus of Mende or Medma) is Euclid, who put to 
gether the Elements, collecting many of Eudoxus’s theorems, 
perfecting many of Theaetetus’s, and also bringing to irre 
fragable demonstration the things which were only somewhat 
loosely proved by his predecessors. This man lived in the 
time of the first Ptolemy. For Archimedes, who came 
immediately after the first (Ptolemy), makes mention of 
Euclid; and further they say that Ptolemy once asked him if 
there was in geometry any shorter way than that of the 
Elements, and he replied that there was no royal road to 
geometry. He is then younger than the pupils of Plato, but 
older than Eratosthenes and Archimedes, the latter having 
been contemporaries, as Eratosthenes somewhere says.’ 1 
This passage shows that even Proclus had no direct know 
ledge of Euclid’s birthplace, or of the dates of his birth and 
death ; he can only infer generally at what period he flourished. 
All that is certain is that Euclid was later than the first 
pupils of Plato and earlier than Archimedes. As Plato died 
in 347 B. C. and Archimedes lived from 287 to 212 B.C., Euclid 
must have flourished about 300 B.C., a date which agrees well 
with the statement that he lived under the first Ptolemy, who 
reigned from 306 to 283 B.C. 
1 Proclus on Eucl. I, p. 68. 6-20.