THE ELEMENTS DOWN TO PLATO’S TIME 171 
the whole summary was directed to the one object of trac 
ing progress in the Elements, particularly with reference 
to improvements of method in the direction of greater 
generality and more scientific order and treatment; hence 
only those writers are here mentioned who contributed to this 
development. Hippocrates comes into the list, not because 
of his lunes, but because he was a distinguished geometer 
and was the first to write Elements. Hippias of Elis, on the 
other hand, though he belongs to the period covered by the 
extract, is omitted, presumably because his great discovery, 
that of the curve known as the quadratrix, does not belong 
to elementary geometry; Hippias is, however, mentioned in 
two other places by Proclus in connexion with the quadratrix, 1 
and once more as authority for the geometrical achievements 
of Ameristus (or Mamercus or Mamertius). 2 Less justice is 
done to Democritus, who is neither mentioned here nor else 
where in the commentary; the omission here of the name 
of Democritus is one of the arguments for the view that 
this part of the summary is not quoted from the History 
of Geometry by Eudemus (who would not have been likely to 
omit so accomplished a mathematician as Democritus), but 
is the work either of an intermediary or of Proclus himself, 
based indeed upon data from Eudemus’s history, but limited to 
particulars relevant to the object of the commentary, that 
is to say, the elucidation of Euclid and the story of the growth 
of the Elements. 
There are, it is true, elsewhere in Proclus’s commentary 
a very few cases in which particular propositions in Euclid, 
Book I, are attributed to individual geometers, e. g. those 
which Thales is said to have discovered. Two propositions 
presently to be mentioned are in like manner put to the 
account of Oenopides; but except for these details about 
Oenopides we have to look elsewhere for evidence of the 
growth of the Elements in the period now under notice. 
Fortunately we possess a document of capital importance, 
from this point of view, in the fragment of Eudemus on 
Hippocrates’s quadrature of lunes preserved in Simplicius's 
commentary on the PJtysics of Aristotle. 3 This fragment will 
1 Proclus on Eucl. I, p. 272. 7, p. 856. 11. 2 Ih., p. 65. 14. 
3 Simpl. in Arisi. Phys. pp. 54-69 Diels.