THE ‘ SUMMARY ’ OF PROCLUS 
119 
different authorship. The author of the earlier portion fre 
quently refers to the question of the origin of the Elements of 
Geometry in a way in which no one would be likely to write 
who was not later than Euclid; and it seems to be the same 
hand which, in the second portion, connects the Elements of 
Euclid with the work of Eudoxus and Theaetetus. Indeed 
the author, whoever he was, seems to have compiled the sum 
mary with one main object in view, namely, to trace the origin 
and growth of the Elements of Geometry; consequently he 
omits to refer to certain famous discoveries in geometry such 
as the solutions of the problem of the duplication of the cube, 
doubtless because they did not belong to the Elements. In 
two cases he alludes to such discoveries, as it were in paren 
thesis, in order to recall to the mind of the reader a current 
association of the name of a particular geometer with a par 
ticular discovery. Thus he mentions Hippocrates of Chios as 
a famous geometer for the particular reason that he was the 
first to write Elements, and he adds to his name, for the pur 
pose of identification, ‘ the discoverer of the quadrature of the 
lune ’. Similarly, when he says of Pythagoras ‘ (he it was) 
who ’ (09 Srj . . .) ‘ discovered the theory of irrationals [or 
“ proportions ”] and the construction of the cosmic figures 
he seems to be alluding, entirely on his own account, to a 
popular tradition to that effect. If the summary is the work 
of one author, who was it 1 Tannery answers that it was 
Geminus; but this seems highly improbable, for the extracts 
from Geminus’s work which we possess suggest that the 
subjects therein discussed were of a different kind ; they seem 
rather to have been general questions relating to the philoso 
phy and content of mathematics, and even Tannery admits 
that historical details could only have come incidentally into 
the work. 
Could the author have been Proclus himself 1 This again 
seems, on the whole, improbable. In favour of the authorship 
of Proclus are the facts (1) that the question of the origin of 
the Elements is kept prominent and (2j that there is no men 
tion of Democritus, whom Eudemus would not have ignored, 
while a follower of Plato such as Proclus might have done 
him this injustice, following the example of Plato himself, who 
was an opponent of Democritus, never once mentions him, and