438 
EUCLID 
same name as that applied to corollaries because they were 
corollaries with respect to conics. 1 This, however, is a pure 
conjecture. 
(y) The Conics. 
Pappus says of this lost work: ‘ The four books of Euclid’s 
Conics were completed by Apollonius, who added four more 
and gave us eight books of Conics.’ 2 It is probable that 
Euclid’s work was already lost by Pappus’s time, for he goes 
on to speak of ‘ Aristaeus who wrote the still extant live books 
of Solid Loci crvve\ij rois koovlkois, connected with, or supple 
mentary to, the conics’. 3 This latter work seems to have 
been a treatise on conics regarded as loci; for ‘ solid loci ’ was 
a term appropriated to conics, as distinct from ‘ plane loci 
which were straight lines and circles. In another passage 
Pappus (or an interpolator) speaks of the ‘ conics ’ of Aristaeus 
the ‘ elder ’, 4 evidently referring to the same book. Euclid no 
doubt wrote on the general theory of conics, as Apollonius did, 
but only covered the ground of Apollonius’s first three books, 
since Apollonius says that no one before him had touched the 
subject of Book IV (which, however, is not important). As in 
the case of the Elements, Euclid would naturally collect and 
rearrange, in a systematic exposition, all that had been dis 
covered up to date in the theory of conics. That Euclid's 
treatise covered most of the essentials up to the last part of 
Apollonius’s Book III seems clear from the fact that Apol 
lonius only claims originality for some propositions connected 
with the ‘ three- and four-line locus ’, observing that Euclid 
had not completely worked out the synthesis of the said locus, 
which, indeed, was not possible without the propositions 
referred to. Pappus (or an interpolator) 5 excuses Euclid on 
the ground that he made no claim to go beyond the discoveries 
of Aristaeus, but only wrote so much about the locus as was 
possible with the aid of Aristaeus’s conics. We may conclude 
that Aristaeus’s book preceded Euclid’s, and that it was, at 
least in point of originality, more important. When Archi 
medes refers to propositions in conics as having been proved 
1 Zeuthen, Die Lehre von den Kegelschnitten im Altertum, 1886, pp. 168, 
178-4. 
5 Pappus, vii, p. 672. 18. 5 Cf. Pappus, vii, p. 636. 23. 
A lb. vii, p. 672. 12. lb, vii, pp. 676. 25-678. 6.