SERENUS 
519 
1NES 
lathematics; it 
;rences to com 
muted nothing 
is and explana- 
point of view, 
j perished, or 
original docu- 
ity. Nor must 
ibly owe to the 
s of the great 
partly, in the 
i the case even 
cius wrote com- 
lentaries which 
! (the colleague 
Constantinople) 
nd caused them 
erever they had 
ad the effect of 
ommented upon 
with the Doric 
jislation of the 
i systematically 
>cius commented 
survive. Again, 
cs is extant for 
r to their having 
s to their being 
our Books alone 
survive in Greek. Tannery, as we have seen, conjectured 
that, in like manner, the first six of the thirteen Books of 
Diophantus’s Arithmetica survive because Hypatia wrote 
commentaries on these Books only and did not reach the 
others. 
The first writer who calls for notice in this chapter is one 
who was rather more than a commentator in so far as he 
wrote a couple of treatises to supplement the Conics of 
Apollonius, I mean Serenus. Serenus came from Antinoeia 
or Antinoupolis, a city in Egypt founded by Hadrian (a. d. 
117-38). His date is uncertain, but he most probably be 
longed to the fourth century a.d., and came between Pappus 
and Theon of Alexandria. He tells us himself that he wrote 
a commentary on the Conics of Apollonius. 1 This has 
perished and, apart from a certain proposition ‘of Serenus 
the philosopher, from the Lemmas ’ preserved in certain manu 
scripts of Theon of Smyrna (to the effect that, if a number of 
rectilineal angles be subtended at a point on a diameter of a 
circle which is not the centre, by equal arcs of that circle, the 
angle nearer to the centre is always less than the angle more 
remote), we have only the two small treatises by him entitled 
On the Section of a Cylinder and On the Section of a Cone. 
These works came to be connected, from the seventh century 
onwards, with the Conics of Apollonius, on account of the 
affinity of the subjects, and this no doubt accounts for their 
survival. They were translated into Latin by Commandinus 
in 1566 ; the first Greek text was brought out by Halley along 
with his Apollonius (Oxford 1710), and we now have the 
definitive text edited by Heiberg (Teubner 1896). 
(a) On the Section of a Cylinder. 
The occasion and the object of the tract On the Section of 
a Cylinder are stated in the preface. Serenus observes that 
many persons who were students of geometry were under the 
erroneous impression that the oblique section of a cylinder 
was different from the oblique section of a cone known as an 
ellipse, whereas it is of course the same curve. Hence lie 
thinks it necessary to establish, by a regular geometrical 
1 Serenus, Opuscula, ed. Heiberg, p. 52. 25-6.