A history of Greek mathematics - Wilbourhall.org

SERENUS 519
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 Conies 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 belonged
to the fourth century A.D., and came between Pappus
and Theon of Alexandria. He tells us himself that he wrote
the philosopher, from the Lemmas '
a commentary on the Conies of Apollonius. 1 This has
perished and, apart from a certain proposition of Serenus
'
preserved in certain manuscripts
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 Conies 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 he
thinks it necessary to establish, by a regular geometrical
1
Serenus, Opuscula, ed. Heiberg, p. 52. 25-6.