A history of Greek mathematics Vol.II from Aristarchus to Diophantus by Heath, Thomas Little, Sir, 1921

ASTRONOMY, ETC. 109
word 'Ao-TpovofjLia (Suidas), which latter word is perhaps a mistake
for 'Ao-rpoOeo-la corresponding to the title 'AcrrpoOeo-icu
(coSloov found in the manuscripts. The work as we have it
contains the story, mythological and descriptive,
of the constellations,
&c., under forty-four heads ; there is little or
nothing belonging to astronomy proper.
Eratosthenes is also famous as the first to attempt a scientific
chronology beginning from the siege of Troy; this was the
subject
of his Xpovoypa(piai, with which must be connected
the separate 'OXv/imovLKai in several books. Clement of
Alexandria gives a short resumS of the main results of the
former work, and both works were largely used by Apollodorus.
Another lost work was on the Octaeteris (or eightyears'
period), which is twice mentioned, by Geminus and
Achilles ; from the latter we learn that Eratosthenes regarded
the work on the same subject attributed to Eudoxus
as not genuine. His Geographica in three books is mainly
known to us through Suidas's criticism of it. It began with
a history of geography down to his own time ; Eratosthenes
then proceeded to mathematical geography, the spherical form
of the earth, the negligibility in comparison with this of the
unevennesses caused by mountains and valleys, the changes of
features due to floods, earthquakes and the like. It would
appear from Theon of Smyrna's allusions that Eratosthenes
estimated the height of the highest mountain to be 10 stades
or about 1/ 8000th part of the diameter of the earth.
XIV
CONIC SECTIONS. APOLLONIUS OF PERGA
A. HISTORY OF CONICS UP TO APOLLONIUS
Discovery of the conic sections by Menaechmus.
We have seen that Menaechmus solved the problem of the
two mean proportionals (and therefore the duplication of
the cube) by means of conic sections, and that he is credited
with the discovery of the three curves ; for the epigram of
Eratosthenes speaks of ' the triads of Menaechmus ', whereas
of course only two conies, the parabola and the rectangular
hyperbola, actually appear in Menaechmus's solutions. The
question arises, how did Menaechmus come to think of obtaining
curves by cutting a cone 1
On this we have no information
whatever.
Democritus had indeed spoken of a section of
a cone parallel and very near to the base, which of course
would be a circle, since the cone would certainly be the right
circular cone. But it is probable enough that the attention
of the Greeks, whose observation nothing escaped, would be
attracted to the shape of a section of a cone or a cylinder by
a plane obliquely inclined to the axis when it occurred, as it
often would, in real life ; the case where the solid was cut
right through, which would show an ellipse, would presumably
be noticed first, and some attempt would be made to
investigate the nature and geometrical measure of the elongation
of the figure in relation to the circular sections of the
same solid ; these would in the first instance be most easily
ascertained when the solid was a right cylinder ; it would
then be a natural question to investigate whether the curve
arrived at by cutting the cone had the same property as that
obtained by cutting the cylinder. As we have seen, the