THE PLAN1SPHAERIUM OF PTOLEMY 293
of oblique circular cones has led to the conjecture that Apollo
nius was the discoverer of the method. But Ptolemy makes no
mention of Apollonius, and all that we know is that Synesius
of Gyrene (a pupil of Hypatia, and born about a.d. 365-370)
attributes the discovery of the method and its application to
Hipparchus; it is curious that he does not mention Ptolemy’s
treatise on the subject, but speaks of himself alone as having
perfected the theory. While Ptolemy is fully aware that
circles on the sphere become circles in the projection, he says
nothing about the other characteristic of this method of pro
jection, namely that the angles on the sphere are represented
by equal angles on the projection.
We must content ourselves with the shortest allusion to
other works of Ptolemy. There are, in the first place, other
minor astronomical works as follows:
(1) ^ao-ei? duXavcou da-Ttpcov of which only Book II sur
vives, (2) 'TiroOecreis tcov TrXavcopeuoou in two Books, the first
of which is extant in Greek, the second in Arabic only, (3) the
inscription in Canobus, (4) Upo^eipcou Kavovcov SLaracns Kal
\jrr](po(f)opca. All these are included in Heiberg’s edition,
vol. ii.
The Optics.
Ptolemy wrote an Optics in five Books, which was trans
lated from an Arabic version into Latin in the twelfth
century by a certain Admiral Eugenius Siculus 1 ; Book I,
however, and the end oi Book Y are wanting. Books I, II
were physical, and dealt with generalities; in Book III
Ptolemy takes up the theory of mirrors, Book IV deals with
concave and composite mirrors, and Book V with refraction.
The theoretical portion would suggest that the author was
not very proficient in geometry. Many questions are solved
incorrectly owing to the assumption of a principle which is
clearly false, namely that ‘ the image of a point on a mirror is
at the point of concurrence of two lines, one of which is drawn
from the luminous point to the centre of curvature of the
mirror, while the other is the line from the eye to the point
1 See G. Govi, L'otticu di Claudio Tolomeo di Eugenio Ammiraglio d*
Sicilia,.. .Torino, 1884 r and particulars in G. Loria. Le acienze exalte
nelV antica Grecia, pp. ¿70, 671.
