A history of Greek mathematics - Wilbourhall.org

:
THE PLAN1SPEAERIUM OF PTOLEMY 293
of oblique circular cones has led to the conjecture that Apollonius
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 projection,
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) $d(T€is anXavtov da-repcou of which only Book II survives,
(2) 'TTTodiareis t&v TrXaucofxeucou in two Books, the first
of which is extant in Greek, the second in Arabic only, (3)
inscription in Canobus, (4) Ilpoxeipcoy kclvovcdv SiaTacns kcu
yjrr)(po(popia. All these are included in Heiberg's edition,
vol. ii.
the
The Optics.
Ptolemy wrote an Optics in five Books, which was translated
from an Arabic version into Latin '
century by a certain Admiral Eugenius Siculus *
; Book
in the twelfth
I,
however, and the end of Book V 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'ottica di Claudio Tolomeo di Euyenio Ammiraglio dA
Skilia, ... Torino, 1884; and particulars in G. Loria. Le scienze e*atte
nelV antica Grecia, pp. 570, 571.