chellensis from the free version in Arabic made in 983 by
Abu 'l-Fath of Ispahan and preserved in a Florence MS. But the best
Arabic translation is that made as regards Books i.-iv. by Hilal ibn Abi
Hilal (d. about 883), and as regards Books v.-vii. by Tobit ben Korra
(836-901). Halley used for his translation an Oxford MS. of this
translation of Books v.-vii., but the best MS. (Bodl. 943) he only
referred to in order to correct his translation, and it is still
unpublished except for a fragment of Book v. published by L. Nix with
German translation (Drugulin, Leipzig, 1889). Halley added in his
edition (1710) a restoration of Book viii., in which he was guided by
the fact that Pappus gives lemmas "to the seventh and eighth books"
under that one heading, as well as by the statement of Apollonius
himself that the use of the seventh book was illustrated by the problems
solved in the eighth.

The degree of originality of the _Conics_ can best be judged from
Apollonius' own prefaces. Books i.-iv. form an "elementary
introduction," i.e. contain the essential principles; the rest are
specialized investigations in particular directions. For Books i.-iv. he
claims only that the generation of the curves and their fundamental
properties in Book i. are worked out more fully and generally than they
were in earlier treatises, and that a number of theorems in Book iii.
and the greater part of Book iv. are new. That he made the fullest use
of his predecessors' works, such as Euclid's four Books on Conics, is
clear from his allusions to Euclid, Conon and Nicoteles. The generality
of treatment is indeed remarkable; he gives as the fundamental property
of all the conics the equivalent of the Cartesian equation referred to
_oblique_ axes (consisting of a diameter and the tangent at its
extremity) obtained by cutting an oblique circular cone in any manner,
and the axes appear only as a particular case after he has shown that
the property of the conic can be expressed in the same form with
reference to any new diameter and the tangent at its extremity. It is
clearly the form of the fundamental property (expressed in the
terminology of the "application of areas") which led him to call the
curves for the first time by the names _parabola_, _ellipse_,
_hyperbola_. Books v.-vii. are clearly original. Apollonius' genius
takes its highest flight in Book v., where he treats of normals as
minimum and maximum straight lines drawn from given points to