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