Book II

of which is entirely devoted to the problem of drawing a circle to touch three given circles (Apollonius's solution can, with the aid of Pappus's auxiliary propositions, be satisfactorily restored); (3) _Plane Loci_, i. e. loci which are straight lines or circles; (4) Νευσεις {Neuseis}, _Inclinationes_ (the general problem called a νευσις {neusis} being to insert between two lines, straight or curved, a straight line of given length _verging_ to a given point, i. e. so that, if produced, it passes through the point, Apollonius restricted himself to cases which could be solved by 'plane' methods, i. e. by the straight line and circle only).

Apollonius is also said to have written (5) a _Comparison of the dodecahedron with the icosahedron_ (inscribed in the same sphere), in which he proved that their surfaces are in the same ratio as their volumes; (6) _On the cochlias_ or cylindrical helix; (7) a 'General Treatise', which apparently dealt with the fundamental assumptions, &c., of elementary geometry; (8) a work on _unordered irrationals_, i. e. irrationals of more complicated form than those of Eucl.