This volume publishes the books b, c, and d of the "Collection," as the first book and part of the second have been lost. It is likely that the first book dealt with numerical problems since the surviving part of the second book addresses Apollonius's theory on large numbers, expressed as powers of 10,000.

The third book discusses the finding of two means in proportion for given two lines, the theory of means, presents some "paradoxes," and, finally, provides a method for inscribing the five regular polyhedra in a sphere, which is entirely different from that of Euclid.

The fourth book formulates a generalization of the Pythagorean theorem, discusses a section known as "arbelos," presents previous as well as his own solutions to the problem of squaring the circle, describes the properties of a spiral inscribed in a sphere, and, finally, presents older and his own solutions to the problem of trisecting an acute angle.