THIS book is intended to form a companion volume to my edition of the treatise of Apollonius on Conic Sections lately published. If it was worth while to attempt to make the work of "the great geometer" accessible to the mathematician of to-day who might not be able, in consequence of its length and of its form, either to read it in the original Greek or in a Latin translation, or, having read it, to master it and grasp the whole scheme of the treatise, I feel that I owe even less of an apology for offering to the public a reproduction, on the same lines, of the extant works of perhaps the greatest mathematical genius that the world has ever seen.