PREFACE.

This book is intended to be a companion volume to my edition of the treatise of Apollonius on Conic Sections, which was published recently. If it was worthwhile to attempt to make the work of "the great geometer" Referring to Apollonius of Perga. accessible to the modern mathematician—who might be unable to read it in the original Greek or in a Latin translation, or who might find it difficult to master its complex structure—I feel I owe even less of an apology for offering a reproduction, on the same principles, of the extant works of perhaps the greatest mathematical genius the world has ever seen.

Michel Chasles has drawn an instructive distinction between the predominant features of the geometry of Archimedes and that of Apollonius. Their works, says Chasles, may be regarded as the origin and basis of two great inquiries that seem to divide the domain of geometry between them. Apollonius is concerned with the Geometry of Forms and Situations, while in Archimedes we find the Geometry of Measurements, dealing with the squaring (quadrature) of curvilinear plane figures and the squaring and cubing (cubature) of curved surfaces. These investigations "gave birth to the calculus of the infinite, conceived and perfected successively by Kepler, Cavalieri, Fermat, Leibniz, and Newton." Whether we view Archimedes as the man who, with limited means, successfully performed what are essentially integrations to find the area of a parabolic segment, or as...

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