PREFACE TO THE THIRD EDITION. THE Geometry of Conics has been recast in the third edition, so as to serve as an introduction to a larger work now approaching completion. The characteristic feature of the edition is the use of the Eccentric Circle, which contributes to a concise and uniform treatment of the three species of conics. The Asymptotes of the hyperbola are shewn to be coincident with its self-conjugate diameters, and their properties are deduced from a limiting case of a property of conjugate diameters in general. The principle that Chord-properties should be proved independently of Tangent-properties is still adhered to, although in the general rearrangement of the text it seemed no longer desirable to confine the two classes of properties to separate chapters. The work now to some extent resembles my first work on Geometrical Conics, published in 1863; but the general chapter has been made more complete than I was then able to make it. October 1879. |