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ANHARMONIC RATIO AND PROJECTION,
WITH NUMEROUS EXAMPLES.
C. TAYLOR, B. A.,
SCHOLAR OF ST. JOHN'S COLLEGE, CAMBRIDGE.
This work contains elementary proofs of the principal properties of Conic Sections, together with Chapters on Projection and Anharmonic Ratio. The term Conic, elsewhere frequently employed as an abbreviation, is here formally adopted, with reference to the fact that it is no longer usual to define the curves in question as sections of a surface. The term Conic Section is introduced in Chapter XI.
In Chapter II., some fundamental propositions are proved by methods applicable to all Conics, a Conic being considered as the locus of a point whose distance from a fixed point bears a constant ratio to its perpendicular distance from a fixed straight line. The propositions of this Chapter have been selected as either important in themselves or useful in their application. To the latter class belong Props. VII., VIII. which are useful in proving the Anharmonic Properties of Conics. Prop. XII., in which the fundamental property of diameters is established, leads to important simplifications. Prop. XIII., which follows immediately from it, has been applied to prove that, in the ellipse, CV.CT=CP, (p. 81). The Lemma is shown, in the Appendix, to be closely connected with some important properties of central Conics.