ON THE GEOMETRY OF THE CIRCLE AND SOME EXTENSIONS TO CONIC SECTIONS BY THE METHOD OF RECIPROCATION WITH NUMEROUS EXAMPLES BY WILLIAM J. M'CLELLAND, M.A. PRINCIPAL OF THE INCORPORATED SOCIETY'S SCHOOL, SANTRY, DUBLIN London MACMILLAN AND CO. AND NEW YORK All rights reserved PREFACE. My object in the publication of a treatise on Modern Geometry is to present to the more advanced students in public schools and to candidates for mathematical honours in the Universities a concise statement of those propositions which I consider to be of fundamental importance, and to supply numerous examples illustrative of them. Results immediately suggested by the propositions, whether as particular cases or generalized statements, are appended to them as Corollaries. The Examples are printed in smaller type, and are classified under the Articles containing the principal theorems required in their solution. The more difficult ones are fully worked out, and in most cases hints are given to the others. The reader who is familiar with the first six books of Euclid with easy deductions and the elementary formulæ in Plane Trigonometry will thus experience little difficulty in mastering the following pages. I have dwelt at length in Chap. II. on the Theory of Maximum and Minimum. Chap. III. is devoted to the more recent developments of the geometry of the triangle, initiated in 1873 by Lemoine's paper entitled "Sur quelques propriétés d'un point remarquable du triangle." |