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Excerpt from Geometrical Treatise on the Conic Sections: With an Appendix, Containing Formulae for Their Quadrature, &C With this view, perspicuity and symmetry have been particularly studied, both in the arrangement of the materials, and the demonstration of the particu lar propositions. Only the most elementary proposi tions of geometry have been made use of; and while each of the three sections has been treated as a distinct curve, a general view has been taken of the subject, and their analogous properties deduced from their respective definitions in an uniform man ner, by the same constructions, and, in many instan ces, in the same words. It might have been easy, in such cases, to have included the three curves in the same general enunciation but the method which has been followed has the advantage of placing in each case a distinct Object before the mind, at the same time that the connection and mutual relations of all the curves is rendered obvious by the comparison of those propositions in which their analogous properties are demonstrated. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.