A Treatise on the Construction, Properties, and Analogies of the Three Conic Sections (Classic Reprint)

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Excerpt from A Treatise on the Construction, Properties, and Analogies of the Three Conic SectionsA cone is a solid figure formed by the revolution of a right an gled triangle about one Of its sides. (euc. Def. Ll. 3. Sup.) From the manner in which this solid is. Generated, it is evident that if it be cut by a plane parallel to its base, the intersection of the plane with the solid, will be a circle, since this section will coincide with the revolution Of a perpendicular to the fixed side Of the triangle and if it be cut by a plane passing through its vertex, the intersection will be a triangle, the sides of which will correspond to the hypothenuse of the generating triangle, in different positions, or at different periods Of the revolution. If the plane by which the cone is out be not paral lel to the base, or do not pass through the vertex, then the line tra Ced out upon its surface will be one of these curves more particular ly distinguished by the name of conic sections, the properties-of which are to be made the subject Of the following Treatise.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.