Geometrical Conic Sections, An Elementary Treatise in Which the Conic Sections Are Defined as the Plane Sections of a Cone, and Treated by the Method of Projections (Classic Reprint)

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Excerpt from Geometrical Conic Sections, An Elementary Treatise in Which the Conic Sections Are Defined as the Plane Sections of a Cone, and Treated by the Method of ProjectionsFor every triangle may be divided by a line through one of the angular points parallel to the line of intersection into two, each having its base parallel and its altitude at right angles to the line of intersection: the base of each will be unaltered by projection, the altitude diminished in the maximum ratio. Hence the area of each and therefore of the two together will be diminished in the maximum ratio. Hence, whatever its magnitude or position, every triangle is diminished by projection in the maximum ratio Of the planes.But every figure, whether rectilinear or curvilinear, may be as nearly occupied by triangles as we please, by making them sufficiently numerous. Each of these will be diminish ed by projection in the maximum ratio of the planes, and therefore the figure composed of them will be diminished in the same ratio.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.