A Mathematical Treatise

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Excerpt from A Mathematical Treatise: Containing a System of Conic-Sections, With the Doctrine of Fluxions and Fluents, Applied to Various Subjects, Viz., To the Finding the Maximums and Minimums of Quantities, Radii of Evolution, Refraction, ReflectionIn order to this, I confider a Curve-line to be generated by the motion of a point, urged by two powers acting in two difi'erent Directions, the one parallel to the Abfci¿'es and the other parallel to the Ordinates. I prove from thence, that if this point (when arrived at a given place) did continue to move with the velocity it has there, it would proceed in a right line touching the Curve in that place: From whence I conclude that the Direc'tion of the point in the faid place, is in the Tangent: So that the three Direétions being known in each place, the proportion between the velocities of the urging powers is likewife known.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.