An Elementary Treatise On The Integral Calculus Containing Applications To Plane Curves And Surfaces And Also A Chapter On The Calculus Of Variations With Numerous Examples PDF Download

Excerpt from An Elementary Treatise the Integral Calculus: Containing Applications to Plane Cur Curves and Surfaces, With Numerous Examples This book has been written as a companion volume to my Treatise on the Differential Calculus, and in its construction I have endeavoured to carry out the same general plan on which that hook was composed. I have, accordingly, studied simplicity so far as was consistent with rigour of demonstration, and have tried to make the subject as attractive to the beginner as the nature of tho Calculus would permit. I have, as far as possible, confined my attention to the general principles of Integration, and have endeavoured to arrange the successive portions of the subject in the order best suited for the Student. I have paid considerable attention to the geometrical applications of the Calculus, and have introduced a number of the leading fundamental properties of the more important curves and surfaces, so far as they are connected with the Integral Calculus. This has led me to give many remarkable results, such as Steiner's general theorems on the connexion of pedals and roulettes, Amsler's Planimeter, Kempe's theorem, Landen's theorems on tho rectification of the hyperbola, Genocchi's theorem on the rectification of the Cartesian oval, and others which have not been usually included in text-books on the Integral Calculus. A Chapter has been devoted to the discussion of Integrals of Inertia. 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.