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Excerpt from Treatise on the Differential and Integral Calculus, and the Calculus of Variations A knowledge of this branch of the Pure Mathematics is absolutely necessary, before any one can successfully undertake the perusal of works on Natural Philosophy, in which the effects of the observed laws that govern the material world are reduced to calculation. For Students deficient in this knowledge, yet anxious to obtain as much as may enable them to master the chief analytical difficulties incident to the study of Elementary Treatises on the Mixed Mathematics, this book has been written: and with the hope that by its means, a subject of high interest may be rendered accessible to an increased number of readers. The Table of Contents which accompanies the work will sufficiently exhibit its plan, as well as the subjects treated of in it. 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.