Excerpt from Newton's Principia, First Book, Sections I., II., III: With Notes and Illustrations, and a Collection of Problems Principally Intended as Examples of Newton's Methods It is generally advisable not to deviate from Newton's words in the demonstrations of the Lammas; but in many cases, I suppose purposely, he expressed himself very concisely, as in Lemmas IV. And x., and he was contented with simply giving the enunciation of Lemma v.; therefore in these cases interpolations have been made which, I believe, are in accordance with Newton's plan of demonstration. Throughout the Problems and Theorems which depend upon the sixth proposition, the variations are replaced by equations. By this method of treating the subject I conceive that clearer ideas of the meaning of each step are obtained by the student. 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.

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