Excerpt from The Elements of the Integral Calculus: With Its Applications to Geometry The third section contains the elements Of a theory of almost boundless extent, the theory Of Differential Equations. As far as equations Of two variables and Of the first order are. Concerned, and beyond which the powers Of the calculus are at present but very limited, the information conveyed in this section will, it is thought, be found to be sufficiently copious. I have endeavoured to render this part of the subject clear and intelligible, and have, in some cases, preferred appearing lengthy where brevity might involve any Obscurity, as in the article on Riccati's equation, for instance In the latter part Of this section I have compressed into small compass several topics Of a nature too difficult and too extensive to be completely discussed in a work Of this kind; but I have taken care to direct the inquiring student to the sources where more satisfactory information may be Obtained I hope, also, to touch again upon these matters at a more convenient opportunity; in the mean time, I trust that the three volumes now finished may contribute something towards improving the taste and exciting the inquiries Of the young analyst. 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.