Encyclopaedia Britannica Or A Dictionary Of Arts Sciences And Miscellaneous Literature Vol 13 Of 18

Author : Thomas Spencer Baynes
Publisher : Forgotten Books
ISBN 13 : 9780282437350
Total Pages : 908 pages
Book Rating : 4.4/5 (373 download)

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Download or read book The Encyclopaedia Britannica, Vol. 13 written by Thomas Spencer Baynes and published by Forgotten Books. This book was released on 2017-07-19 with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Encyclopaedia Britannica, Vol. 13: A Dictionary of Arts, Sciences, and General Literature Mathematicians have differed as to the best way of expounding the principles of the calculus. Newton, as has already been stated, employed the theory of motion as the means of connecting its doctrines with the principles of ordinary analysis. Leibnitz, again, with the same view, conceived quantity as passing from one degree of magni tude to another by the continual addition of infinitely small parts. The mind finds no great dificnlty in dis tinctly apprehending the subject in either way. Objec tions have, however, been taken to both, and attempts made to substitute a better. Euler considered the infinitely small quantities of Leibnits es absolutely zeros, that have to each other ratios derived from those of the vanishing quantities which they replace. D'alembert proposed to make the basis of the calculus the consideration of the ratios of the limits of quantities. This method, as was indeed stated by d'alembert, does not difier in any material respect from Newton's prime and ultimate ratios. An English mathematician, Landon, substituted for the Newtonian method of fiuxions another purely algebraical. His views are contained in a work entitled The Residual Analysis, a new brands of the Algebraic Art Lagrange, too, in the Memoirs of the Berlin Academy for 177 2, proposed to base the calculus alto gether on the expansion of functions, and thus to establish it on algebraical principles merely. He subsequently developed his method in his Thor-is doe Fondionr Analyliquss and in his cons sur ls Calcul des Fondions Lagrange, however, adopted the indai tesimal method as the basis of his most important work, via, the Heeunique Analytique. He states in his preface to its second edition (1811) that when we have properly conceived the spirit of the infinitesimal method, and are convinced of the exactness of. Its results by the geometrical method of prime and ultimate ratios, or by the analytical method of derived functions, we may employ infinitely small quantities as a sure and valuable means of abridging and eimyrlifying our demonstrations. 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.