Newton's Principia - Sections I. II. III., With Notes and Illustrations, Also a Collection of Problems Principally Intended as Examples of Newton's Methods #245306

In publishing the following work, my principal intention is to explain difficulties, which may be encountered by the student on first reading the Principia, and to illustrate the advantages of a careful study of the methods employed by Newton, by showing the extent to which they may be applied in the solution of problems. I have also endeavoured to give assistance to the student who is engaged in the study of the higher branches of Mathematics, by representing in a geometrical form several of the processes employed in the Differential and Integral Calculus, and in the analytical investigations of Dynamics.<br><br>In my version of the first section and the beginning of the second I have adhered as closely as I could to the original form; and, in the cases in which sections have been inters polated, or the form of demonstration changed, I have indicated such changes and interpolations by brackets.<br><br>Although it is generally advisable not to deviate from Newton's words in the demonstrations of the Lemmas, yet 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.; in these cases, therefore, interpolations are made which, I believe, are in accordance with Newton's plan of demonstration.<br><br>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.