OF INFINITESIMAL CALCULUS. BY JOSEPH BAYMA, S.J., Professor of Mathematics in Santa Clara College, S.J., Santa Clara, California. SAN FRANCISCO: A. WALDTEUFEL, 737 MARKET STREET. 1889. 9-21-32 MEI From the Library 9-27-29 PREFACE. THE present treatise, as its title points out, has been based on the principles of the infinitesimal method. I think that this method, besides being the simplest of all for teaching Calculus, as all admit, is also the most consistent and philosophical. Some modern writers, indeed, have tried to discredit it; but, when we examine their reasonings, we soon discover that they have done so because they have failed to grasp the true nature of infinitesimal quantities. This I have endeavored to show in my introduction to this work, where the reader will find not only what I believe to be the exact notion of the infinitesimal, but also a hint at the grounds (elsewhere developed) upon which the infinitesimal method rests its claim to be preferred to its fashionable rival, the method of limits. This work being intended for young men who are supposed to devote a considerable part of their time to the study of mental and of natural philosophy, it has been necessary to limit its developments by giving less prominence to the analytical than to the practical portion of it. But, while anxious not 3 |