INTRODUCTION BY THE TRANSLATOR.
The object of the author, in composing this work, as stated by him in his preface, was to reduce all the known phenomena of the system of the world to the law of gravity, by strict mathematical principles; and to complete the investigations of the motions of the planets, satellites, and comets, begun by Newton in his Principia. This he has accomplished, in a manner deserving the highest praise, for its symmetry and completeness; but from the abridged manner, in which the analytical calculations have been made, it has been found difficult to be understood by many persons, who have a strong and decided taste for mathematical studies, on account of the time and labour required, to insert the intermediate steps of the demonstrations, necessary to enable them easily to follow the author in his reasoning. To remedy, in some measure, this defect, has been the chief object of the translator in the notes. It is hoped that the facility, arising from having the work in our own language, with the aid of these explanatory notes, will render it more accessible to persons who have been unable to prepare themselves for this study by a previous course of reading, in those modern publications, which contain the many important discoveries in analysis, made since the time of Newton. It is expected that the reader should be acquainted with the common principles of spherical trigonometry, conic sections, and those branches of the fluxionary, or differential calculus, usually found in elementary treatises on this subject, in this country; and as frequent use is made of the rules for the products of the sines and cosines of angles, he, it was thought expedient to collect together, at the end of this Introduction, such formulas as are of frequent use. The demonstrations of these formulas may be found in most treatises of trigonometry, and some of them occur in the notes on this work; the methods in which these demonstrations may be obtained, as well as those of the common problems of spherical trigonometry, are also briefly pointed out, in the appendix, at the end of this volume, which may be referred to, in cases where it may be found
