COURSE OF MATHEMATICS. IN TWO VOLUMES. COMPOSED FOR THE USE OF THE ROYAL MILITARY ACADEMY. BY CHARLES HUTTON, LL.D. F.R.S. FORMERLY PROFESSOR OF MATHEMATICS IN THAT INSTITUTION. CONTINUED AND AMENDED BY OLINTHUS GREGORY, LL.D. F.R.A.S. VOL. II. TWELFTH EDITION, WITH CONSIDERABLE ALTERATIONS AND ADDITIONS, BY THOMAS STEPHENS DAVIES, F.R.S. L. & E. F.S.A. ROYAL MILITARY ACADEMY. LONDON: LONGMAN, BROWN, & CO.; J. M. RICHARDSON; J. G. F. & J. RIVINGTON; HAMILTON THE public approbation of my efforts to render the first volume of Dr. Hutton's Course of Mathematics such as the present state of Mathematics requires, has been too undisguisedly manifested by the extensive sale of that volume, to be other than very gratifying to my feelings: and I hope in the next edition of it, to be able to fully carry out those contemplated improvements, which, from various circumstances, I was only able to partially develope in the last. The second volume, here laid before the public, will, I trust, be considered more completely in accordance with the views under which I have officiated as editor, than was the case in the preceding one: and I anticipate with confidence, that the patronage with which the former volume was honoured, will be extended to the present one. This, at least, I can assure my readers, that no exertion or labour has been spared to render it worthy of the continuance of general approbation: and I cannot offer stronger evidence of this, than the fact, that there is not a single line of the original work which has not been recomposed. It may, likewise, be added, that I undertook only the ordinary duties of an editor those of correcting the work for press, and reading the proofs-on corresponding pecuniary conditions. I may, hence, fairly disclaim every mercenary motive in the labours here brought to a close. Hutton's Course was, in fact, the first mathematical work I studied. I may, hence, be allowed to entertain a desire to render it as complete as possible, and, perhaps, to feel a deeper interest in its improvement, than in any work exclusively of my own production. ✓ I now proceed to give a short account of the contents of the present volume. Prefatory to the Spherical Trigonometry there is given a chapter on the Geometry of the Sphere, comprising, besides the propositions usually to be found in other treatises, several curious and important ones used in the course of this work for the completion of discussions of |