OF THE PRINCIPAL FORMULÆ AND RESULTS OF Pure Mathematics. BY CHARLES BROOKE, M. B. OF ST. JOHN'S COLLEGE. CAMBRIDGE: Printed by J. Smith, Printer to the University. SOLD BY J. & J. J. DEIGHTON, CAMBRIDGE; AND C. J. G. & F. RIVINGTON, LONDON. 1829 of ' 10-13-31 244 63 PREFACE. . THE Author of the following pages, having experienced the want of a compendious collection of results, in common probably with most mathematical students, endeavoured, during his undergraduateship, to form such a collection for his own use. This has since that time been arranged, and considerably enlarged, and is now laid before the Public, in the hope that it may in some measure facilitate the labour of the analyst, by enabling him to compare and apply the results of previous investigation. It was originally intended to restrict these pages to a mere collection of formulæ, but it is hoped that in adding an outline of many useful methods of operation, sufficiently detailed to render' them applicable to particular cases, the increased size of the work will not be deemed an objection. The references that have been given will probably be found sufficiently minute to enable the reader to find without difficulty any demonstration he may require; had the proof of each result been separately quoted, the size of the work must unavoidably have been much' increased. The object has been to refer to works of the greatest authority, and to those which can most readily be procured. The principles of Notation that have been adopted in the following pages are explained in the Appendix ; where will also be found an explanation of the very ingenious and |