Excerpt from On the General Principles Analysis, Vol. 1: Being a Series of Original Investigations in Different Departments of Pure Mathematics The work, of which this is the First Part, was intended to be issued in monthly portions, and to embrace the following topics: 1. Conjugate Functions, and their application to the Analysis of Equations. 2. Researches respecting the Theory of Numbers. 3. A Disquisition on Diverging Series. 4. On Zeros, real and imaginary, Conjugate Points, and Imaginary Logarithms. 5. On certain Theorems of Leibnitz, Abel, Murphy, &c. 6. On the Law of Continuity in Analysis. 7. Miscellaneous Investigations in the Calculus of Operations, the Theory of Probability, the Law of Population, &c. 8. Prefatory matter, in a Dedication to the Earl of Clarendon, containing statements and explanations of interest to the friends of Science. The author feels it necessary here to state, that the further prosecution of this design must, for the present, be suspended. The subscribers to the work, although including some of the most distinguished names in the kingdom, are nevertheless too few in number, as yet, to justify him in incurring the expense of the publication. The proceeds of this First Part of the work are t likely to cover one half of the outlay: as soon as this obstacle is removed, the publication will be regularly proceeded with. The Statements, &c., intended for Part VIII will shortly be printed in a distinct form. The pamphlet will be published separately at One Shilling: the subscribers to the work originally proposed will t be considered as pledged to the purchase of it, r will it be forwarded to them unless expressly ordered. One remark more must be made, though it would be gladly avoided. It was the early-formed resolution of the author that duplicate copies should t be forwarded to any individual subscriber; this resolution was founded upon reasons cogent to his own mind, but which he may, perhaps, here be excused from formally stating. Some of the most eminent persons whose names occur in the following list, have each ordered several copies of the publisher. But the author respectfully requests permission to adhere to his original determination, though at the risk of incurring the charge of inconsistency. His hope and aim was, and is, that his book might, in some degree, be acceptable to science; and he must be suffered to indulge the delusion - if delusion it be - that the countenance extended to it is justified by the expectation of at least partial success in his endeavours, irrespective of all considerations personal to the author. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art techlogy to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.