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Excerpt from Lessons Introductory to the Modern Higher Algebra I have to thank my friends Dr. Hart, Mr. Traill, and Mr. Burnside, for help given me at various times in the revision Of the pi'oofs' Of this work, though, in justice to these gentlemen, I must add that there is a considerable part Of it which was printed under circumstances where I could not have the benefit Of their assistance, and for the errors in which they are not responsible. I have already intimated that my Obligations to Messrs. Cayley and Sylvester are not merely those which every one must Owe who writes on a branch of Algebra which they have done so much to create. I was in constant correspondence with them at the time when some of their most important discoveries were made, and I owe my knowledge Of these discoveries as much to their letters as to any printed papers. I must also ex press my thanks to M. Hermite for his Obliging readiness to remove by letter difficulties which cc curred to me in my Study of his published memoirs. 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 technology 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.