Excerpt from The Theory of Determinants: And Their Applications In the present treatise I have attempted to give an exposition of the Theory of Determinants and their more important applications. In every case where it was possible I have consulted the original works and memoirs on the subject; a list of those I have been able to see is appended as it may be useful to others pursuing the same line of study. At one time I hoped to make this list exhaustive, supplementing my own researches from the literary notices in foreign mathematical journals, but even with this aid I found that it would be necessarily incomplete. In consequence of this the list has been restricted to those memoirs which I have seen, the leading results of which are incorporated either in the body of the text or in the examples. The principal novelty of the treatise lies in the systematic use of Grassmann's alternate units, by means of which the study of determinants is, I believe, much simplified. I have to thank my friend Mr Jas. Barnard, M.A. of St John's College and Mathematical Master at the Proprietary School, Blackheath, for the care he has bestowed on correcting the proofs and for many valuable suggestions. 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.