Excerpt from Lessons Introductory to the Modern Higher Algebra The geometrical importance of this theory is now manifest. When we are given the equation of any curve or surface, the theory of linear transformations at once presents us with equations representing other curves and surfaces, and possessing permanent relations to the given one, which will be unaffected by any change of the axes of co-ordinates. And in like manner the same theory presents us with certain functions of the coefficients of the given equation, the vanishing of which must express a property of the given curve or surface, wholly independent of the choice of axes. Besides these geometrical applications, the theory has other important uses, which I shall not stop to enumerate. 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.