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A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.
This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.
Excerpt from A Treatise on the Higher Plane Curves: Intended as a Sequel to a Treatise on Conic Sections Considered as a book for advanced readers, I regret that I have not had leisure for the reading necessary to make this work as complete as it ought to be. My know ledge of the older writers on Geometry is, for the most part, either second-hand or superficial and I cannot even claim acquaintance with all of the most remarkable works and memoirs which of late years have been published on the subject. But even such an imperfect compilation as I have been able to make will, I hope, not be useless. In every branch of Mathematics it is desirable that elemen tary treatises should keep pace with the progress of science. A new province can scarcely be considered as gained to analysis until roads have been made through the conquered territory. It is desirable that each new student who Wishes to devote himself to original investi gation in any branch of Mathematics should have his energies as quickly as possible brought to bear upon the undiscovered parts of the science and that his abilities should not be wasted in rediscovering truths known al ready, nor his time frittered away in hunting for them without 'a guide through the wilderness of scientific periodicals. 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.
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