An Investigation of the Conditions for Reality of Certain Characteristics of the Becercular Cuspidal Quartic Curve PDF Download
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Author: Brother Damian Connelly
Publisher:
ISBN:
Category : Curves, Quartic
Languages : en
Pages : 28
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Book Description
Author: Brother Damian Connelly
Publisher:
ISBN:
Category : Curves, Quartic
Languages : en
Pages : 28
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Book Description
Author: Damian Connelly
Publisher:
ISBN: 9780598768568
Category :
Languages : en
Pages : 17
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Book Description
Author: Damian Connelly (des Frères des écoles chrétiennes, Le F.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
Author: Joseph Nelson Rice
Publisher: Forgotten Books
ISBN: 9781330209219
Category : Mathematics
Languages : en
Pages : 36
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Book Description
Excerpt from On the in-and-Circumscribed Triangles of the Plane Rational Quartic Curve The last and most difficult case is when the six curves are all of them one and the same carve. It is to be noted that this formula gives the same number of triangles as has been found by the method used later. For example, in the case of the rational quartic, where a=4, A=6, a=18, the number of triangles is 8, which corresponds to that found on page 18. For the cuspidal quartic, where a=4, A=5, a=16, the number is two, which also corresponds to the number found on page 22. In this paper it is proposed to look into the existence and actual number of such triangles for the following types of rational quartics: I. Quartic with three double points. II. Quartic with one double point and a tacnode. III. Quartic with a triple point. IV. Quartic with two double points and a cusp. This discussion was led up to by preliminary work on the three-cusped rational quintic. Upon subjection to a quadratic transformation this curve goes into a rational quartic, which, it will be shown, has triangles of the kind here mentioned. Accordingly, it will first be proved that the quintic can have certain conditions imposed upon its coefficients so that it may acquire an additional cusp or a tacnode without degenerating. It will also be shown that it cannot have a triple point. 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.
Author: A. B. Basset
Publisher: Forgotten Books
ISBN: 9781330871584
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Excerpt from An Elementary Treatise on Cubic and Quartic Curves The present work originated in certain notes, made about twenty-five years ago, upon the properties of some of the best-known higher plane curves; but upon attempting to revise them for the press, it appeared to me impossible to discuss the subject adequately without investigating the theory of the singularities of algebraic curves. I have accordingly included Plucker's equations, which determine the number and the species of the simple singularities of any algebraic curve; and have also considered all the compound singularities which a quartic curve can possess. This treatise is intended to be an elementary one on the subject. I have therefore avoided investigations which would require a knowledge of Modern Algebra, such as the theory of the invariants, covariants and other concomitants of a ternary quantic; and have assumed scarcely any further knowledge of analysis on the part of the reader, than is to be found in most of the ordinary text-books on the Differential Calculus and on Analytical Geometry. I have also endeavoured to give special prominence to geometrical methods, since the experience of many years has convinced me that a judicious combination of geometry and analysis is frequently capable of shortening and simplifying, what would otherwise be a tedious and lengthy investigation. 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.
