The Cone And Its Sections Treated Geometrically
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The Cone And Its Sections Treated Geometrically
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Author : S. A. Renshaw
language : en
Publisher:
Release Date : 1875
The Cone And Its Sections Treated Geometrically written by S. A. Renshaw and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1875 with Conic sections categories.
The Cone And Its Sections Treated Geometrically
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Author : S. A. Renshaw
language : en
Publisher: BoD – Books on Demand
Release Date : 2023-11-17
The Cone And Its Sections Treated Geometrically written by S. A. Renshaw and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-17 with Fiction categories.
Reprint of the original, first published in 1875.
The Cone And Its Sections
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Author : S. A. Renshaw
language : en
Publisher: Forgotten Books
Release Date : 2015-06-26
The Cone And Its Sections written by S. A. Renshaw and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
Excerpt from The Cone and Its Sections: Treated Geometrically Of the works of the ancient Geometricians that hare descended to us, none perhaps has been more justly celebrated than the Treatise of Apllonius, of Perga, on the Conic Sections - a work that has, apparently, maintained its superiority over every other Treatise that has since been written on the subject. According to his Commentator, Eutocius, Apollonius was the first to derive the Sections from the Scalene Cone by different inclinations of the Cutting Plane, and in accordance with this derivation of the Curves he deduces the Primary Properties of the Sections from the Cone itself. Modern writers have however to a considerable extent departed from this method - commencing their works by definitions of the Curves described in plano, such definitions being adapted to or derived from Properties of the Curves themselves; a strong tendency has however been shown, and especially by one Geometer of the last century, Hamilton, to revert to the Apollonian method. Accordingly in the present work the Primary Properties of the Sections are derived from the Cone, and it is believed that this is the case to a greater extent than in any previous Treatise. The reasons that have principally led to this course of treatment, are first, that the elementary Properties alluded to, and contained in Prop. V., are by the help of the most elementary Properties of the Cone demonstrated as it were together, and their connection and mutual dependence shown in the clearest manner; and secondly, it is presumed that by becoming acquainted with these principles as thus deduced, a deeper impression is obtained of their great and essential importance than could possibly be the case were that acquaintance made by deductions from any definition of the Curves in plano, seeing that according to the definition adopted the process of deduction must necessarily vary. These Properties will then be found demonstrated both from the Scalene and Right Cone, and although their derivation from the former involves considerable prolixity, it is believed that the reader will be well repaid for the time and patience expended in the investigation. The description of the Curves in plano and the derivation of their Properties thence, has however not been omitted; the method adopted in this part of the work being that of the Generating Circle, by which means not only the elementary, but many other Properties of the Sections can be proved both easily and elegantly. In the Articles on the Anharmonic Properties of the Sections, demonstrations of two important Theorems have been specially added in further illustration of the utility of this principle. 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.
The Cone And Its Sections
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Author : S. A. Renshaw
language : en
Publisher: Forgotten Books
Release Date : 2018-01-17
The Cone And Its Sections written by S. A. Renshaw and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-17 with Mathematics categories.
Excerpt from The Cone and Its Sections: Treated Geometrically Modern writers have however to a considerable extent departed from this method commencing their works by definitions of the Curves described in plano, such definitions being adapted to or derived from Properties of the Curves themselves; a strong tendency has however been shown, and especially by one Geometer of the last century, Hamilton, to revert to the Apollonian method. Accordingly in the present work the Primary Properties of the Sections are derived from the Cone, and it is believed that this is the case to a greater extent than in any previous Treatise. The reasons that have principally led to this course of treatment, are first, that the elementary Properties alluded to, and contained in Pr0p. V., are by the help of the most elementary Properties of the Cone demonstrated as it were together, and their connection and mutual dependence shown in the clearest manner; and secondly, it is presumed that by becoming acquainted with these principles as thus deduced, a deeper impression is obtained of their great and essential importance than could possibly be the case were that acquaintance made by deductions from any definition of the Curves in pla no, seeing that according to the definition adopted the process of deduction must necessarily vary. These Properties will then be found demonstrated both from the Scalene and Right Cone, and although their derivation from the former involves considerable prolixity, it is believed that the reader will be well repaid for the time and patience expended in the 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.
Conic Sections Treated Geometrically
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Author : William Henry Besant
language : en
Publisher:
Release Date : 1869
Conic Sections Treated Geometrically written by William Henry Besant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1869 with Conic sections categories.
Conic Sections Treated Geometrically 1875
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Author : William Henry Besant
language : en
Publisher:
Release Date : 2008-06-01
Conic Sections Treated Geometrically 1875 written by William Henry Besant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-01 with categories.
This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.
Conic Sections
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Author : W. H. Besant
language : en
Publisher: Merchant Books
Release Date : 2009-09-01
Conic Sections written by W. H. Besant and has been published by Merchant Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-01 with Mathematics categories.
An Unabridged, Digitally Enlarged Printing Of The Ninth Edition, To Include: The Construction Of A Conic Section, And General Properties - The Parabola - The Ellipse - The Hyperbola - The Rectangular Hyperbola - The Cylinder And The Cone - The Similarity Of Conics, The Areas Of Conics, And The Curvatures Of Conics - Orthogonal Projections - Of Conics In General - Ellipses As Roulettes And Glissettes - Miscellaneous Problems I - Harmonic Properties, Poles And Polars - Reciprocal Polars - The Construction Of A Conic From Given Conditions - The Oblique Cylinder, The Oblique Cone, And The Conoids - Conical Projection - Miscellaneous Problems Ii
Conic Sections
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Author : W. H. Besant
language : en
Publisher:
Release Date : 2016-11
Conic Sections written by W. H. Besant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11 with categories.
The Construction Of A Conic Section, And General Properties - The Parabola - The Ellipse - The Hyperbola - The Rectangular Hyperbola - The Cylinder And The Cone - The Similarity Of Conics, The Areas Of Conics, And The Curvatures Of Conics - Orthogonal Projections - Of Conics In General - Ellipses As Roulettes And Glissettes - Miscellaneous Problems I - Harmonic Properties, Poles And Polars - Reciprocal Polars - The Construction Of A Conic From Given Conditions - The Oblique Cylinder, The Oblique Cone, And The Conoids - Conical Projection - Miscellaneous Problems ll
Conic Sections
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Author : William Henry Besant
language : en
Publisher:
Release Date : 1907
Conic Sections written by William Henry Besant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1907 with Conic sections categories.
Conic Sections Treated Geometrically Classic Reprint
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Author : W. H. Besant
language : en
Publisher:
Release Date : 2016-06-26
Conic Sections Treated Geometrically Classic Reprint written by W. H. Besant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-26 with Mathematics categories.
Excerpt from Conic Sections, Treated Geometrically For the more general methods of projections, of reciprocation, and of anharmonic properties, the stu dent will consult the treatises of Chasles, Poncelet, Salmon, Townsend, Ferrers, Whitworth, and others. 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.