A Treatise on the Circle and the Sphere (Classic Reprint)

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9781440060380: A Treatise on the Circle and the Sphere (Classic Reprint)
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Excerpt from A Treatise on the Circle and the Sphere

Every beginner in the science of geometry knows that the circle and the sphere have always played a central rôle, yet few people realize that the reasons for this are many and various. Attention was first called to these figures by their mechanical simplicity and importance, and the fortunate position thus won was further strengthened by the Euclidean tradition of limiting geometry, on the constructive side, to those operations which can be carried out with the aid of naught but ruler and compass. Yet these facts are far from sufficient to account for the commanding position which the circle and the sphere occupy to-day.

To begin with, there would seem no a priori reason why those curves which are the simplest from the mechanical point of view should have the greatest wealth of beautiful properties. Had Euclid started, not with the usual parallel postulate, but with the different assumption either of Lobachevski or Riemann, he would have been unable to prove that all angles inscribed in the same circular arc are equal, and a large proportion of our best elementary theorems about the circle would have been lacking. Again, there is no a priori reason why a curve with attractive geometric properties should be blessed with a peculiarly simple cartesian equation; the cycloid is particularly unmanageable in pure cartesian form. The circle and sphere have simple equations and depend respectively on four and five independent homogeneous parameters. Thus, the geometry of circles is closely related to the projective geometry of three-dimensional space, while the totality of spheres gives our best example of a four-dimensional projective continuum.

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Other Popular Editions of the Same Title

9780828402361: A Treatise on the Circle and the Sphere (AMS Chelsea Publishing)

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ISBN 10:  0828402361 ISBN 13:  9780828402361
Publisher: Chelsea Pub Co, 1971
Hardcover

9780821834886: A Treatise on the Circle and the Sphere (Ams Chelsea Publishing)

Americ..., 2004
Hardcover

9781116783018: A Treatise on the Circle and the Sphere

Biblio..., 2009
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9780548968888: A Treatise On The Circle And Sphere (1916)

Kessin..., 2008
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9781345540734: A Treatise on the Circle and Sphere

Arkose..., 2015
Hardcover

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Book Description Forgotten Books, 2017. Paperback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****. Excerpt from A Treatise on the Circle and the Sphere Every writer knows that the pleasantest part of his task consists in writing the preface, for here he has a chance to express his gratitude to the generous friends who have helped him with suggestion and counsel. The present author would especially mention his colleague Professor Maxime bocher, who kindly read the proof of Ch. VIII, and his former pupil Dr. David Barrow, who not only supplied much of the material in Oh. XIV but also did yeoman service in unearth ing mistakes in various parts of the work. Another pupil, Dr. Roger Johnson, has kindly suggested a number of minor corrections, mostly of a bibliographical nature. Yet the greatest debt is not to any one of these. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at 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. Seller Inventory # AAV9781440060380

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Book Description Forgotten Books. Paperback. Condition: New. 612 pages. Dimensions: 9.0in. x 6.0in. x 1.4in.Attention was first called to these figures by their mechanical simplicity and importance, and the fortunate position thus won was further strengthened by theE uclidean tradition of limiting geometry, on the constructive side, to those operations which can be carried out with the aid of naught but ruler and compass. Yet these facts are far from sufficient to account for the commanding position which the circle and the sphere occupy to-day. To begin with, there would seem no a priori reason why those curves which are the simplest from the mechanical point of view should have the greatest wealth of beautiful properties. Had Euclid started, not with the usual parallel postulate, but with the different assumption either of Lobachevski orR iemann, he would have been unable to prove that all angles inscribed in the same circular arc are equal, and a large proportion of our best elementary theorems about the circle would have been lacking. A gain, there is no a priori reason why a curve with attractive geometric properties should be blessed with a peculiarly simple cartesian equation; the cycloid is particularly unmanageable in pure cartesian form. The circle and sphere have simple equations and depend respectively on four and five independent homogeneous parameters. Thus, the geometry of circles is closely related to i the projective geometry of three-dimensional space, while the totality of spheres gives our best example of a four-dimensional projective continuum. (Typographical errors above are due to OCR software and dont occur in the book. )About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology. Forgotten Books Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Seller Inventory # 9781440060380

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Book Description Forgotten Books, 2017. Paperback. Condition: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. Excerpt from A Treatise on the Circle and the Sphere Every writer knows that the pleasantest part of his task consists in writing the preface, for here he has a chance to express his gratitude to the generous friends who have helped him with suggestion and counsel. The present author would especially mention his colleague Professor Maxime bocher, who kindly read the proof of Ch. VIII, and his former pupil Dr. David Barrow, who not only supplied much of the material in Oh. XIV but also did yeoman service in unearth ing mistakes in various parts of the work. Another pupil, Dr. Roger Johnson, has kindly suggested a number of minor corrections, mostly of a bibliographical nature. Yet the greatest debt is not to any one of these. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at 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. Seller Inventory # LIE9781440060380

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Book Description Forgotten Books, 2017. Paperback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****.Excerpt from A Treatise on the Circle and the Sphere Every writer knows that the pleasantest part of his task consists in writing the preface, for here he has a chance to express his gratitude to the generous friends who have helped him with suggestion and counsel. The present author would especially mention his colleague Professor Maxime bocher, who kindly read the proof of Ch. VIII, and his former pupil Dr. David Barrow, who not only supplied much of the material in Oh. XIV but also did yeoman service in unearth ing mistakes in various parts of the work. Another pupil, Dr. Roger Johnson, has kindly suggested a number of minor corrections, mostly of a bibliographical nature. Yet the greatest debt is not to any one of these. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at 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. Seller Inventory # AAV9781440060380

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