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 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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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Circles and spheres are central objects in geometry. This work looks at systems of circles and spheres and the geometry and groups associated to them. It also examines the differential and projective geometry of the space of various spheres in a given space.

The aim of this book is to provide a complete synthetic exposition of plane isometries, similarities and inversions to readers who are interested in studying, teaching, and using this material.The topics developed in this book can provide new proofs and solutions to many results and problems of classical geometry, which are presented with different proofs in the literature. Their applications are numerous and some, such as the Steiner Chains and Point, are useful to engineers.The book contains many good examples, important applications and numerous exercises of various level and difficulty, which are classified in the three groups of: general exercises, geometrical constructions, and geometrical loci. Some lengthy exercises or groups of related exercises can be viewed as projects. On the basis of the above, this book, besides Classical Geometry, is an important addition to Mathematics Education.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.