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Excerpt from Elements of Quaternions, Vol. 2
In other words, the calculation of 1' and P introduces no differentials higher than the third order but that of R' requires the fourth order of differentials. In the language of modern geometry, the former can be determined by the consideration of four consecutive points of the curve, or by that of two consecutive osculating circles; but the latter requires the consideration of two consecutive osculating spheres, and therefore of five consecutive points of the curve (supposed to be one of double curvature). Other investigations, in the present and immediately following Series (398.
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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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Excerpt from Elements of Quaternions, Vol. 2
In other words, the calculation of 1' and P introduces no differentials higher than the third order but that of R' requires the fourth order of differentials. In the language of modern geometry, the former can be determined by the consideration of four consecutive points of the curve, or by that of two consecutive osculating circles; but the latter requires the consideration of two consecutive osculating spheres, and therefore of five consecutive points of the curve (supposed to be one of double curvature). Other investigations, in the present and immediately following Series (398.
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.
Reseña del editor
Excerpt from Elements of Quaternions, Vol. 2
I have reserved for the Appendix to this Volume the longer additional and illustrative notes which I have written for the new edition of the "Elements."
Some of those notes would have been inconveniently long as footnotes; others would have been inconveniently placed. For example, although the Note on Screws relates naturally to Art. 416 and that on the Kinematical Treatment of Curves to Art. 396, I have placed the Note on Screws before the Note on Curves because Hamilton's remarks on screw motion in the earlier Article required some development in order to make the Note on Curves easily intelligible. Accordingly the order of the notes has been arranged with reference to the notes themselves rather than with reference to the text. The selection and treatment of the subjects of these notes have been subordinated to the illustration of quaternion methods. I have not hesitated to sacrifice brevity for suggestiveness, and above all I have tried to render the notation as explicit as possible.
An analysis of the Appendix will be found on pages xlv-xlix.
For greater convenience I have provided an Index to the whole work referring to the pages, the volumes being distinguished by the numbers i and ii.
I take this opportunity of testifying to the extraordinary accuracy both of matter and of printing in the first edition of the "Elements." Every portion of the work bears evidence of Hamilton's unsparing pains. I cannot recall a single sentence ambiguous in its meaning, or a single case in which a difficulty is not honestly faced. I see no sign of diminished vigour or of relaxed care in those portions of the work written in his failing health. My task as editor has convinced me of the extreme caution with which any endeavour should be made to improve or modify the calculus of Quaternions.
In conclusion, I desire to express my thanks to the College Printer, Mr. George Weldrick, for the great care he has taken in printing this edition for the Board of Trinity College, and for his unvarying courtesy to myself.
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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Paperback. Zustand: New. Print on Demand. This book delves into the fascinating world of quaternions, a mathematical concept developed by the Irish mathematician William Rowan Hamilton in the mid-19th century. Quaternions extend the familiar system of complex numbers to three-dimensional space, offering a powerful tool for representing and manipulating geometric objects and relationships. The author explores the applications of quaternions in diverse areas of geometry, including the study of curves in space, surfaces of the second order, and lines of curvature. He examines concepts like osculating circles and spheres, geodetic lines, and the unique properties of umbilics on central quadrics. Through a combination of rigorous analysis and insightful explanations, the book illuminates the elegance and depth of quaternion methods. It reveals how this mathematical tool can be used to express and derive complex geometric theorems in a concise and elegant manner. This book offers a valuable resource for anyone seeking a deeper understanding of the power and beauty of quaternion mathematics, and its implications for various branches of geometry. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781330441169_0
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