Introduction To Quaternions By P Kelland And P G Tait

Introduction to Quaternions, by P. Kelland and P.G. Tait

"Introduction to Quaternions" by Philip Kelland and Peter Guthrie Tait offers a comprehensive exploration of quaternion algebra, a mathematical system that extends complex numbers. This historical text delves into the theory and application of quaternions, providing a foundation for understanding their role in various fields of physics and mathematics. The book covers fundamental concepts, algebraic properties, and practical uses of quaternions, with a focus on their application to three-dimensional space and mechanics. Readers will gain insights into the relationship between quaternions and vector analysis, as well as their significance in Hamiltonian mechanics and other areas of theoretical physics. This edition remains valuable for mathematicians, physicists, and students interested in the historical development of mathematical tools and their enduring relevance in modern science. 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.

Introduction to Quaternions, by P. Kelland and P. G. Tait

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1873 edition. Excerpt: ...points of section diameters be drawn to both circles, their other extremities and the other point of section will be in a straight line. 2. If a chord be drawn parallel to the diameter of a circle, the radii to the points where it meets the circle make equal angles with the diameter. 3. The locus of a point from which two unequal circles subtend equal angles is a circle. 4. A line moves so that the sum of the perpendiculars on it from two given points in its plane is constant. Shew that the locus of the middle point between the feet of the perpendiculars is a circle. 5. If 0, (y be the centres of two circles, the circumference of the latter of which passes through 0; then the point of intersection A of the circles being joined with 0' and produced to meet the circles in C, D, we shall have AC.AD = 2A0'. 6. If two circles touch one another in 0, and two common chords be drawn through 0 at right angles to one another, the sum of their squares is equal to the square of the sum of the diameters of the circles. 7. A, B, G are three points in the circumference of a circle; prove that if tangents at B and C meet in D, those at C and A in E, and those at A and B in F; then AD, BE, CF will meet in a point. 8. If A, B, C are three points in the circumference of a circle, prove that V(AB. BC. CA) is a vector parallel to the tangent at A. 9. A straight line is drawn from a given point 0 to a point P on a given sphere: a point Q is taken in OP so that OP.OQ = V. Prove that the locus of Q is a sphere. 10. A point moves so that the ratio of its distances from two given points is constant. Prove that its locus is either a plane or a sphere. 11. A point moves so that the sum of the squares of its distances from a number of given points is constant. Prove...

Introduction to quaternions, by P. Kelland and P.G. Tait