An Elementary Treatise on QuaternionsAn Elementary Treatise on Quaternions by Peter Guthrie Tait, first published in 1890, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
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Page v
... examples of Analytical Geometry in Todhunter's Collection , and I had made various physical appli- cations of the Calculus , especially to Crystallography , to Geo- metrical Optics , and to the Induction of Currents , in addition to ...
... examples of Analytical Geometry in Todhunter's Collection , and I had made various physical appli- cations of the Calculus , especially to Crystallography , to Geo- metrical Optics , and to the Induction of Currents , in addition to ...
Page vi
... examples I have given , though not specially chosen so as to display the full merits of Quaternions , will yet sufficiently show their admirable simplicity and naturalness to induce the reader to attack the Lectures and the Elements ...
... examples I have given , though not specially chosen so as to display the full merits of Quaternions , will yet sufficiently show their admirable simplicity and naturalness to induce the reader to attack the Lectures and the Elements ...
Page vii
... Examples are appended ) . After this he may work at the first five , with their ( more difficult ) Examples ; and the remainder of the book should then present no difficulty . Keeping always in view , as the great end of every mathe ...
... Examples are appended ) . After this he may work at the first five , with their ( more difficult ) Examples ; and the remainder of the book should then present no difficulty . Keeping always in view , as the great end of every mathe ...
Page viii
... Examples appended to each Chapter , hints ( which will not be lost to the intelligent student ) of farther developments of the Calculus . Many of these are due to Hamilton , who , in spite of his great originality , was one of the most ...
... Examples appended to each Chapter , hints ( which will not be lost to the intelligent student ) of farther developments of the Calculus . Many of these are due to Hamilton , who , in spite of his great originality , was one of the most ...
Page xii
... Examples with solutions , §§ 40-44 . EXAMPLES TO CHAPTER I. 29-31 I CHAPTER II . - PRODUCTS AND QUOTIENTS OF VECTORS Here we begin to see what a quaternion is . 32-59 When two vectors are parallel their quotient is a number , §§ 45 , 46 ...
... Examples with solutions , §§ 40-44 . EXAMPLES TO CHAPTER I. 29-31 I CHAPTER II . - PRODUCTS AND QUOTIENTS OF VECTORS Here we begin to see what a quaternion is . 32-59 When two vectors are parallel their quotient is a number , §§ 45 , 46 ...
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Common terms and phrases
a₁ axis Cartesian centre Chapter circle commutative law cone conjugate constant cöordinates coplanar curvature curve diameters differential direction drawn easily ellipsoid envelop equal evidently expression extremity Find the equation Find the locus formula geometry given equation given lines given point given vectors gives Hamilton Hence indeterminate intersection inverse function LAOB last section length linear and vector multiply obviously origin osculating plane P. G. TAIT P₁ parallel perpendicular properties prove quaternion radius rectangular represented right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate sides solution sphere spherical conic ẞ² straight line student surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vector Vaß vector function vector perpendicular versor written φρ
Popular passages
Page 153 - Find the locus of a point the ratio of whose distances from two given points is constant. Let the given points be 0 and A, the extremities of the vector a.
Page 149 - Find the equation of the locus of a point the sum of the squares of whose distances from a number of given planes is constant. 11. Substitute " lines" for "planes
Page 174 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 14 - The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. Let the -l. bisectors EE' and DD
Page 309 - Dub. Math. Journal, II. p. 62), that the forces produced by given distributions of matter, electricity, magnetism, or galvanic currents, can be represented at every point by displacements of such a solid producible by external forces. It may be useful to give his analysis, with some additions, in a quaternion form, to show the insight gained by the simplicity of the present method. Thus, if...
Page 150 - ABC, iu terms of a, /3, y. 19. Find the locus of a point equidistant from the three planes Sap = 0, Spp = 0, Syp = 0. 20. If three mutually perpendicular vectors be drawn from a point to a plane, the sum of the reciprocals of the squares of their lengths is independent of their directions.
Page 38 - Elementary Treatise it is accomplished by the help of the fundamental properties of the curves known as Spherical Conies, discovered only in recent times by Magnus and Chasles. Doubtless many a one has been discouraged from the study of quaternions by the abstruse nature of the fundamental principles. It is clear from the figure that the summing of versors cannot be adequately represented by a versor rotating a line...
Page 23 - Then, generally, p may be expressed as the sum of a number of terms, each of which is a...