An Elementary Treatise on QuaternionsUniversity Press, 1867 - 422 strani An 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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a₁ arcs axis Cartesian centre Chapter circle commutative law cone conjugate constant coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression extremity Find the equation Find the locus formula geometrical given equation given lines given point given vectors gives Hamilton Hence indeterminate intersection inverse function LAOB last section length linear and vector multiply normal obviously origin osculating plane 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 straight line student surface surface of revolution tangent plane tensor theorem three vectors triangle unit-vector Vaß vector function vector perpendicular versor written α² αβ β² Γαβ δρ δρφρ ρ² Τρ φρ χα
Priljubljeni odlomki
Stran 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.
Stran 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
Stran 174 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Stran 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
Stran 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...
Stran 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.
Stran 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...
Stran 23 - Then, generally, p may be expressed as the sum of a number of terms, each of which is a...