An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 páginas |
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Términos y frases comunes
a₁ axes axis Cartesian centre of inertia Chapter circle condition cone conjugate cöordinates coplanar curvature curve cylinder developable surface diameters differential direction drawn easily Eliminating ellipsoid envelop equal evidently expression extremity Find the equation Find the locus given equation given lines given point given vectors gives Hamilton Hence hodograph integral intersection last section length linear and vector normal obviously once operator origin osculating osculating circle osculating plane P₁ parabola parallel pass perpendicular properties prove quaternion radius represents result right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate shew solution sphere Spopp ẞ² straight line suppose surface of revolution tangent plane tensor theorem three vectors triangle unit-vector Vaß vector function versor write written φρ
Pasajes populares
Página 120 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
Página 140 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Página 13 - 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
Página 124 - The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Página 215 - If <p' be the function conjugate to <£, we have so that 2^ and 2F.e( ) = <£ -<£', which completely determine the first decomposition. This is, of course, perfectly well known in quaternions, but it does not seem to have been noticed as a theorem in the kinematics of strains that there is always one, and but one, mode of resolving a strain into the geometrical composition of the separate effects of (1) a pure strain, and (2) a rotation accompanied by uniform dilatation perpendicular to its axis,...
Página 25 - B), sin (A + B), and sin (A — B}, in terms of sines and cosines of A and B. 8. If two tangents be drawn to a hyperbola, the line joining the centre with their point of intersection bisects the lines joining the points where the tangents meet the asymptotes : and the tangent at the point where it meets the curves bisects the intercepts of the asymptotes. 9. Any two tangents, limited by the asymptotes, divide each other proportionally. 10. If a chord of a hyperbola be one diagonal of a parallelogram...
Página 264 - 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...
Página 107 - If from the vertical angle of a triangle three straight lines be drawn, one bisecting the angle, another bisecting the base, and the third perpendicular to the base, the first is always intermediate in magnitude and position to the other two.
Página 41 - It is curious to compare the properties of these quaternion symbols with those of the Elective Symbols of Logic, as given in BOOLE'S wonderful treatise on the Laws of Thought...
Página 20 - Then, generally, p may be expressed as the sum of a number of terms, each of which is a...