Oxford, Cambridge and Dublin Messenger of MathematicsMacmillan and Company, 1885 - Mathematics |
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Common terms and phrases
a₁ algebraical angle ascending powers astatically ax+by+cz axes axis bisects centre circle coefficients column condition cone congruency conic conicoid considered continued fractions coordinates corresponding cubic surface curve cyclide denote determined digit distance divisors dx dy dy dz element Elliptic Functions equal equation expression factor fixed fluid focal quadrics formula function given gives Hence hyperboloid integral intersection magnetic force negative obtain octonary P₁ P₁₁ P₂ perpendicular plane Poisson's equation positive Q₂ quadric surface quantities quaternion r₁ radius result root of unity rotation scalar solution sphere substituting symmetric symmetric functions tangent theorem trajectory triangle twisted cubic u₁ u₂ vector velocity vortex Waring's formula wrench write zero
Popular passages
Page 121 - T. (1884). [Note on the determinantal equation connected with the investigation of the small oscillations of a system about a position of equilibrium.
Page 75 - Descartes influenced by hereditary preposessions calls radices falsce] is made exact through the intermediation of the conception of sides to a line. D'Alembert and Carnot are entitled to the gratitude of Geometers, and all lovers of truth for raising objections so perfectly well founded to the then, and even now, too prevalent interpretation of the meaning of the geometrical positive and negative, but the difficulty which they so justly appreciated and so clearly expressed is overcome and exists...
Page 118 - Construction for the centre of gravity of three weights placed at the corners of a triangle, proportional to the fourth powers of the opposite sides 532 K.
Page 17 - EMF only vanishes when the axis of rotation is parallel to the direction of the magnetic field.
Page 145 - It will be convenient to establish the definition of counterpoints in regard to a given line : two points such that the line joining them is bisected at right angles by the given line, are said to be counter-points in regard to that line.
Page 17 - SUvyuds =± the elementary solid angle subtended at the point by ds, the upper or lower sign being taken according as the point is on the negative or positive side of the element.
Page 134 - Substituting these values of x and y in (1) and (2), we...
Page 18 - It the radius of the sphere, let a, b, e be the components of magnetic induction, F, G, H the components of the vector potential; ^ the electrostatic potential ; u, w, w the components of the current, and a the specific resistance of the sphere.
Page 147 - Concerning the problems of the quadrature of the circle, the duplication of the cube, and the trisection of the angle, L.