A Book of Mathematical Problems on Subjects Included in the Cambridge CourseMacmillan, 1867 - 344 páginas |
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A Book of Mathematical Problems, on Subjects Included in the Cambridge Course Joseph Wolstenholme Sin vista previa disponible - 2015 |
Términos y frases comunes
angular points angular velocity asymptotes ax² axes bisected centre of perpendiculars chord circumscribed circle common focus common tangents cone conicoid constant cos² cos³ curvature curve described directrix eccentricity ellipse envelope equation fixed point fixed straight line focal distances foci four points given conic given point given straight line horizontal inscribed circle latus rectum length let fall locus major axis meet middle points minor axis normal opposite parabola parallel plane point of contact point of intersection polar position prove radical axis radii radius radius of curvature ratio rectangular hyperbola respectively right angles roots self-conjugate sin² sin³ straight line joining string subtends a right tan-¹ tangents are drawn tangents drawn tetrahedron touches the sides triangle ABC values vertex vertical whole number
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Página 1 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Página vi - ... the order of the Text-Books in general use in the University of Cambridge has been followed, and to some extent the questions have been arranged in order of difficulty. The collection will be found to be unusually copious in problems in the...
Página 251 - E, act along the sides of a triangle, ABC, and their resultant passes through the centres of the inscribed and circumscribed circles : prove that P _ Q _ R cos B — cos C ~~ cos C — cos A cos A — cos B ("Wolstenholme's Book of Mathematical Problems).
Página 260 - Q of similar material, resting on a double inclined plane, are connected by a fine string passing over the common vertex, and Q is on the point of motion down the plane. Prove that the...
Página iii - Trace Science then, with Modesty thy guide; First strip off all her equipage of Pride, Deduct what is but Vanity, or Dress, Or Learning's Luxury, or Idleness; Or tricks to shew the stretch of human brain, Mere curious pleasure, or ingenious pain; Expunge the whole, or lop th...
Página 56 - T' formulae. 2 sin A . cos B = sin (A + B) + sin (A -B), ' 2 cos A . sin B = sin (A + B) — sin (A - B), h 1v.
Página 257 - A uniform rod of length c rests with one end on a smooth elliptic arc whose major axis is horizontal and with the other on a smooth vertical plane at a distance h from the centre of the ellipse ; the ellipse and the rod being in a vertical plane.
Página 62 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...