A Book of Mathematical Problems on Subjects Included in the Cambridge Course

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Macmillan, 1867 - Mathematics - 344 pages
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Page 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...
Page 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...
Page 249 - 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).
Page 258 - 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...
Page 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...
Page 54 - 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.
Page 255 - 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.
Page 60 - 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...

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