Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 40
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Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 40

Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 40


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 Excerpt: ...+ (sec a cos b--cose)2 (1--cosec2- sin2 A) = tan2 a cos2 B cos2 C. The formula is employed, without proof, on p. 69 of Vol. 37 of Reprints. 7426. (By Professor Haughton, F.R.S.)--In a work erroneously attributed to Sir Isaac Newton, it is stated, that if two spheres, each one foot in diameter, and of a like nature to the Earth, were distant by but the fourth part of an inch, they would not, even in spaces void of resistance, come together by the force of their mutual attraction in less than a month's time. Investigate the truth of this statement. Solution by R. Rawson; Professor Matz, M.A.; and others. Let D, D D2 be the diameters of Earth (= 7912-41 x 5280 feet) and of (Earthy, (Earth.2) similar in material to'the Earth; O the common centre of the three spheres; Q another point such that OQ = a; and A, Ai the attractive forces of the (Earth) and (Earth, ) at the point Q; then (eahnshaw's Dynamics, p. 318) if p is the density of the (Earth) we have A-'A---i'=i O.m). 7448. (By D. Edwardes.)--If a rectangular hyperbola pass through the centre of the ellipse b2x2 + ah/ = a"b', touch it at a point P, whose eccentric angle is o, and intersect it in Q, R; prove that tangents to the ellipse at Q, R intersect on the straight line Px cos a + a3y sin a + ab (a2 +b1) = 0. 7450. (By K-Tucker, M.A.)--If a circle passing through the focus Of a given conic intersects the conic in points (fl 82, 8, 84), prove that (1) 2 cos 6 is dependent upon the execntricity only; and (2) if the diameter of the circle be inclined to the axis of the conic at an angle sin-'/ / d, where 11 is the latus rectum and d the diameter of the circle, then one of the angles (8) is a right angle. Solution by J. Hammond, M.A.; Margaret T. Meyer; and others. The intersections of...


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Product Details
  • ISBN-13: 9781235999253
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 26
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1235999254
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr


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