Mathematical Questions and Solutions in Continuation of the Mathematical Columns of the Educational Times. Volume 25
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Mathematical Questions and Solutions in Continuation of the Mathematical Columns of the Educational Times. Volume 25

Mathematical Questions and Solutions in Continuation of the Mathematical Columns of the Educational Times. Volume 25


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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. 1876 Excerpt: ... which can bs drawn from a point to the plane cubic U being thrown into the form XV &c. = 0, show that the nine points of intersection of V and U lie on three right lines drawn from the above point. 4254. (Proposed by J. J. Walker, M.A.)--Let K3 = 0 be any proper plane cubic curve; Kg and u its first and second polars with respect to a point (: r0, j/0, z0) not on the curve; and w0 the result of substituting (o yoi 2n) iu prove that the cubic S4-0-V3--lo-)-."2 + u?--" nas-ne point (j-c, y0, z0) as a double point, and passes. through the six points in which the tangents to -s from that point meet w2, not being points of contact. 4883. (By the Editor.)--Given one side of a right-angled triangle; construct it, so that the difference between the other side and the adjacent segment of the hypotenuse, cut off by a perpendicular from the right angle, may be a maximum. Prove that the perpendicular divides the hypotenuse in extreme and mean ratio, and that the greater segment is equal to the remote side of the triangle. 4435. (Proposed by S. Porde.)--Two equal parabolas, of parameters 4-, have a common focus and their axes inclined at an angle a; show that the area common to both is y a2 cosec3 ia. Solution by Rev. J. R. Wilson, M.A.; Prof. Nash, and others. Let TP, TQ be tangents to one of the parabolas at the extremities of the common chord PQ, which will also pass through the focus S. The area required = $ A PTQ = %. PQ. ST, since ST is perpendicular to PQ. Now, if the equation to the parabola be r------:, we have, since PSX = $a, 4444. (By Rev. J. R. Wilson, M.A.)--Two equal parabolas, of parameters 4a, have a common focus and their axes at riIrht angles. One of them is turned round the focus through an angle of 180, in the ...


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Product Details
  • ISBN-13: 9781231348741
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 24
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1231348747
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 64 gr


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