Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 51
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Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 51

Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 51


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About the Book

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. 1889 Excerpt: ... This is the reciprocal of Question 8733--That if the 2m intersections of a conic and an --ic curve be joined two and two, the m right lines so determined will cut the m-ic again in m(m--2) points lying on an (m--2)-ic. Question 9513 follows when the conic consists of two coincident points and this introduces the idea of a curve which is the satellite of a point with respect to a given curve of class m. In the particular case of a class cubic, say a cuspidal cubic or tricuspidal qiiartic, it follows that, if three tangents be drawn from a point to the curve, the three tangents which can be drawn to the curve from the points of contact all pass through the same point. Similarly, if tangents be drawn from any point to a class quartic, nodal cubic say, the eight tangents which can be drawn from the points of contact touch the same conic. 9958. (R-H. W. Whapham.)--ABC is a given triangle, Pany point in BC; find points Q and R in CA and AB respectively, such that the centroid of the triangle PQR may coincide with that of the triangle ABC. Solution by R. F. Davis, M.A.; J. C. St. Clair; and others. Let G be the common centroid; produce PG to p so that PG = 2Qp, then p is the mid-point of the side QR. Produce Ap to U so that Ap = pV, parallels through U to CA, AB will then determine Q, P. 9941. (Professor Madhavarao.)--Two conies ACBD, GEFH have double contact at A and B. CD is the polar of a point in AB with regard to the first conic. If right lines ACE, ADF, BCG, BDH be drawn, show that the lines CD, EF, GH concur in a fixed point. Solution by J. C. S, t. Clair; Rev. T. Galliers, M.A.; and others. Since the pole of CD lies on AB, CD passes through P, the intersection of the tangents at A and B. Let AB, CD meet in O. Then (A. PCOD) = (A. PEBF) is an harmonic ..


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Product Details
  • ISBN-13: 9781130771633
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 34
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130771636
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr


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