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Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 61

Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 61


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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. 1894 Excerpt: ... BMN N (from A, M, B, N are concyclic) = MBS, BMS; therefore QMS = MBS; therefore RMQ touches the parabola. 12212. (E. M. Langley, M.A.)--If O, A, B, C, D, E be six concyclic points, prove that the projections of O on the pedal-lines of the five quadrilaterals BCDE, ODEA, DEAB, EABC, ABCD lie in a straight line. Solution by Profs. Steggall, Aiyar, and others. Draw OB OC OD OE, perpendicular to AB, AC, AD, AE; then the pedal line of ABCD is easily seen to be that of 6, C,0, . For ABC, ABD, ACD are any three of the four triangles derivable from ABCD; their pedals are B, C C, D D, B; and the feet of the perpendiculars from O on them are collinear. From O draw OC2, OD2, OE2 perpendicular to B, C B, D B, E; then C2D2 is the pedal of ABCD, D2E2 of ABDE, E2C2 of ABEC; but the feet of the perpendiculars from O on these lines are collinear; and ABCD, ABDE, ABEC are any three of the five quadrilaterals derivable from ABCDE. Hence all the quadrilaterals yield the same line, and we have a pedal of the pentagon. The reasoning can obviously be extended to polygons of any number of sides. 12114. (R-Knowles, B.A.)--PQ. is a chord, normal at a fixed point P of a conic; XX' are the ends of a chord parallel to the tangent at P. Prove that (1) the locus of the centre of the circle PXX' is a straight line; (2) if this line meet the conic in YY', P, Q, Y, Y' are concyclic. Solution by Prof. Droz-farny; H. W. Cubjel, B.A.; and othert. On sait que dans tout quadrilatere inscrit dans une conique les cotes opposes sont antiparalleles par rapport aux axes. Menons PM antiparallele a XX' par rapport aux axes; le quadrilatere PMXX' sera inscriptible; or XX' ayant une direction fixe, il en sera de mem...


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Product Details
  • ISBN-13: 9781236222695
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 32
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1236222695
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 77 gr


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