Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 29
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Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 29

Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 29


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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. 1878 Excerpt: ... Parabola. The negative focal pedal of the ellipse has been investigated in the Reprints (Vols. XVI., pp. 77--83; XVII., pp. 92--96; XX., pp. 106, 107), under Quests. 3430, 3560; and the form of the curve---which resembles that of the central pedal given above--is shown in the diagram on p. 77 of Vol. XVI. The central pedal is discussed in Vols. XVI., pp. 83--86, and XX., pp. 107, 108, under Quest. 3431. It was, however, inadvertently stated (XVI., p. 84, Art. 2) that "the curve lies wholly inside the ellipse"; whereas, by eq. (5) on p. 84, it is at once seen that y = 0 when b b (1--e2fi cos it =--=--=, which is possible when c1 i; and that then ae c e by eq. (4) the pedal crosses the axis at O where CO = x = 2eb, as found above. The form of the curve may be easily traced from eqs. (1) to (7), as done for the focal pedal in Art. (8) on p. 80 of Vol. XVI. The excentrio angle 4. that corresponds to the node O is constructed (as in the figure to Quest. 3656, Reprint, Vol. XXVII., p. 96) by drawing to the circle on the minor axis a tangent from the focus, which, since -3 J, must in this case lie outside the circle. 54-79. (By A. W. Pantox, M.A.)--1. If circles be drawn on a pair of opposite sides of a square; prove that (1) the polars of any point on either diagonal with respect to the two circles meet on the other diagonal, and (2) the four tangents from the point form an harmonic pencil. I. Solution by Professor Townsend, F.E.S. Let ABCD be the square, G the intersection of its diagonals, E and F the centres of the two circles, PQ any chord parallel to EF of the angle determined by the diagonals, and XX' and YY' the two chords of intersection, real or imaginary, of PQ with the circles; then, since XX' and YY' are manifestly both cut harmonicall...


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Product Details
  • ISBN-13: 9781130986822
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 34
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130986829
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr


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