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

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


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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 edition. Excerpt: ... at each of the infinite cusps. The points of contact of the double tangents CI and CJ are easily found by putting R---0 in (2), whence it is seen that they lie on the imaginary ellipse Q4 = 0, the other points where they cut the curve lying on the ellipse Q4 = (a2 + i2)2. In the figure, besides the negative pedal, we have inserted its reciprocal, the inverse of the ellipse, in order to show the double tangent and two inflexions corresponding to the node and two cusps of the negative pedal. Mr. Hammond remarks that it would be interesting to investigate the forms and properties of some other negative pedals. Of these one of the simplest is that of the parabola, with the origin at the vertex, where the inverse is a Cissoid and the negative pedal a Semicubical 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, 3550; 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--85, 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--cosJ, =--=--=, which is possible when e2 i; and that then ae e 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 exeentric angle 4' that corresponds to the node O is constructed (as in the figure to Quest. 3656, Reprint, Vol. XXVII., p. 96)...


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Product Details
  • ISBN-13: 9781130411218
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 32
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130411214
  • Publisher Date: 13 Sep 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 77 gr


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