Mathematical Questions with Their Solutions, from the "Educational Times" Volume 29
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Mathematical Questions with Their Solutions, from the "Educational Times" Volume 29

Mathematical Questions with Their Solutions, from 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. 1885 Excerpt: ...a cos a when a varies, referred to X and a line through C perpendicular to it is, xy =.1-c2, an equilateral hyperbola whose foci are S and S'. Again, it may be remarked that, as a tangent from any point to a conic is, at the point of contact, normal to a confocal conic, the same circular cubic will be the locus of the extremities of all normals drawn from a given point O to a system of confocals. The equation of this cubic may also be obtained by combining the equation of the pair of tangents to a conic from a point, referred to elliptic coordinates, with the equation of the polar of the point similarly referred. 7350. (By Dr. Cuetis.)--If there be circumscribed to a given conic a polygon of m sides, such that the ares between the consecutive points of contact subtend equal angles at a focus, and 2a denote the angle which the axis of the conic makes with the radius vector drawn to any one of the points of contact, prove that (1) the product of the squares of the perpendiculars from the focus on the sides of the polygon varies inversely as C--cos 2ma, where C is a constant which becomes unity when the conic is a parabola; and (2) any symmetrical function of the positive powers of the squares of the reciprocals of the perpendiculars of a degree inferior to the mh remains constant, however the polygon may change consistently with the conditions of its construction. An extension of Quest. 7317. Solution by the Proposer. The following theorem is due to the late Professor Maccullaqh: --If any point O, taken on the circumference of a circle of radius, be joined to all the angular points of a regular polygon of m sides inscribed in a concentric circle of radius a, and the angle subtended at the centre by the point O, and any angular point of the polygon, e.g., the a...


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Product Details
  • ISBN-13: 9781231865033
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 40
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1231865032
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 91 gr


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