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Proceedings of the Edinburgh Mathematical Society Volume 17-18

Proceedings of the Edinburgh Mathematical Society Volume 17-18


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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. 1899 Excerpt: ...conies connected with the triangle. I shall limit myself to enunciating two of these. (i) If a conic be circumscribed to a triangle ABC, and s be the line on which the tangents at the vertices meet the opposite sides, then the vertices of every triangle in perspective with ABC with respect to s as axis of perspective, connect with the non-corresponding vertices of ABC by pairs of lines which touch a conic having double contact (real or imaginary) with the original conic (Art. 4, ii). (ii) If ABC be a triangle inscribed in a conic, and if two variable points be taken on the conic, connecting with A, B, C, the one by the lines L, M, N and the other by the lines I, m, n respectively, then the variable triangle determined by the points of intersection of the pairs M and n, N and I, L and m (or m and N, n and L, I and M) is in perspective with ABC with respect to a fixed line s as axis of perspective, 8 being the line on which the tangents to the conic at A, B, C meet the opposite sides. Systems of Spheres connected with the Tetrahedron. By J. A Third, M.A. References in square brackets are to my paper on Systems of Circles analogous to Tucker Circles. 1. If Aj and B3 (Fig. 17), B, and C3, C2 and D3, Dj and A3, A2 and C2, B2 and J)2 be pairs of points on the edges AB, BC, CD, DA, AC and BD respectively of a tetrahedron A.BCD, such that the two points on any edge are concyclic with the two points on any other edge--a manifestly possible condition of things--then the twelve points lie on a sphere. Demonstration. Since Ajaob3c, AnA3C, and A3ajb3d, are concyclic quartets, it is obvious that the six points AjAoACnD, lie on a sphere cutting the edges of the trihedral angle A in three pairs of points. Again since Ajaobjco, Bjb3c3ad and Cocasbj are quartets of concycli...


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Product Details
  • ISBN-13: 9781130594669
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 64
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1130594661
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 132 gr

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