Mathematical Questions and Solutions in Continuation of the Mathematical Columns of the Educational Times Volume 60

Mathematical Questions and Solutions in Continuation of the Mathematical Columns of the Educational Times Volume 60

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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. 1894 edition. Excerpt: ...en n parties egales au moyen de cordes issues d'un point fixe de la circonference. Trouver la moyenne arithmetique des longueurs de ces cordes lorsque n croit indefiniment. Solution by C. MommN, M.A.; H. W. CUnJEL, B.A.; and others. 440, (J. W. ELL1oTT, M.A.)--Given two concentric conics; then, if lines be drawn from each point in one of them to touch the other, the chords of contact will touch another curve of the second order. Solution by J. C. ST. CLAIn. The theorem that the polar reciprocal of one conic with respect to another is a third conic is true generally (SAmsoN, Art. 303; PoNcELET, 1. 231). It may be shown, however, that if the comics are concentric the third conic is concentric with them. For, if ABCD are the intersections of two concentric conics X, Y, the tangents at these points to Y are the polars of the points, considered as belonging to X, and are therefore tangents to the third conic Z. But these tangents obviously form a parallelogram having the same centre as Y; and therefore Z, which is inscribed in it, must also have the same centre. 549, (J. H. SwALE.)--If, in the diameter (AB), or in the diameter produced, of a given circle, and on the same side of the centre (0) with A, there be taken a given point (P); and right lines AN, BN, PN be drawn from A, B, P to any point N whatever in the periphery, then will AN2: PN2--PA2 = BN2: BP2-JPN2 be a given constant ratio. Solution by W. J. GannrxsTnaET, M.A.; Professor Znna; and others. 11942, (D. BmnL14: .)--The series consisting of the reciprocals of figurate numbers of the third order (1, 3, 6, 10, &c.) is summed, from the nth term onwards to infinity, by 2/21; or if the number of the first term be not known, but this and the next term be..show more

Product details

  • Paperback | 30 pages
  • 189 x 246 x 2mm | 73g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236864182
  • 9781236864185