The Educational Times

The Educational Times

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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. 1882 edition. Excerpt: ...the value of tho integral f'(l + --)E(-, l)-(l-F(-, l)&, where F (e, 1) and E (-, 1) denote complete elliptic functions of tho first and second kinds. 7230. (By the Editor.)--On a square (A) of a chess-board, a knight is placed at random, find the probability (1) that it can march from that square (A) to a given square (B), --as, for example, one of tho cornersquares, --within a moves; and (2) that it can march over b squares in less than o moves, --for instance, the four corner squares of the board. 7231. (By Elizabeth Blackwood.)--A, B, C are candidates for an office, the eloction to which is in the hands of 8wi + 1 electors. 3m votes, together with the casting vote if necessary, are promised to A, and 2w- votes to B. In how many ways can the remaining votes be given so that A may bo successful? 7232. (By R. F. Scott, M.A.)--If (a, b, c) stand for the straight line ax + by + ez = 0, show that the six lines obtained by permutating a, b, c in (a, b, e) in all possible ways, all touch the conic x + y + z 2(yz + zr + xy) -2 + 2 + cs a' + bi + ci-2bc-2ca-2ab S-i' +-S)'" S(a!-o8-: --S)' a being b and tho + or--sign being read according as tho smallest circle is within or without tho largest. 7234. (By the Rev. T. P. Kirkmax, M.A., F.R S.)--One or more 6-partitions of any number - 2 can be written in tho order -, +Oj+rt3+04 + (7s + r6 = - (Tr 0), on the sides of a 6-gon, such that, if on the side carrying r a (4 + r)-gon be drawn, the figure can bo completed by pentagons only into a polyedron having only triad summits. Tho proposition is true when for 6 we read 5 or 4, and for "any number n" demanded numbers n, retaining the word pentagons. In line 7 of Mr. Kirkman's Quest. 7199, more

Product details

  • Paperback | 1022 pages
  • 189 x 246 x 51mm | 1,783g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236508165
  • 9781236508164