The Mathematical Diary; Containing Collections of Original Questions, Proposed and Resolved by Ingenious Correspondents Volume 1

The Mathematical Diary; Containing Collections of Original Questions, Proposed and Resolved by Ingenious Correspondents Volume 1

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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. 1825 edition. Excerpt: ...(p--m--1 i and that of the second is-. - conse" L. (n-/n+l) (n-2), quently the register number is=------f (m-f) (m-2) (ot-3) (2n-tn-p) (p-m-1) 6 + 2 +7 Pi substitute the numbers 2, 5, 9, and 4, 8, 11, in this formula, and we obtain 64 and 127 for the respective registers. To determine the combination when the register is given, sum the terms of the series f n2n----+&c. until another term added would render the amount equal to or greater than the register number; the number of terms thus sumed being m--1, m is determined; then sum the terms of the series (n--in--1)+ (n--m--2) + &c. until another term added, would with the former series make an amount equal to, or greater than the register, the number of terms of the latter series beingp--irt--l, p is determined; then the sum of the two series substracted from the register number leaves a remainfer=y--p, which determines q; thus for the register 86, we have 45+36=81 =sum of the first series;, therefore m--1=2, m=3, again n--m--1 = 11--3--1=7, and 81+7=8886, consequently p--m--l=o, p=m+l =4 and 86--81 =5=9--p, wherice =5+4=9; 3, 4, 9 is therefore the combination. For 123, we have 45+36 +28=109, and m = 4, then 109+6 + 5= 120, and p=7, again 123--120=3 and 7 = 10, consequently 4, 7, 10 is the combination answering to the register 123. THind Solution.--By Mr. CharlesFarqvhar, Alex. D. C. By an inspection of the law of combinations, we may readily obtain the-following general formala. Put R= the register, and m, n, and p, the corresponding combina (9-tn). (10--m). (II--m) tion; then R = 16S------'-. (ll--). (12-n), Y7i +Pn If m=2, n--5, and p=9; then, r=64. If m=4; i=8, andp=l; then R = 127. if the register be given, and the combination be required, the above equation must be...show more

Product details

  • Paperback | 64 pages
  • 189 x 246 x 3mm | 132g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • Illustrations, black and white
  • 1236550129
  • 9781236550125