The Elements of Universal Mathematics, or Algebra; To Which Is Added, a Specimen of a Commentary on Sir Isaac Newton's Universal Arithmetic. Containin

The Elements of Universal Mathematics, or Algebra; To Which Is Added, a Specimen of a Commentary on Sir Isaac Newton's Universal Arithmetic. Containin

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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. 1728 edition. Excerpt: ...before about Problems in general, the Solution of Problems of two Dimenfions will not be difficult. Problem XVI. 230. A andB together ewe 208; A pays each day 9, and B pays the firfi day 1, the fecond day 2, the third 3, &c. Qu. How many days will the-whole Debt be paid in, and how much does each pay? Let A's Debt be x, Bsj, and the Number of Days z.. x--y--108 oz. = x y is equivalent to the Sum of an Arithmetic Progreffion, whofe firftTerm is 1, laft z., and Number of Terms z.; which Sum is equal to 1 + z x fz. (126), therefore 4-+ f---J Which three Equations, by adding the two laft together, and then comparing it with die firft, are reduced to this: x 4-y--iz.z, + Jt = 208 z.z, + 19 = 416 7A + 1pZ, + 90-J--f JO5 z, = 13 Problem XVII. 240. A Perfon huys a Horfe, which he fells again for a, and gains as much per Cent, as the Horfe cofi him. Qu. What did the Horfe cofi him? Let the Price of the Horfe be x. 100, 100--x:: x, a Problem XVIII. '241. There are two Numbers fought, -whofe Pro duB is 12, and the Difference of their Squares 7. Let the Numbers be x and y. 12 144 xy = 12, y =--tyy=-22 X XX 144 xx--yy = 7, xx--= 7 xx x4--144 = 7 This Equation is folv'd as an Equation of two Dimenfions (217), if we feek the Value of the Square of xx. x4--7xx = 144 X4 7XX+ 12: ? = 15tf xx--37 37-xxs 121 XX = ' 1--9.X = 4, J = 3 I neglect the fecond Value xx----9, becaufe it is impoffible (218). I neceffarily difcover the Value of the Square xx in the Solution, becaufe not only x =4, y=2, but alfo x =--4, y =--3, folve the Problem. I alfo difcover two other Values of the Square xx, becaufe the Problem has befides two impoffible Solutions, which may be algebraically exexpreffed: Thefe are x =-/--9, y=--/--i6t and x----/--9, y----V--16. Problem XIX. 242show more

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  • Paperback | 34 pages
  • 188.98 x 246.13 x 1.78mm | 81.65g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236548213
  • 9781236548214