 | John Bonnycastle - Algebra - 1811 - 230 pages
...proportion. Ans. 1225, 49, and 25. 14. To find three numbers in arithmetical progression, such that the sum of every two of them may be a square number. Ans. 120-J, 840i,ond I560£. 15. To find three numbers, such that, if to the square of each of them... | |
 | Thomas Leybourn - Mathematics - 1817 - 456 pages
...case. vi. QUESTION 974, by Mr. James Cunliffe, Weslhoughton. To find three whole numbers such, that the sum of every two of them may be a square number, and also that their squares may be in arithmetical progression. Answered by Amiens. Let a* + 2a*o"... | |
 | John Ryley, John Gawthorp, John Whitley - Mathematics - 1818 - 308 pages
...(143,) By Mr. JOHN BAINES, Jun. . Find three numbers in arithmetical progression such than n times the sum of every two of them may be a square number. Answeredby MR. E. WEBSTER, Armley Mills. Suppose x — y,x,and *+^tobe'the required numbers. t(2x+y-)xn=p''nn... | |
 | James Thomson - 1844 - 328 pages
...4x, and 2* + 1, as the required numbers, and he thus obtains very simply the answers here given. 9. Required three numbers, such that the sum of all three, and the sum of every pair of them, may be square numbers. An,. K«2—l), T,V(t,.2—i)2_|(t.2—i), and 10. Render fa:3... | |
 | James Thomson - Algebra - 1845 - 328 pages
...4x, and 2x+ 1, as the required numbers, and he thus obtains very simply the answers here given. 9. Required three numbers, such that the sum of all three, and the sum of every pair of them, may be square numbers. An*. K«2-l), TIW«2-1)2-K«2-l)> *"* i(«2 + 2). 10. Render G^... | |
 | C. Gill - Algebraic spaces - 1848 - 114 pages
...and taking ¿ = 82, we have x = 6242, у =3362, z =482. PROBLEM. VII. To find four numbers, such that the sum of every two of them may be a square number. ¿Solution. The equations to be solved are and they give These last equations may be solved by Prob.... | |
 | Industrial arts - 1851 - 556 pages
...solutions to three Diophantine Problems, the first of which finds "three square numbers, such that the sum of every two of them may be a square number ;" the second determines " values for the sides of a triangle in whole numbers, such that the lengths... | |
 | Technology - 1851 - 552 pages
...solutions to three Diophantine Problems, the first of which finds "three square numbers, such that the sum of every two of them may be a square number;" the second determines " values for the sides of a triangle in whole numbers, such that the lengths... | |
 | Perry Fairfax Nursey - Industrial arts - 1851 - 552 pages
...solutions to three Diophantine Problems, the first of which finds " three square numbers, such that the sum of every two of them may be a square number;" the fécond determines "values for the sides of a triangle in whole numbers, such that the lengths... | |
 | Mathematics - 1893 - 146 pages
...elsewhere has been made the subject of a dispute.] 731. (Amicus.) — Find three numbers such that the sum of every two of them may be a square number, and that the sum of the three squares thus found may be also a square number. 741. (JW Elliott.) —... | |
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Problems, the first of which finds "three square numbers, such that the sum of every two of them may be a square number;" the second determines " values for the sides of a triangle in whole numbers, such that the lengths of the three lines from the angles... 