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Books Books 1 - 3 of 3 on ... square of any one of them added to the next following gives a square. Let the....  
" ... square of any one of them added to the next following gives a square. Let the first be x, the second 2x + i, and the third 2(2*+ i)+ i or 4*rt- 3, so that two conditions are satisfied. "
Diophantine Analysis - Page 110
by Robert Daniel Carmichael - 1915 - 118 pages
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Elements of algebra, by A. Ingram and J. Trotter

Alexander Ingram, James Trotter (arithmetician.) - History - 1844
...which the sum is ^. 2. To find three square numbers in arithmetical progression. Ans. 1, 25, and 493. To find three numbers such, that the square of any one of them added to the other shall be a square. Ans. Any three fractions of which the sum is j. 4. To find two...
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The Theory of Numbers and Diophantine Analysis: Two Volumes Bound As One

R. D. Carmichael - Mathematics - 2004 - 118 pages
...square. (Diophantus; Hart, 1876.) 5. Show how to find three numbers such that the product of any two of them plus or minus the sum of the three is a square. (Diophantus.) 6. Show how to find four numbers such that the product of each two of them increased by unity shall...
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Diophantus of Alexandria: A Study in the History of Greek Algebra

Sir Thomas Little Heath - Mathematics, Greek - 2012 - 393 pages
...gives (4* + 3)= + x = square = (4* 4)*, say. Therefore x = -^, and the numbers are ^, 2? ^. 33. To find three numbers such that the square of any one of them minus the next following gives a square. Assume x+ \, 2x+ i, 4* + i for the numbers, so that two conditions...
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