They can be got from right-angled triangles2 by dividing the square of one of the sides about the right angle by the square of the other. Let the squares then be The continued product = -J^ffax... Diophantine Analysis - Page 4by Robert Daniel Carmichael - 1915 - 118 pagesFull view - About this book
| Sir Thomas Little Heath - Mathematics, Greek - 1885 - 248 pages
...13 Therefore we have simply to divide ^j intо three squares. 24. To find three squares such tiiat **their continued product added to any one of them gives a square.** Let the " solid content" = x*, and we want three squares such that each increased by 1 gives a square.... | |
| Hugh Chisholm - Encyclopedias and dictionaries - 1910
...squares (III. 22) ; To find two numbers such that their product =t their sum gives a cube (IV. 29) ; **To find three squares such that their continued product added to any one of them gives a square** (V. 2l). Book VI. contains problems of finding rational right-angled triangles such that different... | |
| Hugh Chisholm - Encyclopedias and dictionaries - 1910
...squares (III. 22); To find two niimbfrs such that their product * their sum gives a cube (IV. 29); **To find three squares such that their continued product added to any one of them gives a square** (V. 21). Book VI. contains problems of finding rational right-anglfd triangles such that different... | |
| Sir Thomas Little Heath - Mathematics, Greek - 393 pages
...the sum of three squares + /?. Hence we have to divide £f into three squares, "which is easy'." 21. **To find three squares such that their continued product added to any one of them gives a square.** Let the " solid content " = x-. We want now three squares, each of which increased by I gives a square.... | |
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