Hypotenuse

Definition and stakes

Portrait of David Hilbert David Hilbert,  Mathematical Problems (1902)

“ Occasionally it happens that we seek the solution under insufficient hypotheses or in an incorrect sense, and for this reason do not succeed. The problem then arises: to show the impossibility of the solution under the given hypotheses, or in the sense contemplated. Such proofs of impossibility were effected by the ancients, for instance when they showed that the ratio of the hypotenuse to the side of an isosceles right triangle is irrational. ”
Source: Gutenberg

Portrait of Aryabhata Aryabhata,  The Aryabhatiya of Aryabhata (1930)

“ It is impossible as a translation of the Sanskrit.
13. The circle is made by turning, and the triangle and the quadrilateral by means of a karna; the horizontal is determined by water, and the perpendicular by the plumb-line. Tribhuja denotes triangle in general and caturbhuja denotes quadrilateral in general. The word karna regularly denotes the hypotenuse of a right angle triangle and the diagonal of a square or rectangle.
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Source: Wikisource

George Rusby Kaye,  Indian Mathematics — Appendices… (1915)

“ L. 1. I propound this easy process of calculation, delightful by its elegance, perspicuous with concise terms, soft and correct and pleasing to the learned.
*⁠*⁠*⁠*⁠* L. 139. A side is put. From that multiplied by twice some assumed number and divided by one less than the square of the assumed number a perpendicular is obtained. This being set aside is multiplied by the arbitrary number and the side as put is subtracted—the remainder will be the hypotenuse. Such a triangle is termed 'genuine.'
*⁠*⁠*⁠*⁠*
L. 189. Thus, with the same sides, may be many diagonals in the quadrilateral.
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Source: Wikisource

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