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Published online by Cambridge University Press: 20 January 2009
The square described on the hypotenuse of a right-angled triangle is equal to the squares described on the other two sides.
About half a hundred proofs of this theorem have been given, but few of them have been “ocular,” that is, few have shown how the two smaller squares may be decomposed so as to fit into the largest square. One of the most elegant of the ocular proofs is that of Henry Perigal, and was discovered about 1830. A demonstration of its correctness is not difficult to obtain, but the following demonstration is believed to be new. It depends somewhat on algebra, and presupposes a simple lemma.
This is the 47th proposition of the 1st book of Euclid's Elements, and is called in France le pont aux ânes, the asses' bridge. This name, in English-speaking countries, is bestowed ou the 5th proposition of the 1st book of Euclid's Elements.
* This is the 47th proposition of the 1st book of Euclid's Elements, and is called in France le pont aux ânes, the asses' bridge. This name, in English-speaking countries, is bestowed ou the 5th proposition of the 1st book of Euclid's Elements.
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