172—173 Oxford University Press, 1999 | , A History of Greek Mathematics, Oxford University Press, 1921; reprinted by Dover, 1981 |
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For full text of 2nd edition of 1940, see Elisha Scott Loomis | In , the , the dates of which are given variously as between the 8th and 5th century BC, contains a list of and a statement of the Pythagorean theorem, both in the special case of the right triangle and in the general case, as does the Shulba Sutra c |
For the formal proof, we require four elementary :• The comparatively late writers who attribute it to him add the story that he sacrificed an ox to celebrate his discovery.
5Reprint of Prentice-Hall 1965 2nd ed | "The pentagram and the discovery of an irrational number" |
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Generalizations Similar figures on the three sides A generalization of the Pythagorean theorem extending beyond the areas of squares on the three sides to was known by in the 5th century BC, and was included by in his : If one erects similar figures see with corresponding sides on the sides of a right triangle, then the sum of the areas of the ones on the two smaller sides equals the area of the one on the larger side | Consider a rectangular solid as shown in the figure |
524 July 2008 , pp.
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