 | John Beck - Education - 1978 - 582 pages
...importance of what it is we are trying to do. 'This morning,' I said to them, 'we are going to prove that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.' 'Is that a likely thing to happen?' Mason asked. I... | |
 | G. S. Kirk, J. E. Raven, M. Schofield - Philosophy - 1983 - 520 pages
...Apollodorus the calculator says that he [se. Pythagoras] sacrificed a hundred oxen when he discovered that the square on the hypotenuse of a right-angled triangle is equal to the squares on the sides containing the right angle. And there is an epigram which runs as follows:... | |
 | Daniel Pedoe - Mathematics - 1983 - 338 pages
...side a + b is equal to (aj-6)2, find the area of the square PQRS. Deduce the theorem of Pythagoras that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. (You will have to use the algebraic identity: 2 ALBRECHT... | |
 | Edward Regis - Philosophy - 1984 - 284 pages
...accountants or surveyors. Anything that purports to overturn or impugn our recognition that 7 x 7 = 49 or that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the adjacent sides would merely discredit itself by reductio ad absurdum.... | |
 | René Descartes - Philosophy - 1984 - 444 pages
...these geometrical proofs. And how often do you find a believer who, if he is asked why he is certain that the square on the hypotenuse of a right-angled triangle is equal to the squares on the other sides, will answer: 'Because I know that God exists and cannot deceive, and... | |
 | F. C. White - Philosophy - 1992 - 208 pages
...that he rejects. To illustrate this point with a representative example, Euclid holds with Pythagoras that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides: s 2 = a 2 + b 2 . Schopenhauer holds this too. But in... | |
 | John Ewing - Mathematics - 1994 - 348 pages
...out of them, and nothing else." To quote an example which the author himself gives, the proposition that "the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides" is a categorical proposition, and is not therefore mathematical.... | |
 | Rudolf Steiner - Anthroposophy - 1995 - 180 pages
...your geometry lessons to reach their climax, their summit, in the Theorem of Pythagoras, which states that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. It is a marvelous thing if you see it in the right light.... | |
 | David R. Olson, Nancy Torrance - Education - 1996 - 324 pages
...at their strongest. Surely no one is going to deny that 2 + 2 is 4 in both China and Greece. Surely the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides, whether we call this Pythagoras' theorem, or Gou Gu.... | |
 | Plinio Prioreschi - Medicine - 1996 - 651 pages
...Pythagoras himself discovered what we call the Pythagorean Theorem. In Proclus's In Euclidem, we find: The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides enclosing the right angle. If we pay any attention to those who... | |
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Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. 
