 | John Dougall - 1810 - 554 Seiten
...that the square ACDE, is equ; 1 to the sum or the two squares AFGB and BHIC : or, in other words, that the square of the hypothenuse of a rightangled triangle is equal to the sum of the squares of the two sides containing the right angle. To illustrate this proposition by arithmetic,... | |
 | 1816 - 600 Seiten
...their destiny in that which is to come. Had all this been at stake in verifying the proposition, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, we somewhat question whether Pythagoras, or any body else, would... | |
 | John Gummere - 1814 - 398 Seiten
...legs ; the square root of the sum will be the hypotheuuse.* Or by logarithms thus, * DEMONSTRATION. The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the sides (47.1). Therefore the truth of the first part of each of the rules, is evident.... | |
 | Thomas Thomson - 1816 - 518 Seiten
...accomplished is a manifest corollary from the 47th proposition of Euclid's first book, which teaches us that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two sides ; so that we have only to form a rightangled triangle of a proper length... | |
 | Thomas Thomson - 1816 - 514 Seiten
...accomplished is a manifest corollary from the 47th proposition of Euclid's first book, which teaches us that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two sides; so that we have only to form a rightangled triangle of a proper length... | |
 | 1816 - 644 Seiten
...their destiny in that which is to come. Had all this been at stake in verifying the proposition, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, we somewhat question whether Pythagoras, or any body else, would... | |
 | Adrien Marie Legendre - 1825 - 570 Seiten
...algebraic formula (a + 6)x(a— 6) = (a3— 63) (Alg. 34). THEOREM. 186. The square described upon the hypothenuse of a right-angled triangle is equal to the sum of the squares described upon the two other sides. . 109. Demonstration. Let ABC (fig. 109) be a triangle... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 Seiten
...algebraic formula (a + 6) X (a — &)= (a»— b') (Alg. 34). THEOREM. f / 186. The square described upon the hypothenuse of a right-angled triangle is equal to the sum of the squares described upon the two other sides. 109. Demonstration. Let ABC (fig. 109) be a triangle... | |
 | Thomas Morell - 1827 - 614 Seiten
...His name is rendered immortal among geometricians, by his well-known discovery, " that the square on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the other two sides;" a discovery which is said to have occasioned such an ecstacy of... | |
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Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice a hecatomb when he made out its proof ? 
