| John Dougall - 1810 - 732 pages
...ACDE, is eqii: 1 to the sum of the two squares AFGB and EH 1C : 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 pages
...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 - Surveying - 1814 - 398 pages
...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 - Agriculture - 1816 - 514 pages
...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 pages
...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... | |
| Thomas Thomson - Agriculture - 1816 - 518 pages
...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... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...algebraic formula (a + 6) X (a — &)= (ať— 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... | |
| Adrien Marie Legendre - 1825 - 570 pages
...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... | |
| Thomas Morell - Philosophy - 1827 - 614 pages
...discoveries. 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... | |
| Timothy Walker - Geometry - 1829 - 156 pages
...the study of geometry with wonderful ardour and success. It was he who discovered that the square of **the hypothenuse of a right-angled triangle is equal to the sum of** the squares of the other two sides. To express his joy and gratitude for this great discovery, we are... | |
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