| Adrien Marie Legendre - 1825 - 570 pages
...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 right-angled at A. Having constructed squares... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...(Alg. 34). THEOREM. j'' 186. The square described upon the hypothmuse of a right-angled {riangle is equal to the sum of the squares described upon the two other sides. Fig. 109. Demonstration. Let ABC (fig. 109) be a triangle right-angled at A. Having constructed squares... | |
| Adrien Marie Legendre - Geometry - 1825 - 276 pages
...62) (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. Fig. 109. Demonstration. Let ABC (fig. 109) be a triangle right-angled at A. Having constructed squares... | |
| Walter Henry Burton - Astronomy - 1828 - 84 pages
...described upon the hypothenuse (or side opposite to the right angle) of a right-angled triangle, is equal to the sum of the squares described upon the two other sides. Thus, let ABC be a triangle, having a right angle at A. It is intended to prove that a square described... | |
| Philosophy - 1871 - 396 pages
...material bodies or in the infinite world of conceivable atoms ; and so, also, the theorem that the square upon the hypotenuse of a right triangle is equal to the sum of the squares upon its other two sides, is necessary in its truth, and universal in its application,... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...the diameter and the segment adjacent to that chord. PBOPOSITION XIV.— THEOREM. 48. The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Let ABC be right angled at C; then, AB' = A For, by the preceding... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...the diameter and the segment adjacent to that chord. PROPOSITION XIV.— THEOREM. 48. The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Let ABC be right angled at C; then, IB* = AC-' + BC\ For, by the... | |
| Samuel Mecutchen, George Mornton Sayre - Arithmetic - 1877 - 200 pages
...corners; what is the area of the field? Note. — It is established by Geometry that "The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides." Hence the following : — To find the hypotenuse of a right triangle.... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...squares of two lines is 81, and one of the lines is 12; required the other. THEOREM XL The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Let ABC be a right triangle, whose hypotenuse is AB; then will... | |
| James Wallace MacDonald - Geometry - 1889 - 80 pages
...SCHOLIUM. Compare (a + b) (a — b) = a* — P. Proposition XI. A Theorem. 246. The square described on the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. COROLLARY. The square described on either side forming the right... | |
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