 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...AU, and making the reductions as in tho preceding theorem, we obtain AB = BC + AC + ZBC X CD. 193. Scholium. The right-angled triangle is the only one in which the sum of the squares of two of the sides is equal to the square of the third ; for, if the angle contained by their sides... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...term AD, and making the reductions as in the preceding theorem, we obtain MB = BC + AC + 2BCx CD. 193. Scholium. The right-angled triangle is the only one in •which the sum of the squares of two of the sides is equal to the square of the third ; for, if the angle contained by their sides... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...each term AD, and making the reductions as in the preceding theorem, we obtain = BC+AC+ IBC x CD. 193. Scholium. The right-angled triangle is the only one in which the sum of the squares of two of the sides is equal to the square of the third ; for, if the angle contained by their sides... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...term AD, and making the reductions as in the preceding theorem, we obtain AB = BC + AC + 2BCx CD. 193. Scholium. The right-angled triangle is the only one in which the sum of the squares of two of the sides is equal to the square of the third; for, if the angle contained by their sides... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...(Prop. XL), and AB ' is equal to BD'+AD'; therefore AC'=BC'+ AB'+2BCxBD. Therefore, in obtuse-an- DB c Scholium. The right-angled triangle is the only one in which the sum of the squares of two sides is equivalent to the square on the third side; for, if the angle contained by the two... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...by squaring (p. 8), £>. DC~EB Adding AD to both, and reducing as in the last theorem, and we have' CD. Scholium. The right-angled triangle is the only one in which the sum of the squares described on two sides is equivalent to the square described on the third ; for, if the angle contained... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...*+2BCxCD. DC Adding AD3 to both members, and reducing as in the last theorem, and we have AB*oBl?+AC0~+2BCx CD. Scholium. The right•angled triangle is the only one in which the sum of the squares described on two sides is equivalent to the square described on the third ; for, if the angle contained... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...consequently (p. 8), .CD. DC Adding AI? to both members, and reducing as in the last theorem, and we have Scholium. The right-angled triangle is the only one in which the sum of the squares described on two sides is equivalent to the square described on the third; for, if. the angle contained... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...BD'+AD' ; therefore AC' = BC'+ AB'+2BCxBD. Therefore, in obtuse-anDB C gled triangles, &c. Scholium. Tire right-angled triangle is the only one in which the sum of the squares of two sides is equivalent to the square on the third side ; for, if the angle contained by the two... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...AlS2 = B~D2 + AD2, and ACa = CDa + ADa (Prop. XI.) ; therefore, AB2 = B~C2 + A~Ca + 2 BCX CD. 246. Scholium. The right-angled triangle is the only one in which the sum of the squares of two sides is equivalent to the square of the third ; for if the angle contained by the two sides... | |
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Scholium. The right-angled triangle is the only one in which the sum of the squares of two sides is equivalent to the square of the third ; for if the angle contained by the two sides is acute, the sum of their squares will be greater than the square... 
