 | Euclides - 1874 - 342 páginas
...(I. 37), because they are on "the same base DE, and between the same parallels DE, BC ; but ADE is another triangle ; and equal magnitudes have the same ratio to the same magnitude (V. 7) ; therefore 1. As the triangle, BDE fe to the triangle ADE, so is the triangle CUE to the triangle ADE ; B CD EBC... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 páginas
...triangles BDE and CDE are upon the same base, and of the same altitude, they are equal. Now, ADE is another triangle, and equal magnitudes have the same ratio to the same magnitude ; therefore as the triangle BDE is to the triangle ADE, so is the triangle CDE to the triangle AD;S..... | |
 | Robert Potts - 1876 - 446 páginas
...CDE, (I. 37.) because they are on the same base DE, and between the same parallels DE, BC; but ADE is another triangle ; and equal magnitudes have the same...ADE, so is the triangle CDE to the triangle ADE: but as the triangle BDE to the triangle A DE, so is BD to DA, (VI. 1.) because, having the same altitude,... | |
 | Āryabhaṭa - 1878 - 100 páginas
...as CE is to EA. . Join BE and CD. The triangle BDE is equal to tho triangle CDE (P. 15). Bat ADE is another triangle; and equal magnitudes have the same ratio to the same magnitude (16. cor. 6). Therefore as the triangle BDE is to the triangle AUE, 'so is the triangle CDE to' tho... | |
 | Isaac Todhunter - 1880 - 426 páginas
...CDE, because they are on the same base DE and between the same parallels DE, BC. [I- 37. And ADE is another triangle ; and equal magnitudes have the same ratio to the same magnitude ; fV. 7. therefore the triangle BDE is to the triangle ADE as the triangle CDE is to the triangle ADE.... | |
 | Euclides - 1881 - 236 páginas
...(I. 37), because they are on the same base DE, and between the same parallels DM, and B C. But ADE is another triangle ; and equal magnitudes have the same...Therefore, as the triangle BDE is to the triangle AEE, so is the triangle CDE to the triangle AD E. But the triangle BDE is to the triangle ADE, as BD... | |
 | Euclid, Isaac Todhunter - 1883 - 428 páginas
...the same magnitude ; [V. 7. therefore the triangle BDE is to the triangle ADE as the triangle CDE is to the triangle ADE. But the triangle BDE is to the triangle ADE as BD is to DA ; because the triangles have the same altitude, namely, the perpendicular drawn from E to AB, and therefore... | |
 | Euclid - 1908 - 456 páginas
...triangle ADE, and, as CE is to EA,, so is the triangle CDE to the triangle ^Z?^, [vi. i] therefore also, as the triangle BDE is to the triangle ADE, so is the triangle CDE to the triangle ADE. [v. 1 1] Therefore each of the triangles BDE, CDE has the same ratio to ADE. Therefore the triangle... | |
 | Richard Fitzpatrick - 2006 - 411 páginas
...are on the same base DE and between the same parallels DE and BC [Prop. 1.38]. And AD E is some other triangle. And equal (magnitudes) have the same ratio to the same (magnitude) [Prop. 5.7]. Thus, as triangle BDE is to [triangle] ADE, so triangle CDE (is) to triangle ADE. But,... | |
 | Euclid - 452 páginas
...triangle ADE, and, as CE is to EA, so is the triangle CDE to the triangle ^Z^fi1, [vi. i] therefore also, as the triangle BDE is to the triangle ADE, so is the triangle CDE to the triangle ADE. [v. n] Therefore each of the triangles BDE, CDE has the same ratio to ADE. Therefore the triangle BDE... | |
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DE, and between the same parallels DE, BC; but ADE is another triangle ; and equal magnitudes have the same ratio to the same magnitude; (v. 7.) therefore, as the triangle BDE is to the triangle ADE... 
