 | Robert Simson - Trigonometry - 1806 - 546 pages
...triangle, and equal magnitudes have to the same the same ratiob; therefore, as the b 7. 5. triangle BDE to the triangle ADE, so is the triangle CDE to the triangle ADE; but as the triangle BDIi to the triangle ADE, so isc BD to DA, because having the same altitude, viz. c1.... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...triangle BDE is equal to the triangle CDEa. But ADE is another triangle, therefore as the triangle BDE to the triangle ADE, so is the triangle CDE to the triangle ADEb. But, as the triangle BDE to the triangle ADE, so isc BD to DA; and as the triangle CDE to the... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...triangle, and equal magnitudes have, to the same, the same ratio (7. 5.) ; therefore, as the triangle BDE to the triangle ADE, so is the triangle CDE to the triangle ADE ; but as the triangle BDE to the triangle ADE, so is (1. 6.) BD to DA, because having the same altitude,... | |
 | Euclides - 1826 - 226 pages
...to the triangle ADE," but as CE is to < i. 6. ŤA so is the triangle CDE to the triangle ADE ; and therefore as the triangle BDE is to the triangle ADE so is the triangle CDE to the triangle ADE. Hence eaph of the triangles BDE, CDE, has the same ratio to the triangle ADE. Therefore the triangle... | |
 | Euclid - 1826 - 234 pages
...to the triangle ADE,C but as CE is to • i. 6. EA so is the triangle CDE to the triangle ADE; and therefore as the triangle BDE is to the triangle ADE so is the triangle CDE to the triangle ADE. Hence each of the triangles BDE, CDE, has the same ratio to the triangle ADE. Therefore the triangle... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...parallels DE, BC : ADE is another triangle; and equal magnitudes have to the * 7- 5. same* the same ratio ; therefore, as the triangle BDE •is to the triangle...ADE, so is the triangle CDE to the triangle ADE: but as the triangle BDE to the triangle * 1• 6, ADE so is* BD to DA, because, having the same altitude,... | |
 | Euclides - 1834 - 518 pages
...DE, BC: ADE is another triangle ; and equal magni• 7. 5. tudes have to the same * the same ratio ; therefore, as the triangle BDE is to the triangle...ADE, so is the triangle CDE to the triangle ADE : but as the triangle BDE • 1. 6. to the triangle ADE, so is * BD to DA, because, having the same altitude,... | |
 | John Playfair - Geometry - 1836 - 148 pages
...triangle, and equal magnitudes have to the same, the same ratio (13. 4.) ; therefore as the triangle BDE to the triangle ADE, so is the triangle CDE to the triangle ADE ; but as the triangle BDE to the triangle ADE, so is (Cor. 2. 2. 5.) BD to DA, because having the same altitude,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...triangle, and equal magnitudes have, to the same, the same ratio (7. 5.) ; therefore, as the triangle BDE to the triangle ADE, so is the triangle CDE to the triangle ADE ; but as the triangle BDE to the triangle ADE, so is (1. 6.) BD to DA, because, having the same altitude,... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...triangle, and equal magnitudes have to the same the same ratio (V. 7) ; therefore, as the triangle BDE to the triangle ADE, so is the triangle CDE to the triangle ADE; but as the triangle BDE to the triangle ADE, so is BD to DA (VI. 1) ; because, having the same altitude,... | |
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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... 
