 | John Playfair - Euclid's Elements - 1842 - 332 pages
...: D ; but A : B : : C : D, therefore (11. 5.) A -C:BD::A:D. COR. AC : BD : : C : D. PROP. D. THEOR. If four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : A— B : : C : C— D. For, since A : B : : C : D, by division... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...: C : D, therefore (11. 5.) A — C: BD :: A : D.~ COR. A— C : B— D : : C : D. PROP. D. THEOR. If four magnitudes be proportionals, they are also proportionals by conversion, that ie, the first is to its excess above the second, as the third to its excess above the fourth. If A... | |
 | Euclid - Geometry - 1845 - 218 pages
...Book 5. XVII. Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth. Prop. EBook 5. XVIII. Ex sequali (sc. distantia), or ex sequo, from equality of distance; when there... | |
 | James Wood - Algebra - 1845 - 442 pages
...— d that is, — - — = — ; — ; о il or a — b : b :: с — d : d. 246. Again, convertendo, the first is to its excess above the second, as the third to its excess above the fourth. (EUCLID, B. v. Prop. E.) i . , a - b с - d ay the last article, — - — = — - — ; bd bd and... | |
 | Euclides - 1845 - 546 pages
...Book v. XVII. Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth. Prop. E. Book v. XVIII. Ex aequali (sc. distantia), or ex aequo, from equality of distance : when there... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...17th Prop. Book V. 18. JBy conversion: when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth, f Prop. E, Book V. 19. Ex ceqw, or ex equali (scil. dislantiA), from equality of distance : when there... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...-C:BD:: A: D. COR. AC : BD : : C : D. PROP. D. THEOR. If four magnitudes be proportionals, they arc also proportionals by conversion, that is, the first...second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : A— B : : C : C— D. For, since A : B : : C : D, by division... | |
 | Euclides - 1846 - 292 pages
...17) : xvn. Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth (S. E) : XVIII. Ex tequali (sc. distantia), or ex cequo, from equality of distance ; when there is... | |
 | W. M. Buchanan - Science - 1846 - 768 pages
...vertor, to be turned. CONVER'SION (of proportion), is when, of four proportionals, It is inferred that the first is to its excess above the second, as the third to its excess above the fourth. 2. In logic, a proposition is said to be converted when the terms are so transposed that the subject... | |
 | Euclides - 1846 - 272 pages
...there be four magnitudes proportional, but the first be greater than the second, the first will be to its excess above the second, as the third to its excess above the fourth. COR. 2. — If there be four magnitudes proportional, A to B as C to D, the difference between the... | |
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Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth. 
