 | Euclides - 1834 - 518 sider
...that taken from the other. The demonstration is contained in the preceding. PROPOSITION E. THEOR. — If four magnitudes be proportionals, they are also proportionals by conversion ; that is, theJtrst is to its excess above the second, as the third to its excess above the fourth. Let AB be... | |
 | Euclid - 1835 - 540 sider
...other: The demonstration is contained in the preceding. PROP. E. THEOR. a 17. 5. b B. 5. c la 5. See N. If four magnitudes be proportionals, they are also...as the third to its excess above the fourth. Let AB be to BE, as CD to DF : then, by conversion, BA is AE, as DC to CF. Because AB is to BE, as CD to DF,... | |
 | 1836 - 488 sider
...fourth. 18. 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 is to its excess above the fourth. 19. Ex cequali, (sc. distanlia,) or ex aqua, from equality of distance... | |
 | Euclid, James Thomson - 1837 - 410 sider
...analogy will become B + A:B— A::D + C:D — C. IF four numbers be proportional ; then, by conversion, the first is to its excess above the second, as the third to its excess above the fourth. If A : B : : C : D ; then, by conversion, A:A — B::C:C — D. ™ /ia . " \ BD . . AC For, since... | |
 | Andrew Bell - 1837 - 290 sider
...the second, as the excess of the third above the fourth, is to the fourth. 26. By conversion, when the first is to its excess above the second, as the third is to its excess above the fourth. 27- By mixing, when the sum of the first and second, is to their... | |
 | Robert Simson - 1838 - 434 sider
...first to that taken from the other: the demonstration is contained in the preceding. PROP. E. THEOR. IF four magnitudes be proportionals, they are also...second, as the third to its excess above the fourth. i C FLet AB be to BE, as CD to DF ; then BA is to AE, as DC to CF. Because AB is to BE, as CD to DF,... | |
 | Euclides - 1840 - 192 sider
...alternately, A — C:B— D: :C:D; but A : B : : C : D, therefore AC:BD::A:B(v. Prop. n). 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:AB::C:CD. For, since A:B::C:D, by division, AB : B:: CD : D (v.... | |
 | James Wood - 1841 - 492 sider
...that is L_c~. nidi/ is, ~ : , b а or a — b : b :: с — d : d. 235. Again, convertendo, the ßrst is to its excess above the second, as the third to its excess above the fourth. T> ii • ia -b с - d By the last article, - = - ; od bd and — = - (Art. 231) ; a с a — bb с... | |
 | Euclides - 1841 - 378 sider
...that taken from the other. The demonstration is contained in the preceding. PROP. E. THEOR. Tf fonr magnitudes be proportionals, they are also proportionals by conversion: that is, the first is to its ejrcess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF;... | |
 | Oliver Byrne - 1841 - 140 sider
...conversion, is made use of by geometricians, when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third is to its excess above the fourth. See the following proposition : — PROP. E. THEO. If four magnitudes... | |
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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. 
