 | Euclides - 1834 - 518 σελίδες
...the first to 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 σελίδες
...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...first is to its excess above the second 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... | |
 | 1836 - 488 σελίδες
...magnitude taken from the other ; the remainder will be to the remainder as the whole to the whole. D. If four magnitudes be proportionals, they are also...first is to its excess above the second, as the third to its excess above the fourth. XX. If there be three magnitudes, and other three, which taken two... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...of the first to the remaining part of the second. The demonstration is contained in the preceding. PROP. E. THEOR. IF four magnitudes be proportionals,...first is to its excess above the second, as the third to its excess above the fourth. Let AB : BE : : CD : DF; then BA : AE : : DC : CF. (See the figure... | |
 | John Playfair - 1837 - 332 σελίδες
...C : 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...first is to its excess above the second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : A— B : : C : C— D. For,... | |
 | Andrew Bell - 1837 - 290 σελίδες
...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 difference, as the sum of the third... | |
 | Robert Simson - 1838 - 434 σελίδες
...taken from the first to that taken from the other: the demonstration is contained in the preceding. PROP. E. THEOR. IF four magnitudes be proportionals,...first is to its excess above the 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.... | |
 | Euclides - 1840 - 192 σελίδες
...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...first is to its excess above the 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,... | |
 | Oliver Byrne - 1841 - 140 σελίδες
...as the third is to its excess above the fourth. See the following proposition : — PROP. E. THEO. If four magnitudes be proportionals, they are also...first is to its excess above the second, as the third to its excess above the fourth. Let OÔ = 0 » DO : 0' then shall OÔ • О :: ПО : D. Because OÔ:Ô:... | |
 | Euclides - 1841 - 378 σελίδες
...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;... | |
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THEOB.—If four magnitudes be proportionals, they are also proportionals by conversion; that is, the first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF: then BA shall be to AE, as DC to... 
