 | Robert Simson - 1806 - 546 σελίδες
...taken from the first to that taken from the other : the demonstration is contained in the preceding;. B 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. a 17. 5. bB.5. c 18. 5. See N. Let AB be to BE as CD to DF ; then BA... | |
 | John Playfair - 1806 - 320 σελίδες
...: B. Therefore, &c. QE D, COR. A— C : B— D : : C : D. PROP. D. THEOR. a 17. 5. b A. 5. c 18. 5. 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. If A : B : : C : D, by conversion, A : A— B : : C : C— D. For,... | |
 | Euclid - 1810 - 554 σελίδες
...is contained in the preceding. PROP. E. THEOR, IF four magnitudes be proportionals, they are als« 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 is to AE, as DC to CF. Because... | |
 | John Mason Good - 1813 - 714 σελίδες
...magnitude taken from the other; the remainder shall be to the remainder, as the whole to the whole. Prop. E. Theor. If four magnitudes be proportionals,...proportionals by conversion, that is, the first is to its exciss above the second, as the third to its excess above the fourth. Prop. XX. Theor. If there he... | |
 | Charles Butler - 1814 - 582 σελίδες
...— — , that is, a—b:b::c—d:d; thii is called 01 viha DESDO. Euclid 17, 5. 68. In like manner, the first is to its excess above the 'second, as the third to its excess above the fourth. a— b c—d , , ,. , . bd Because — ; — = — - — by the preceding,... | |
 | Euclides - 1816 - 588 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. Let AB be to BE, as CD to DF; then BA istoAE, as DC to CF. Because... | |
 | John Playfair - 1819 - 354 σελίδες
...but A : B : : fore (11. 5.) AC : BD : : A : B. Therefore, &c. Q, ED 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 : AB : : C : CD. For, since A... | |
 | Daniel Cresswell - 1819 - 446 σελίδες
...shewn that A : B : : A— B : B— C ; And .(%>.) A>B; .-. (S. 1. 5.) AB>BC. PROP. XVI. 18. THEOREM. 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 A+B : B : : C + D : D ; then A+B : A : : C+D:C. For (dividendo)... | |
 | Adrien Marie Legendre - 1819 - 574 σελίδες
...the fourth is to the fourth ; convertendo, by conversion, when it is inferred that the first is to iU excess above the second, as the third is to its excess above the fourth. VI. When a proportion is said to exist among certain magnitudes, these magnitudes are supposed to be... | |
 | John Playfair - 1819 - 350 σελίδες
...Books. XVIII. 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. D. Book 5. XIX. Ex aaquali (sc. distantia), or ex aequo, from... | |
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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... 
