 | Euclid - Euclid's Elements - 1789 - 296 pages
...fecond, will be to the firft or fecond, as the difference of the third and fourth, is to the third or fourth. Let AB be to BE as CD is to DF ; then will AE be to AB, or EB, as CF is to CD, or FD. For, For, of AE, EB, CF, FD take any equimultiples... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...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 proportionals...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 division1,... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...that taken from the other : the demonstration is contained in the preceding;. B PROP. E. THEOR. IF four magnitudes be proportionals, they are also proportionals...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 is to AE as DC to CF. Because... | |
 | Euclid - Geometry - 1810 - 554 pages
...is contained in the preceding. PROP. E. THEOR, IF four magnitudes be proportionals, they are als« proportionals by conversion, that is, the first is...its excess above the fourth. Let 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, by divia 17. 5. sion *, AE... | |
 | John Mason Good - 1813 - 714 pages
...from the other; the remainder shall be to the remainder, as the whole to the whole. Prop. E. Theor. If four magnitudes be proportionals, they are also 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... | |
 | Euclides - 1814 - 560 pages
...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 proportionals...its excess above the fourth. Let 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, by di' 17. 5. vision 3 , AE... | |
 | Charles Butler - 1814 - 582 pages
...— — , 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, and since — = — , odac... | |
 | Euclides - 1816 - 588 pages
...; when there are four proportionals, and it is inferred, that the first Is to its excess I B6on V. above the second, as the third to its excess above the ' — ^ fourth. Prop. E. Books. XVIII. Ex aequali (sc. distantia), or, ex aequo, from equality of distance ; when there... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...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 proportionals...the third to its excess above the fourth, Let A+B : B : : C + D : D ; then A+B : A : : C+D:C. For (dividendo) A : B : : C : D ; .•. (invertendo) B... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...fore (11. 5.) AC : B- D : : A : B. Therefore, &c. QE D, COR. AC : BD : : C : D. PROP. D. THEOR. If four magnitudes be proportionals, they are also proportionals...second, as the third to its excess above the fourth. If A : B : : C : D, by conversion, A : AB : : C : C -D. For, since A : B : : C : D, by division (17.... | |
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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. 
