| Robert Simson - Trigonometry - 1806 - 546 pages
...to that taken from the other : the demonstration is contained in the preceding;. B PROP. E. THEOR. **IF four magnitudes be proportionals, they are also...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... | |
| John Playfair - Euclid's Elements - 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...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,... | |
| 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...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 AB is to BE, as CD to DF, by divia 17.... | |
| 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...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 AB is to BE, as CD to DF, by di' 17.... | |
| 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... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...there 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...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.... | |
| John Mason Good - 1819 - 800 pages
...Theor. If four magnitudes he proportional«, they are also proportionals by conversion, that is, i liv **first is to its excess above the second, as the third to its excess above the fourth.** Prop. XX. Theor. If there be three magnitudes, and other three, which, taken two and two, have the... | |
| Euclid - 1822 - 222 pages
...be proved, that if there be four magnitudes proportional, and the first be greater than the second, **the first is to its excess above the second, as the third to its excess above the fourth.** Cor. 2. If there be four magnitudes proportional, AF,g, 34. to B as C to D ; the difference between... | |
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