| Euclides - 1855 - 230 pages
...V. 13, cor. . V.17. . . V. i». . V. 19, oar. V.15. . . Or if the first be greater than the second. **If the first have to the second the same ratio which the third has to the fourth,** and the fifth to the second the same ratio which the sixth has to the fourth. Idem . If the first has... | |
| John Playfair - Geometry - 1855 - 334 pages
...A : B :: C : D. Therefore mA/nB, and roE/nF, wherefore, A : B/E : F (def. 7. 5.). PROP. XIV. THEOR. **If the first have to the second the same ratio which the third has to the** founti, and if the first be greater than the third, the second shall be greater than the fourth; if... | |
| John Playfair - Euclid's Elements - 1855 - 340 pages
...: B : : C : D. Therefore mA.ynB, and mE/nF, wherefore, A : B7E : F (def. 7. 5.). PROP. XIV. THEOR. **If the first have to the second the same ratio which the third has to** thefounn, and if the first be greater than the third, the second shall be greater than the fourth;... | |
| Mathematics - 1887 - 422 pages
...parallelogram whose sides are the two quantities. (12) DEF. The first of four quantities is said to **have to the second the same ratio which the third has to the fourth** : when the first has in length to the second the same ratio which the third has in length to the fourth... | |
| Euclides - 1855 - 270 pages
...F together (V. Def. 5). Wherefore, if anj number, &c. QE D, PROP. XIII. THEOREM. If tiie first has **to the second the same ratio which the third has to the fourth,** but the third to the fourth a greater ratio than the fifth has to the sivtht thefirst has also to the... | |
| Euclid - 1859 - 150 pages
...тро; esurtpov ТОУ aurоv ?Ç« Xóyo» rai rpiVox fai terov л-pàç rtraprov. If the first has **to the second the same ratio which the third has to the fourth** ; and thefiflh to the second the same ratio which the sixth has to the 'fourth; the first and fifth... | |
| Eucleides - 1860 - 396 pages
...&C. BC _ GFE ' C ' D ~ H ' G ' F' AE 01 therefore A : D :: E : H. "DHPROPOSITION XXIV. THEOREM. — **If the first have to the second the same ratio which the third has to the fourth** ; and the fifth to the second, the same ratio which the sixth has to the fourth ; the first and fifth... | |
| Euclides - 1860 - 288 pages
...second the same ratio which the third, together with the fourth, has to the fourth, "the first shall **have to the second the same ratio which the third has to the fourth.** G!VenthatA+B:B::C + D:D; to prove that A:B::C:D. (Dem.) Since A + B:B::C+D:D, A + B = —"£-5 ; 1»... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...magnitudes. Therefore, if there be any number, &c. QED PROPOSITION XXIV. THEOREM. If the first 1uts **to the second the same ratio which the third has to the fourth;** and the fifth to the second the same ratio which the sixth has to the fourth; tin first and fifth together... | |
| James Elliot - 1860 - 252 pages
...: , a DEM. Since a : b :: c : d, a = -, and, since c : d : : e : f, oa THEOREM V. If the first has **to the second the same Ratio which the third has to the fourth,** but the Oiird to the fourth a greater Ratio than theffth has to the suth, the first shall also have... | |
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