 | 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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THEOREM. lf the 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 sixth ; the first shall also have to the second a greater ratio than the fifth, has to the... 
