| Oliver Byrne - Mathematics - 1841 - 140 pages
...... ad = »Т т a Т e Л а/ = »с • _ 9 h ... a A = * У. т PROP. XIII. THEO. If 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... | |
| Miles Bland - Algebra - 1841 - 458 pages
...three of which are in arithmetic and the last three in harmonic progression ; prove that the first has **to the second the same ratio which the third has to the fourth.** 18. The sum of three terms of an harmonic progression, «'hose first term is -, is = — ; determine... | |
| Euclides - Geometry - 1841 - 378 pages
...number of magnitudes. Therefore, if there be any number, &c. QED PROP. XXIV. THEOR. //' the first has **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 together... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...A : B : : C : D. Therefore mA7nB, 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 the fourth,** and if the first be greater than the third, the i the fourth; if equal, equal; and if less, less. If... | |
| Euclides - 1842 - 316 pages
...just as often as the third contains the fourth, or a like part of the fourth, the first is said to **have to the second, the same ratio which the third has to the fourth** ; or, the ratio of the first to the second is said to be equal to the ratio of the third to the fourth.... | |
| George Peacock - Algebra - 1842 - 426 pages
...observation would apply to the following proposition : " if there be six magnitudes, and if the first has **to the second the same ratio which the third has to the fourth,** but if the third has to the fourth a greater ratio than the fifth to the sixth : then the first has... | |
| Euclides, James Thomson - Geometry - 1845 - 382 pages
...are A, C, E together, to B, D, F together : wherefore, if any number, &c. • PROP. XIII. THEOR. — **If the first have 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 will also have... | |
| Euclides - 1845 - 546 pages
...together. (v. def. 5.) Wherefore, if any number, &c. QED PROPOSITION XIII. THEOREM. Ifthefirst 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 Jifth has to the sixth ; thefirst shall also have... | |
| Euclid - Geometry - 1845 - 218 pages
...B, D, F t together. Wherefore, if any number, &c. QED PROPOSITION XIII. THEOB. — If 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... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...: B : : C : D. Therefore mA/nB, and mE/»F, 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 fourth,** and if the first be greater than the third, the second shall be greater than the fourth; if equal,... | |
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