 | 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 - 456 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... | |
 | Euclid, 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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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... 
