| Euclides - 1840 - 192 pages
...multiples or submultiples which are equal, those pairs of numbers are proportional, or the first has **the same ratio to the second which the third has to the fourth.** But it must be remembered that there are incommensurable magnitudes, the relative values of which,... | |
| Oliver Byrne - 1841 - 144 pages
...understand this definition before proceeding further. с 2 PROP. IV. THEO. If the first of four magnitudes **have the same ratio to the second, which the third has to the fourth,** then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| Euclides - 1841 - 378 pages
...the fourth. If, therefore, the first, &c. QED PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth;** then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| Oliver Byrne - 1841 - 140 pages
...a, artd (m — n) b с = b, when m — n = 1. PROP. A. THEO. If the first of the four magnitudes has **the same ratio to the second, which the third has to the fourth,** then, if the first be greater than the second, the third is also greater than the fourth ; and if equal,... | |
| Euclides - 1842 - 316 pages
...the ratio of the third to the fourth. Definition of proportion according to Euclid, (Def. V., Book " **The first of four magnitudes is said to have the same...being " taken, and any equimultiples whatsoever of the** second and " fourth ; if the multiple of the first be equal to, greater " than, or less than the multiple... | |
| Wales Christopher Hotson - 1842 - 306 pages
...:: a + c + e ... : 6 + d +/... 149. Geometrical Definition of Proportion. (Euclid, book v. def. 5). **The first of four magnitudes is said to have the same...first and third being taken, and any equimultiples** whatsover of the second and fourth ; if the multiple of the first, be less than that of the second,... | |
| John Playfair - 1842 - 332 pages
...mB=mnC, and by hypothesis A=mB, therefore A=wmC PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** and if any equimultiples whatever be taken of the first and third, and any whatever of the second and... | |
| Scottish school-book assoc - 1845 - 444 pages
...geometrical magnitudes, and therefore it is necessary to substitute another, which is as follows: — Def. **The first of four magnitudes is said to have the same ratio to the second,** that the third has to the fourth, when any equimultiples whatever of the first and third being taken,... | |
| Euclides, James Thomson - 1845 - 382 pages
...whatever of G, H: therefore (V. def. 5) as E : G : : F : H. Therefore, &c. Cor. Likewise, if the first **have the same ratio to the second, which the third has to the fourth,** then also any like multiples whatever of the first and third have the same ratio to the second and... | |
| Euclid - 1845 - 218 pages
...ratio to the second, than the fifth has to the sixth. PROPOSITION XIV. THEOR. — If the first has **the same ratio to the second which the third has to the fourth;** then, if the first be greater than the third, the second shall be greater than the fourth ; and if... | |
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