 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...multiple of the second, but the multiple of the third is not greater than the multiple of the fourth, then the first is said to have to the second a greater ratio than the third has to the fourth ; and the third is said to have to the fourth a less ratio than the first has to the second, 8. Analogy,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...multiple of the second, out the multiple of the third is not greater than the multiple of the fourth, then the first is said to have to the second a greater ratio than the third has to the fourth ; and the third is said to hare to the fourth a less ratio than the first has to the second. 8. Analogy,... | |
 | Euclides - 1884 - 434 pages
...a less ratio than the first has to the second. COR. — Conversely, if the first of four magnitudes have to the second a greater ratio than the third has to the fourth, two numbers in and n may be found, such that, while m times the first magnitude is greater than n times... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...that of the second, but the multiple of the third not greater than that of the fourth, the first has to the second a greater ratio than the third has to the fourth. This, instead of being a definition, is a theorem. We hare altered the last clause from that given in Simson's... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...than that of the second, but the multiple of the third is not greater than that of the fourth, then the first is said to have to the second a ' greater ratio ' than the third has to the fourth. This may be expressed symbolically thus : — If A, B, X, Y are four magnitudes and two whole numbers, m... | |
 | Euclid - Geometry - 1890 - 442 pages
...than that of the second, but the multiple of the third is not greater than that of the fourth; then the first is said to have to the second a greater ratio than the third has to the fourth ; and the third is said to have to the fourth a less ratio than the first has to the second. Or, in... | |
 | Joseph Battell - Force and energy - 1903 - 722 pages
...of the second, but the multiple of the third is not greater than the multiple of the fourth : then the first is said to have to the second a greater ratio than the third has to the fourth : and, on the contrary, the third is said to have to the fourth a less ratio than the first has to... | |
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When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have... 
