| Pierce Morton - Geometry - 1830 - 272 pages
...magnitude of the other ; and conversely (ax. 1, 2, 3, 4).* ' " The first of fonr magnitudes is enid to bare **the same ratio to the second, wh'ich the third has...the fourth, when any equimultiples whatsoever of the** fir>t aiid third being taken, ”ind any equimultiples whatsoever of the second and fourth ; if the... | |
| George Peacock - Algebra - 1830 - 685 pages
...be equal to that of the second, the multiple of the third will be equal to that of the fourth : and **if the multiple of the first be less than that of the second, the multiple of the third** will be less than that J of the fourth. It is this proposition which is deduced as a necessary consequence... | |
| Euclid - Euclid's Elements - 1833 - 183 pages
...controversy among geometers. Euclid defines them thus : The first of four magnitudes is said to have **the same ratio to the second, which the third has...equimultiples whatsoever of the second and fourth** being taken, the equi-multiples of the first and third either together exceed, are equal to, or are... | |
| Euclides - 1834
...the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have **the same ratio to the second, which the third has...taken, and any equimultiples whatsoever of the second** arid rt fourth, if the multiple of the first be less than that of li T.* • * the second, the multiple... | |
| Mathematics - 1835
...and conversely (ax. 1, 2, 3, 4).* • "The first of four magnitudes is said to have the same ratio tu **the second, which the third has to the fourth, when...equimultiples whatsoever of the second and fourth ; if the** inulliple of the first be less than that of the second, the multiple of the third is also less than... | |
| Euclid - 1835 - 513 pages
...is to G, so is c F to H. Therefore, " if the first," &c. QED See N. Cou. Likewise, if the first has **the same ratio to the second, which the third has to the fourth,** then also any equimultiples LFCDH whatever of the first and third have the same ratio to the second... | |
| Mathematics - 1836 - 472 pages
...oft as there are units in the product of these two numbers. IV. 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 tcriken of the first and third, and any whatever of the second... | |
| William Whewell - Mechanics - 1837 - 182 pages
...*i, *II, *III, IV. Book v. *Definition of Proportion. The first of four magnitudes is said to have **the same ratio to the second which the third has to the fourth, when^ — any** eq'wi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples whatsoever of... | |
| Euclid, James Thomson - Geometry - 1837 - 390 pages
...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... | |
| John Hind - Algebra - 1837 - 539 pages
...there being taken any equimultiples whatever of the first and third, and any equimultiples whatever **of the second and fourth : if the multiple of the first be** greater than the multiple of the second, the multiple of the third will be greater than that of the... | |
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