| Pierce Morton - Geometry - 1830 - 584 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 - 732 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 - 216 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 - 518 pages
...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 - 684 pages
...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 - 540 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 - 488 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 - 1837 - 226 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 - 410 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 - 584 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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