 | John Hind - Algebra - 1837 - 584 pages
...follows that me will be greater than, equal to, or less than nd. Hence, of the terms of a proportion there being taken any equimultiples whatever of the...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... | |
 | James Elliot - 1860 - 252 pages
...if ma < nb, me < nd. THEOREM XVII. If four Quantities are so related to each other, that, on taking any Equimultiples whatever of the first and third,...the second and fourth, the Multiple of the third is equal to that of the fourth, greater than it, or less, according as the Multiple of the first is equal... | |
 | Isaac Todhunter - Algebra - 1876 - 350 pages
...equimultiples be taken of the first and the third, and also any equimultiples of the second and the fourth, the multiple of the third is greater than, equal to, or less than^the multiple of the fourth, according as the multiple of the first is greater than, equal to,... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...that the third has to the fourth, when, any equimultiples whatever of the first and third being taken, and any equimultiples whatever of the second and fourth,...multiple of the third is greater than, equal to, or less than that of the fourth, according as the multiple of the first is greater than, equal to, or less... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples... | |
 | David Eugene Smith - Geometry - 1911 - 370 pages
...ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples... | |
 | Sir Thomas Little Heath - Mathematics - 1921 - 474 pages
...ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples... | |
 | Cambridge Philosophical Society - Philosophy - 1923 - 676 pages
...ratio, the first to the second and the third to the fourth, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples... | |
 | Mathematicians - 1927 - 578 pages
...ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples... | |
 | Robert S. Cohen, J.J. Stachel, Marx W. Wartofsky - Biography & Autobiography - 1974 - 702 pages
...ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples... | |
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Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike... 
