 | Robert Simson - 1806 - 546 pages
...called proportionals. NB < When four magnitudes are proportionals, it is usually « expressed by saying, the first is to the second, as the third to < the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of... | |
 | John Playfair - 1806 - 320 pages
...first be the same multiple of the second, or the same part of it, that the third is of the fourth, the first is to the second as the third to the fourth. First, if mA and mB be equimultiples of the magnitudes A and B, mA : A : : »iB : B. Take of mA and... | |
 | John Mason Good - 1813 - 714 pages
...called proportionals. NB When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second, as the third to the fourth. 7. When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of... | |
 | Euclides - 1816 - 588 pages
...called proportionals. ' NB When four magnitudes are proportion' als, it is usually expressed by saying", the first is to the ' second, as the third to the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition),' the multiple... | |
 | John Playfair - 1819 - 354 pages
...does when divided by the fourth, we say of these magnitudes, as we did of the numbers above described, that the first is to the second as the third to the fourth. There are only two more circumstances necessary to be considered, in order to bring us precisely to... | |
 | Pierre Simon de Marquis Laplace, Thomas Young - 1821 - 372 pages
...27. DEFINITION. If the quotients of two pairs of numbers are equal, the numbers are proportional, and the first is to the second, as the third to the fourth ; and any quantities, expressed by such numbers, are also proportional. If a ; 6~c ; d, a is to b as... | |
 | James Ryan, Robert Adrain - 1824 - 542 pages
...comprehended by the other. VJ. When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second as the third to the fourth. The Seventh Definition according to Euclid. When of the equimultiples of four magnitudes, (taken as... | |
 | James Ryan - 1824 - 550 pages
...— b, +6. 24. If the quotients of two pairs of numbers are equal, the numbers are proportional, and the first is to the second, as the third to the fourth ; and any quantities, expressed by such numbers, are also proportional ; thus, if r=-, ; then, a is... | |
 | Robert Simson - 1827 - 546 pages
...called proportionals. 'NB When four magnitudes are pro' portionals, it is usually expressed by saying, the ' first is to the second, as the third to the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple... | |
 | Euclid, Dionysius Lardner - 1828 - 542 pages
...called proportionals. ' NB When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second as the third to the fourth.' The equality of two ratios is expressed by the sign :: or = interposed between them thus, A : B : :... | |
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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... 
