 | Luke Herbert - Industrial arts - 1829 - 394 pages
...weight, as the velocity of the weight to the velocity of the power ; and as, in these 4 quantities, the first is to the second as the third to the fourth, it follows, that the 1st multiplied by the 4th, equals the 2nd multiplied by the 3rd.. Therefore, the... | |
 | Luke Hebert - 1829 - 392 pages
...weight, as the velocity of the weight to the velocity of the power $ and as, in these 4 quantities, the first is to the second as the third to the fourth, it follows, that the 1st multiplied by the 4th, equals the 2nd multiplied by the Std, Therefore, the... | |
 | James Ryan, Robert Adrain - Algebra - 1835 - 388 pages
...— 5ab have unlike signs ; also, the quantities — Sax, -\-Sa*x : and the quantities —b, -f-4. 24. If the quotients of two pairs of numbers are equal,...the fourth ; and any quantities, expressed by such ac numbers, are also proportional; thus, if -7- = —; then a is to b as c to d. The abbreviation of... | |
 | Euclid - 1835 - 540 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... | |
 | Mathematics - 1836 - 488 pages
...first be the saine multiple of the second, or the same part of it, thut the third is of the fourth; the first is to the second as the third to the fourth. C. If the first be to the second as ths tlu'rd to the fourth ; and if the first be a multiple or a... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 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, mB, be equimultiples of the magnitudes A and B, mA : A : : mB : B. Take of mA and mB... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...proportion or analogy. When magnitudes are proportionals, the relation is expressed briefly by saying, that the first is to the second as the third to the fourth, the fifth to the sixth, and so on.f .7. When of the multiples of four magnitudes, taken as in the fifth... | |
 | James Ryan - Algebra - 1838 - 412 pages
...signs ; thus, the quantities +3a and — 5ab have unlike signs ; also, the quantities —3ax, -\-3a2x : and the quantities — b, -\-b. 24. If the quotients...proportional; thus, if -7-= -?••, then a is to b as c to A. The abbreviation of the proportion ; a : b : : c : d ; and it is sometimes written a : l—c: d;... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...mean proportional between them. (323.) ' Four quantities are said to he directly proportional, when the first is to the second as the third to the fourth.' Thus, A, B, C, and D, are directly proportional when A : B = С : D. So 3, 4, (5, and 8, are directlv... | |
 | Euclides - 1840 - 192 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, mB be equimultiples of the magnitudes A and B; mA:A::mB:B. Take of mA and mB equimultiples... | |
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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 the first is greater... 
