 | George Peacock - Algebra - 1830 - 732 pages
...= =-, and mvertcndo, ac ac a — bc — d' or a : a — b :: c : c — d. 411. " If four magnitudes be proportionals, the sum of the first and second...their difference as the sum of the third and fourth is to their difference." Let a : b :: c : d, then also a + b : a — b :: c + d : c — d. T. .ac Forif... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...miscendo .-* viz. If four magnitudes A, B, C, D be proportionals, the sum of the first and second will be to their difference, as the sum of the third and fourth to their difference. For, since A : В : : С : D, componenda A + B : В : : С +D : D. And again, because ínvertendo В... | |
 | Mathematics - 1835 - 684 pages
...miscendo :* viz. If four magnitudes A, B, C, D be proportionals, the sum of the first and second will be to their difference, as the sum of the third and fourth to their difference. For, since A : В : : С : D, componenda A + B : В : : С +D : D. And again, because invertendo В... | |
 | Mathematics - 1836 - 366 pages
...other fraction equal to j whose terms are not equimultiples of a and b. 232. When four quantities are proportionals, the sum of the first and second is...the sum of the third and fourth to their difference. 234. Express a + b . Jl]. and log, (a + 6 v'~) in the c + « v __ l form A -|- BV _ 1. 235. Shew how... | |
 | Andrew Bell - Euclid's Elements - 1837 - 240 pages
...to its excess above the second, as the third is to its excess above the fourth. 27- By mixing, when the sum of the first and second, is to their difference,...the sum of the third and fourth to their difference. 28. By equality, when there is any number of magnitudes more than two, and as many others, so that... | |
 | Euclid - Geometry - 1837 - 410 pages
...B:: C + D:C — D: that is, if four numbers be proportional, the sum of the first and second terms is to their difference, as the sum of the third and fourth terms \a to their difference. It is evident that if B be greater than A, the analogy will become B... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 498 pages
...is to the secoml, as the excess of the third above the fourth to the fourth ; (332.) By mixing, when the sum of the first and second is to their difference,...the sum of the third and fourth to their difference ; (333.) By direct equality, when there are several analogies, and two homologous terms in each are... | |
 | Bewick Bridge - Algebra - 1839 - 282 pages
....-. inversely a : a±» :: c : c±d. TH. 8. " If four quantities be proportional, then the sum of Ihe first and second is to their difference as the sum of the third arid fourth is to their difference." For by TH. 6, — =— = — 5- , and od a — bc — d . , ,... | |
 | John D. Williams - Algebra - 1840 - 636 pages
...: c±rf : с ; .•. inversely a : «z±& : : с Тн. 8. If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. For, by theorem 6, g ' c~*~ ; ; ' bd . a — bb — d ... bd and — — —... | |
 | John D. Williams - Algebra - 1840 - 193 pages
...a±4 : a :: c±d : c; .-. inversely a : a±b ;• c TH. 8. If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. For, by theorem 6, ~|~ ~\ • od , a — bb — d , . . . . . bd and — ;... | |
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