| 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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