| Silvestre François Lacroix - Algebra - 1825 - 324 pages
...we make m = 1, we have simply 6 -f- a: b — a : : d + c : d — c, which may be enunciated thus ; The sum of the first two terms is to their difference...as the sum of the last two is to their difference. 225. The proportion a : b : : c : d may be written thus ; a : c : : b : d; we have then < c _, d .... | |
| William Smyth - Algebra - 1830 - 278 pages
...whence making ro= 1, we have b-\- a:b — a:;d + c:d — c a proportion which may be enunciated thus The sum of the first two terms is to their difference,...as the sum of the last two is to their difference. 180. The proportion n : l::c : d may be written thus, a : c::b : d, we have then e , d_ from which... | |
| Silvestre François Lacroix - Algebra - 1831 - 324 pages
...we make m •=. I, we have simply b + a ib — ai id -\- c id — c, which may be enunciated thus ; The sum of the first two terms is to their difference as the sum of th» last two is to their difference. 225. The proportion aib ncid may be written thus ; aici ib id;... | |
| Benjamin Peirce - Algebra - 1837 - 300 pages
...nB:mC—nD = A : C=B : D, and A + B : A — B = C+ D .C — D m A-\-nB:mA — nB = mC-\-nD : mC — nD; that is, the sum of the first two terms of a proportion....the consequents may be multiplied by any number. 73. Two proportions, as A: B = C: D and Ratio of Reciprocals. may evidently be multiplied together,... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...of the last two, as the difference of the first two terms is to the difference of the last two, and as the first term is to the third, or as the second...as the sum of the last two is to their difference. Two proportions, as A :B = CD and E : F = G '. Hy may evidently be multiplied together term by term,... | |
| Benjamin Peirce - Geometry - 1841 - 186 pages
...andthe difference of the first two terms is to the difference of the last two in the same ratio ; also the sum of the first two terms is to their difference...as the sum of the last two is to their difference. Proof. The proportion A: B= C :D gives, by transposing the means, A : C = JB : D ; from which we obtain,... | |
| Thomas Sherwin - Algebra - 1841 - 320 pages
...the last two, as the difference of the first two terms is to thf. difference of the last two ; also, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference. Remark. It is manifest that the last two proportions might be written... | |
| James Bates Thomson - Algebra - 1844 - 272 pages
...b : b — a : : d : d — c, &c. 7. Adding and subtracting, a-\-b:a — b::c-\-d:c — d. That is, the sum of the first two terms, is to their difference, as the sum of the last two, to their difference. Cor. If any compound quantities, arranged as in the preceding examples, are proportional,... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...the difference of the first two terms is to the difference of the last two in the same ratio ; also the sum of the first two terms is to their difference as the sum of the last lilo is to their difference. Proof. The proportion A:B= C : D gives, by transposing the means, A :... | |
| William Smyth - 1847 - 276 pages
...whence making m = 1, we have b-\-a:b — a::d-\-c:d — c, a proportion which may be enunciated thus, The sum of the first two terms is to their difference, as the sum of the last turn is to their difference. 165. The proportion a : b : : c : d may be written thus, a : c : : b :... | |
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