| Silvestre François Lacroix - Algebra - 1825 - 322 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 - 264 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 - 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... | |
| Benjamin Peirce - Algebra - 1843 - 308 pages
...: C — D = mA — nB:mC — nD and A + B : A — B = C+ D : C— D mA-\-nB:mA — nB = mC + nD:mC **that is, the sum of the first two terms of a proportion...both the consequents may be multiplied by any number.** 98. Two proportions, as A: B = C : D and Ratio of Reciprocals. may evidently be multiplied together,... | |
| Jeremiah Day, 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,... | |
| William Smyth - 1847 - 278 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 :... | |
| Benjamin Peirce - Geometry - 1847 - 150 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 :... | |
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