| 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 :... | |
| Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...c, or b : b—a: : d : d — c, &c. 7. Adding and subtracting, o+6: 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 - Algebra - 1851 - 294 pages
...—nB:mC—nD = A:C=B:D; and A -f - B : A — B = C + D : C — D mA-\-nB:mA—nB = mC-\-nD :mC—nD; that is', the sum of the first two terms of a proportion...consequents may be multiplied by any number. 98. Two proportions,'as A : B = C : D and Ratio of Reciprocals. may evidently be multiplied together, term... | |
| William Somerville Orr - Science - 1854 - 534 pages
...not be of the same kind as those in the other set. PROPOSITION XVIII.— THEOREM. In any proportion the sum of the first two terms is to their difference as the sum of the other two is to their difference. Let A : В . . С : D ; then A + В : АсяВ::С + О:С^ D. For... | |
| Benjamin Peirce - Algebra - 1855 - 308 pages
...D D = mA — nB:mC — nD and A + B : A — B = C + D : C— D mA-\-nB:mA — nB = mC-\.nD:mC—nD; that is, the sum of the first two terms of a proportion...multiplied by any number. 98. Two proportions, as A: B = C : D and E : P ' = G : H, Ratio of Reciprocals. may evidently be multiplied together, term... | |
| Benjamin Peirce - Algebra - 1855 - 296 pages
...— nB:m C — n D = A:C=B:D; and A + B : A — B = C+ D : C— D mA-\-nB:mA—nB = mC-\-nD:mC—nD; that is, the sum of the first two terms of a proportion...multiplied by any number. 98. Two proportions, as A : B = C : D and E :F= G: H, Ratio of Reciprocals. may evidently be multiplied together, term by term,... | |
| William Smyth - Algebra - 1855 - 370 pages
...whence making m=l, we have b-\-a: b — a:: d-\- c: d — c, a proportion which may he enunciated thus, The sum of the first two terms is to their difference, as the sum of the last two is to their differencc. 165. The proportion a : b : : c : d may be written thus, a: c : : b : d, we hare then cd... | |
| 1855 - 424 pages
...: d : d — с, etc. 7. Adding and subtracting, a -\- b : a — b : : с -\- d : с — 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,... | |
| Thomas Sherwin - Algebra - 1855 - 262 pages
...the last two, as the difference of the first two terms is to the 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. If we had taken proportion (2) in (x), we might have obtained... | |
| William Smyth - Algebra - 1858 - 344 pages
...whence making m = 1, we have b-\-a:b — a::d-\-c:d — c, a proportion which may he enunciated thus, The sum of the first two terms is to their difference,...as the sum of the last two is to their difference. 165. The proportion a : b :: c: d may be written thus, a: c :: b : d, we hare then -±m = -±m; ab... | |
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