 | 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,... | |
 | 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...both the consequents may be multiplied by any number. 98. Two proportions, as A: B = C : D and E : P ' = G : H, Ratio of Reciprocals. may evidently be multiplied... | |
 | 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... | |
 | 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... | |
 | 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,... | |
 | 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... | |
 | William Smyth - Algebra - 1861 - 496 pages
...making m=\, we have b -f- a : bf — 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. 165. The proportion a : b : : c : d may be written thus, a : c : : b : d, we have then c . d -±m=-±m;... | |
 | Thomas Sherwin - 1862 - 252 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... | |
 | Benjamin Peirce - Algebra - 1865 - 300 pages
...A+B:C+D = A — B:C— D = A:C = B:D; and A + BA — B = C+D:C — D mA-\-nB:mA — nB=mC-\-nD:m C — n D ; 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 Ritio of Reciprocals. may evidently be multiplied together,... | |
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In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference. 
