| 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... | |
| 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,...sum of the last two terms is to their difference. Remark. If we had taken proportion (2) in (x), we might have obtained from it 6 + а: d-\-c = b —... | |
| 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,... | |
| Benjamin Peirce - Algebra - 1855 - 308 pages
...of the last two, or as the first term is to the third, or as the second is to the fourth. Likewise, the sum of the first two terms is to their difference, as the sum of the last two is to their difference. Moreover, in finding these sums and differences, both the antecedents may be... | |
| 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... | |
| 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... | |
| Theodore Strong - Algebra - 1859 - 570 pages
...and division), we say that the sum of the first two terms of any proportion is to their difierence as the sum of the last two terms is to their difference. А С (22.) From the equation — — _, or proportion A : В : : С : D, when A is greater than B,... | |
| 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,...sum of the last two terms is to their difference. Remark. If we had taken proportion (2) in (x), we might have obtained from it b-\-a:d-\-c=.b — a:... | |
| Benjamin Peirce - 1870 - 200 pages
...first two terms is to the difference of the last two in tht same ratio ; also the sum of the Jirst two terms is to their difference as the sum of the last two is to their difference. Proof. The proportion A: C = B : D; from which we obtain, by the preceding... | |
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