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. Common School Algebra - Page 221by Thomas Sherwin - 1855 - 238 pagesFull view - About this book
| 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;... | |
| 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... | |
| 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, and 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. Two proportions, as A :B = CD and E : F = G '. Hy may evidently be multiplied... | |
| Benjamin Peirce - Algebra - 1837 - 302 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... | |
| Benjamin Peirce - Algebra - 1837 - 300 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... | |
| Thomas Sherwin - Algebra - 1841 - 314 pages
...— a : d — c; changing the means, b-\-a:b — a = d-\-c:d — c. From the last two proportions, we infer, that, In any proportion, the sum of the...the last two terms is to their difference. Remark. It is manifest that the last two proportions might be written thus : a-\-b :c-\-d—a — b : c —... | |
| Thomas Sherwin - Algebra - 1841 - 320 pages
...first two terms is to the sum of the last two, as the difference of the first two terms is to thf. difference of the last two ; also, the sum of the...the last two terms is to their difference. Remark. It is manifest that the last two proportions might be written thus : a-\-b :c-\-d=a — b:c — d,... | |
| 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... | |
| 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,... | |
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