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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. "
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 47
by Benjamin Peirce - 1837 - 288 pages
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Elements of Algebra

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 ....
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Elements of Algebra

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...
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Elements of Algebra, Volume 1

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;...
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An Elementary Treatise on Plane and Solid Geometry

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,...
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An Elementary Treatise on Plane and Solid Geometry

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,...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

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...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

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,...
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Elements of Algebra: Being an Abridgement of Day's Algebra Adapted to the ...

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,...
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Elements of Algebra

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 :...
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An Elementary Treatise on Plane and Solid Geometry

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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