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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 ... - Página 46
por Benjamin Peirce - 1843 - 284 páginas
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Elements of Algebra

Silvestre François Lacroix - 1825 - 276 páginas
...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 - 1830 - 264 páginas
...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

JOHN FARRAR - 1831
...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 Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - 1837 - 276 páginas
...nB:mC—nD = A : C=B : D, and A + B : A — B = C+ D .C — D m A-\-nB:mA — nB = mC-\-nD : mC — nD; that is, the sum of the first two terms of a proportion....the consequents may be multiplied by any number. 73. Two proportions, as A: B = C: D and Ratio of Reciprocals. may evidently be multiplied together,...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1837 - 159 páginas
...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 - 1841 - 150 páginas
...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 - 1841 - 300 páginas
...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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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

James Bates Thomson - 1844 - 252 páginas
...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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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1847 - 150 páginas
...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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Elements of Algebra

William Smyth - 1847
...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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