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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 to their difference. "
The Elements of Geometry - Page 123
by Webster Wells - 1894 - 378 pages
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Elements of Algebra

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;...
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Elements of Algebra

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...
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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 Algebra: To which are Added Exponential Equations ...

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...
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An Elementary Treatise on Plane and Solid Geometry

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

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

James Bates Thomson - Algebra - 1844 - 272 pages
...c : c, or 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 - 276 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 - 204 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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