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" In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term. "
Plane and Solid Geometry - Page 80
by James Howard Gore - 1898 - 210 pages
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University Algebra

Webster Wells - Algebra - 1879 - 468 pages
...: d then, ad = b с Whence, b : a = d : c. 347. If four quantities are in proportion, they will be in proportion by COMPOSITION ; that is, the sum of the first two terms will be to the first term, as the sum of the last two terms is to the third term. Thus, if a : b =...
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A Complete Course in Algebra for Academies and High Schools

Webster Wells - Algebra - 1885 - 372 pages
...as the fourth term is to the third. Let a : b = с : d. Then, ad — be. Whence, b : a = d : c. 299. In any proportion the terms are in proportion by Composition;...term, as the sum of the last two terms is to the third ter.n. Let a : b = с : d. Then, ad = be. Adding both members to ac, ac + ad = ac + be, or, a Whence...
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A Complete Course in Algebra for Academies and High Schools

Webster Wells - Algebra - 1885 - 324 pages
...prove that 300. In any proportion the, terms are in proportion by Division ; that is, the difference of the first two terms is to the first term, as the difference of the last two terms is to the third term. Let a : b = с : d. Then, ad = be. Subtracting...
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A Complete Course in Algebra for Academies and High Schools

Webster Wells - Algebra - 1885 - 370 pages
...prove that 300. In any proportion the terms are in proportion by Division; that is, the difference of the first two terms is to the first term, as the difference of the last two terms is to the third term. Let a : b = с : d. Then, ad = be. Subtracting...
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A Complete Course in Algebra

Webster Wells - 1885 - 368 pages
...(Art. 296), • 300. In any proportion the terms are in proportion by Division; that is, the difference of the first two terms is to the first term, as the difference of the last two terms is to the third term Let a : b = с : d. Then, ad — be. Subtracting...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...VI. THEOREM. 248. In any proportion the terms are in proportion by DIVISION ; that is, the difference of the first two terms is to the first term as the difference of the last two terms is to the third term. Let a:b = c:d, Then ad = be. Subtracting both...
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A Short Course in Higher Algebra: For Academies, High Schools, and Colleges

Webster Wells - Algebra - 1889 - 584 pages
...as the fourth term is to the third. Let a : & = с : d. Then, aa = bc. Whence, b : a = d : c. 315. In any proportion the terms are in proportion by Composition...sum of the last two terms is to the third term. Let a : b = с : d. Then, ad = bc. Adding both members to ac, ac + ad = яc + &e, or, a(c + d) = c( Whence...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...= be. (281) .-. a:c = b:d. (283) QED Proposition 5. 287. If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first and second is to the second as the sum of the third and fourth is to the fourth. Hyp. Let a : b = c...
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College Algebra

Webster Wells - Algebra - 1890 - 604 pages
...b:b = c+d:d. 388. In any proportion the terms are in proportion by Division; that is, the difference of the first two terms is to the first term as the difference of the last two terms is to the third term. Let o : 6 = c : d. Then, ad = be. Subtracting...
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The Elements of Algebra

George W. Lilley - Algebra - 1892 - 420 pages
...= -j-~ Therefore, a + b :b :: c + d : d. Hence, VI. If four numbers are in proportion, they will be in proportion by composition; that is, the sum of the first two will be to the second as the sum of the last two is to the fourth. Let a : b : : с : d. ac By definition,...
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