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" If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. "
Solid Geometry - Page 254
by John H. Williams, Kenneth P. Williams - 1916 - 162 pages
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A Complete Course in Algebra for Academies and High Schools

Webster Wells - Algebra - 1885 - 370 pages
...the third. Let ч :l!:- r : d. Then, ad = be. Whence, b : a = d : c. 299. 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 tern. Let a : b = с : d. Then, ad = be....
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A Complete Course in Algebra

Webster Wells - 1885 - 368 pages
...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 ; 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 ter.n. Let a : b — с : d. Then, ad...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...have, AC -FT = -rr ; whence, B : A : : D : C ; b U which was to be proved. PROPOSITION VI. THEOREM. If four quantities are in proportion, they are in proportion by composition or division. Assume the proportion, RD A : B : : C : D ; whence, -v- = -.-' If we add 1 to each member,...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...ad = bc. Whence by § 244, b : a = d : c. PROPOSITION V. THEOREM. 247. 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 *<> the third term. Let a : 6 = c : d. Then, ad = be....
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College Algebra

Webster Wells - Algebra - 1890 - 604 pages
...the third. Let a : b = с : d. Then, ad = 6e. Whence, b : a = d : c. 387. 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. Let a : b = с : d. Then, ad = 6e....
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...: d, . • . ad = be. (281) . • . a : c - b : d. (283) Proposition 5. 207. If four quantities arc 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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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...bd .• . a — b : b = c — d : d. QED Similarly, a — b : a = c — d : c. Proposition 7. 289. If four quantities are in proportion, they are in proportion by composition and division; that is, (he sum of the first and second is to their difference as the sum of the third...
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Numbers Universalized: An Advanced Algebra, Volume 2

David Martin Sensenig - Algebra - 1890 - 556 pages
...whence a — b : a ::c — d:c by alternation, and a — b : b : : e — d : d by alternation. 436. If four quantities are in proportion, they are in proportion by composition and division. Given a : Ъ : : с : d to prove a-\-b : a — Ъ : : c-\-d : c — d Demonstration :...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1891 - 424 pages
...: c = b : d. Proof. Since a : b = c : d, .-.ad = bc. (281) .-. a:c = b:d. (283) Proposition 5. 287. If four quantities are in proportion, they are in proportion by composition; that is, the gum of the first and second is to the second as the sum of the third and fourth is to the fourth. Hyp....
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...(AxiOM vI.); BD by canceling, — = — ,- or, B : A : : D : CQED A (f PROPOSITION IV. 316. Theorem : If four quantities are in proportion, they are in proportion by composition. Statement : If A : B : : C : D, then, A + B : B : : C + D : D. AC Demonstration : — = — ; adding...
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