 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.  A Text-book of Geometry - Page 134by George Albert Wentworth - 1889 - 242 pagesFull view - About this book
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...be, are the means, and the factors of the first product, ad, are the extremes. PROPOSITION III. — If four quantities are in proportion, they will be in proportion by ALTERNATION ; that is, the antecedents will be to each other as the consequents. Let a : b = c : d... | |
 | William Frothingham Bradbury - Algebra - 1877 - 280 pages
...alternation. Let a : b — с : d By Theorem I. ad = b о By Theorem II. a : с = b : d THEOREM IV. 205. If four quantities are in proportion, they will be in proportion by inversion. Let a : b = с : d By Theorem I. ad = be By Theorem II. b : a = d : с THEOREM V. 206. If... | |
 | Horatio Nelson Robinson - Algebra - 1879 - 332 pages
...: b = c : d. From (A), l From (B), d Hence (Ax. 7), | = |, or, a : 5 = c : d. PROPOSITION VIL 269. If four quantities are in proportion, they will be in proportion by COMPOSITION or DIVISION ; that is, the sum of the first and second will be to the second, as the sum of the third... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...the consequents. Thus, if a : b = с : d then (Art. 343), ad = bc Whence (Art. 344), a:c = b:d. 346. If four quantities are in proportion, they will be in proportion by INVERSION ; that is, the second term will be to the first, as the fourth is to the third. Thus, if... | |
 | Webster Wells - Algebra - 1880 - 498 pages
...Whence, a — ¿i : a = с — d : c. Similarly, we may prove that a — b : b = c — d : d. 349. If four quantities are in proportion, they will be in proportion by COMPOSITION AND DIVISION ; that is, the sum of the. first two terms will be to their difference, as the sum of... | |
 | James Bates Thomson, Elihu Thayer Quimby - Algebra - 1880 - 360 pages
...— = r = r = &c. (Art. 200.) 6 + Й+/+&С. 6 369. These changes may all be expressed as follows : If four quantities are in proportion, they will be in proportion by Alternation, Inversion, Composition, or Division. ТНЕОвЕМ V. 370. If four quantities are in... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...that is j £ Adding 1 to each member j + 1 = 5 ~^~ 1 that is o + o , b = c T « : ll THEOREM VI. 18. If four quantities are in proportion, they will be in proportion by division. Let a :b = c : d ac that is l — 'd Subtracting 1 from each member ^ — 1 = ^ — 1 o —... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...aXd-hXc - - Th. I. (1) -f- dc = (2) ~ = T/ 'whence, a : c :: b : d. Therefore, etc. THEOREM IV. *• If four quantities are in proportion, they will be in proportion by inversion. Let a : b :: c : d; then will b : a :: d : c. For, (1) a x d = b xc / and taking the factors... | |
 | Webster Wells - Algebra - 1885 - 324 pages
...third. Let a : & = 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 tico terms is to the third term. Let a : b = с : d. Then,... | |
 | Webster Wells - Algebra - 1885 - 370 pages
...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,... | |
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