| 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 the last two... | |
| 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 —... | |
| 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... | |
| 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... | |
| George Albert Wentworth - Geometry - 1888 - 272 pages
...295 Divide each member of the equation by ac. Then £ = £ ac or, b : a = d : c. PEOPOSITION VI. 300. **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 second term as the sum of the last two terms... | |
| Edward Brooks - Algebra - 1888 - 344 pages
...their product, Let a : b :: b : c; then (Theo. L), b'-ac, and 6 — j/ac. Therefore, etc. THEOREM V. **If four quantities are in proportion, they will be in proportion by** ALTERNATION. Let a : о :: о: d; then, ad — be; dividing by do, — - — ; о а whence, a : о... | |
| Edward Albert Bowser - Algebra - 1888 - 868 pages
...a: c : : b : d, b: a : : d : c, b:d :: a : c, c: d :: a:b, etc., are all true provided that ad = be. **If four quantities are in proportion they will be in proportion by** (3) Inversion. — If a:b :: c : d, then b : a : : d:c. TI ac * , a , c For - = - ; therefore 1 -t-... | |
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