 | Webster Wells - Geometry - 1894 - 394 pages
...= d:c. (§ 233.) PROPOSITION V. THEOREM. 236. In any proportion, the terms are in proportion £,t7 COMPOSITION ; that is, the sum of the first two terms...the sum of the last two terms is to the third term. Let the proportion be a : b = c: d. (1) To prove, a + b : a = c + d : c. We have from (1), ad = be.... | |
 | George P. Lilley - Algebra - 1894 - 522 pages
...~ь~Т" 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 wi\l be to the second as the sum of the last two is to the fourth. Let a : b :: с : d. ac By definition,... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...be to the first as the fourth to the third. 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 to the fourth term. 301. If four quantities... | |
 | Webster Wells - Algebra - 1897 - 386 pages
...third. Let the proportion be a : b = с : d. Then, ad = be. (§ 306) Whence, h:a = d:c. (§309) 312. In any proportion, the terms are in proportion by...the sum of the last two terms is to the third term. Let the proportion be a : b = с : d. Then, ad = be. Adding each member of the equation to ac, ac +... | |
 | Webster Wells - Algebra - 1897 - 422 pages
...Let the proportion be а : b = с : d. Then, ad = bс. (§ 306) Whence, b : a = d : c. (§ 309) 312. In any proportion, the terms are in proportion by...the sum of the last two terms is to the third term. Let the proportion be a : b = с : d. Then, ad = bс. Adding each member of the equation to ac, ac... | |
 | Webster Wells - Algebra - 1897 - 522 pages
...prove that 313. 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 the proportion be a : b = с : d. Then,... | |
 | Webster Wells - Algebra - 1897 - 434 pages
...prove that 313. 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 the proportion be a : b = с : d. Then,... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...„. ., , be ad ac ac that is. - = -» ... . bd ac or b : a = d: c. QED PROPOSITION V. THEOREM. 204. In any proportion the terms are in proportion by Composition...the sum of the last two terms is to the third term. Let a:b = c:d. To prove a + &:a::c + d:c. If a:b = c:d, then (by 199) ad = be. Adding both members... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 714 pages
...у г и У и 8. In any proportion, the sum of the first two terms is to the first (or the second) term as the sum of the last two terms is to the third (or the fourth) term. Let a : b = с : d. Then 2 = £. bd Adding 1 to both members, f + 1 = £ + 1,... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...equation by ac. Then bd ac PROPOSITION VI. THEOREM. 332. 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. Let a: b = c : d. To prove that... | |
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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. 
