 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 - 1894 - 437 pagesFull view - About this book
 | Webster Wells - Geometry - 1899 - 424 pages
...Proof. From (1), ad = be. (?) .-. b:a = d:c. (?) PROP. V. THEOREM. 237. 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. Given the proportion a... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...by ac. Then - = -• 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 ,s to the second term as the sum of the last two terms is to the fourth term. Let a: b = c: d. To prove... | |
 | 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... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...are in proportion, they are in proportion by composition ; that in, 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 : bc : d. To prove that a + b:b = c + d:d, -KT ac Now - = -• bd Then... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...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. QED PROPOSITION VII. THEOREM. 333. If four quantities are... | |
 | Education - 1900 - 612 pages
...would have taken 10 hours. Find the rate of a) the crew in still water, b) the stream. 7 Prove that if four quantities are in proportion they will be in proportion by a) composition, b) alternation. 8 In a school of 25 boys and 18 girls how many classes could be formed... | |
 | James Harrington Boyd - Algebra - 1901 - 812 pages
...the same kind, the alternation may take place. 490. THEOREM VI. — In any proportion, the terms 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 the proportion be... | |
 | James Harrington Boyd - Algebra - 1901 - 818 pages
...the same kind, the alternation may take place. 490. THEOREM VI. — In any proportion, the terms 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 the proportion be... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...quantities are in proportion, they are in proportion by composition, ie 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. Hyp. a : 6 = c : d. To prove a+b:b = c + d:d. Proof. bd (Ax. 2.) or — ! —... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...Whence, a+ b :b = cf d : d. Similarly, a+ b : a = c + d: c. Therefore, etc. PROPOSITION VII. — THEOREM. If four quantities are in proportion, they will be in proportion by division; that is, the difference of the first two terms will be to the second term as the difference... | |
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