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 130by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
| 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... | |
| 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, 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 - 1901 - 260 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 f+lf + <,... | |
| 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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