| John Hind - 1837 - 584 ÆäÀÌÁö
...consequent: and if the consequents be equal, the ratio is the greater which has the greater antecedent. 165. A ratio of greater inequality is diminished, and a...inequality is increased, by adding the same quantity to both its terms. Let a : b be a ratio of inequality, and suppose on to be added to both its terms, so... | |
| Alexander Ingram - 1844 - 262 ÆäÀÌÁö
...: 9; and since —^ is less than £, the ratio of a : a+b a -f- bb is less than that of a: b. III. A ratio of greater inequality is diminished, and a...inequality is increased, by adding the same quantity to both of its terms. then these two ratios will be T and 7 , which are equivaoo + n lent to 77 —r and... | |
| Scottish school-book assoc - 1845 - 444 ÆäÀÌÁö
...inequality is diminished by adding the same quantity to both its terms ; whereas a ratio of lesser inequality is increased by adding the same quantity to each of its terms. For — is a ratio of greater inequality, and if c be added to each of its terms, it becomes - . Reducing... | |
| Harvey Goodwin - 1846 - 500 ÆäÀÌÁö
...a ratio of less inequality. 84. A ratio of greater inequality is diminished, and of less inequality increased, by adding- the same quantity to each of its terms. Let - be any ratio, and let x be added to each of its o terms; then a + x . a b + xb — - is > or < -,... | |
| Harvey Goodwin - 1849 - 588 ÆäÀÌÁö
...a ratio of less inequality. 84. A ratio of greater inequality is diminished, and of less inequality increased, by adding the same quantity to each of its terms. Let - be any ratio, and let a> be added to each of its terms; then a + at . a according as (a + x) b is... | |
| James Haddon - 1850 - 210 ÆäÀÌÁö
...or of equality, according as the antecedent is greater than, less than, or equal to, the consequent. A ratio of greater inequality is diminished, and a...inequality is increased, by adding the same quantity to both its terms. If a : ft be the original ratio, and x be added to both its terms, the new ratio is... | |
| Elias Loomis - 1852 - 366 ÆäÀÌÁö
...of these is the greatest, we infer that the ratio of 2 to 7 is less than the ratio of 3 to 8. (207.) A ratio of greater inequality is diminished, and a...inequality is increased, by adding the same quantity to both terms. 2 2+1 3 To prove the proposition generally, let j represent any ratio, and let x be added... | |
| Benjamin Greenleaf - 1852 - 348 ÆäÀÌÁö
...than 17 : 9 ; and, since — rr is less than T ,the ratio of a-.a-4-b a-\-bo is less than a : b. 236. A ratio of greater inequality is diminished, and a...inequality is increased by adding the same quantity to both terms. Let j- represent any ratio, and add n to each of the terms, then these two ratios will... | |
| Benjamin Greenleaf - 1854 - 374 ÆäÀÌÁö
...17 : 9; y and, since —— is less than T , the ratio of a : a-4-6 is less than a-\-bb a : b. 240. A ratio of greater inequality is diminished, and a...inequality is increased, by adding the same quantity to both terms. Let — represent any ratio, and add n to each of the tenna then these two ratios will... | |
| Benjamin Greenleaf - 1854 - 414 ÆäÀÌÁö
...greater than 17 : 9; y and, since is less than -, the ratio of a : a-4-b is less than a : b. afo b 240. A ratio of greater inequality is diminished, and a...inequality is increased, by adding the same quantity to both terms. Let T represent any ratio, and add n to each of the terms. b then these two ratios will... | |
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