 | John Hind - Algebra - 1837 - 584 pages
...: 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 ratio of less inequality is increased, by adding the same quantity to both its terms. Let a : b be a ratio of inequality, and... | |
 | William Scott - Algebra - 1844 - 568 pages
...proper fraction increased, by the addition of the same quantity to both its terms (Art. 39), it follows that a ratio of greater inequality is diminished,...and a ratio of less inequality increased, by adding the same quantity to both its terms. Conversely, a ratio of greater inequality is increased, and a... | |
 | Alexander Ingram - 1844 - 262 pages
...and since — —. is less than £, the ratio of a : a + b a + bb is less than that of a : b. III. A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both of its terms. Let - represent any ratio, and add... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...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 ratio of less inequality is increased, by adding the same quantity to both terms. i>i&-r' 2 2 + 1 3 To prove the proposition... | |
 | Great Britain. Committee on Education - School buildings - 1850 - 790 pages
...Required the sum and difference of »/ 16 cfx and >J 4o*z. 2. Find the square root of 1 1 + 6^2. 3. Shew that a ratio of greater inequality is diminished, and a ratio of lesser inequality is increased by adding the same quantity to both its terms. , cccxxvi General Examination... | |
 | Benjamin Greenleaf - Algebra - 1852 - 348 pages
...: 9 ; and, since — :-=• is less than T , the ratio of a : a-4-b ajo o is less than a : !>. 236. A ratio of greater inequality is diminished, and a ratio of less inequality is increased by adding the same quantity to both terms. Let j- represent any ratio, and add n to each... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...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 ratio of less inequality is increased, by adding the same quantity to both terms. 3 3+1 4 Thus, 2>2+l'0r3; 2 2+1 3 3<3TT' °r... | |
 | Isaac Todhunter - Algebra - 1858 - 530 pages
...equality, according аз the antecedent is greater than, less than, or equal to, the consequent. 376. A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding any quantity to both terms of the ratio. Let the ratio be j- , and let a new... | |
 | John Robertson (LL.D., of Upton Park sch.) - 1861 - 140 pages
...or more ratios may be compared by comparing the values of the vulgar fractions which represent them. A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both its terms. If the terms of a ratio be multiplied... | |
 | Robert Fowler - 1861 - 426 pages
...proved, and they should all be carefully written out by the student. (i.) A ratio of less inequality is increased by adding any positive quantity to both terms of the ratio. (ii.) A ratio of greater inequality is increased by taking from both terms of the ratio any positive... | |
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A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both its terms. 
