...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...of less inequality is increased, by adding the same quantity to both terms. 2 2+1 3 3 < 3+T' ° r 4' To prove the proposition generally, let r represent...

...between a and h ; — G is a geometrical mean between A and H. Ratio ; — simple or compound; — a ratio of greater inequality is diminished, and a ratio of less inequality increased, by adding the same quantity to each of its terms ; — what, if we subtract the same quantity...

...equality, according as 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 ratio be formed by adding...

...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...of less inequality is increased, by adding the same quantity to both its terms If a : b be the original ratio, and x be added to both its terms, the new...

...the arithmetical GCM will be the product of the numerical value of h and this common factor. RATIO. A ratio of greater inequality is diminished, and a...of less inequality is increased by adding the same quantity to both terms of the ratio, Let the ratio be represented by the fraction j , and let x be...

...Arithmetic Section of this work for definitions and observations which need not be repeated here. 23. A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by increasing t/\& terms of the ratio by the same quantity. Let a : b or '=- be the ratio, and let each...

...ratio a : b is said to be a ratio of greater or less inequality according as a > or < b. Prove that a ratio of greater inequality is diminished, and a ratio of less inequality increased, by adding any positive quantity to both terms of the ratio. (21) Prove that a2 - 2 ab +...

...equality, according as the antecedent is greater than, less than, or equal to, the consequent. 97. A ratio of greater inequality is diminished and a ratio of less inequality is increased by adding any quantity to both its terms. Let a : Ъ be the ratio, and let х be added to both its terms so that...

...As (3.28)2: (3-18)2 :: 9:» or 107584 ; 10.1124 : : 9 : 8.459 Prussian sq. feet. A 33 4 б-7' (2) " A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by an equal increase of the numerator and denominator." 5. (1) 79. (2) 2-1646. 6. (1) By 132. (2) By 13»....

...multiple, part, or parts which the former is of the latter. • Thus, the ratio of a : b = -. b 103. A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by increasing the terms of the ratio by the same quantity. Lst a : b or .- be the ratio, and let each...