New Elements of Mathematics: Or Euclid Corrected. Containing Plane Gometry; General Investigation of Areas, Surfaces, and Solids; Greatest and Least ... Principles of Algebra, by Way of Introduction - Softcover

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1773. Excerpt: ... PROPORTIONS. Definitions. 1. Ratio, is the relation between two quantities of the same kind, in respect to their contents. 2. In comparing two quantities a, b, the first a is called antecedent, and the second b consequent. 3. The ratio between two quantities, is the same as the quotient of the antecedent divided by the consequent. Thus the ratio of 20 to 5 is 4; that is, the antecedent contains 4 times the consequent; and the ratio of 12 to 4 is 3, or the antecedent contains 3 times the consequent. 4. Four quantities a, b, c, d, are said to be proportional, when the ratio of the first a to the second b, is equal to the ratio of the third c to the fourth d. The proportion is marked thus a: b;: c: d, in words, a is to b as c is to d. 5. Quan 5. Quantities are said to be in a continued proportion, when the consequent of any ratio is always equal to the antecedent of the succeeding ratio. As in a: b:': b: c:: c: d, which sometimes is also marked:: a: b: c: d. 6. If four quantities a, b, c, d, are in a continued proportion, the ratio of the first a to the third c, is said to be duplicate-, and the ratio of the first a to the fourth d, triplicate to, the ratio of the first a to the second b. On the contrary, the ratio of the first a to the second b, is said to be subduplicate to that of the first a to the third c, and subtriplicate to that of the first a to the fourth d. 7. If there be any number of quantities, a, b, c, d, of the same kind, the ratio of the first a to the last d, is said to be compounded of the ratios of the first to the second, of the second to the third, of the third to the fourth, and so on to the last, viz. x-x '-; = 7. 0 c d 4 I 19. ¥ 19. If four quantities a, b, c, d, are proportional, the product of the means is equal to that of th...