This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1831 edition. Excerpt: ... D A: o:: B: D, and c: A:: B: o. 80. Of three proportional quantities, the middle one is said to be a Mean Proportional between the other two; and the last, a Third Proportional to the first and second. 81. Of four proportional quantities, the last is said to be a Fourth Proportional to the other three ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1831 edition. Excerpt: ... D A: o:: B: D, and c: A:: B: o. 80. Of three proportional quantities, the middle one is said to be a Mean Proportional between the other two; and the last, a Third Proportional to the first and second. 81. Of four proportional quantities, the last is said to be a Fourth Proportional to the other three, taken in order. 82. Quantities are said to be Continually Proportional, or in Continued Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio. As in the quantities 1, 2, 4, 8, 16, &c.;. whore the common ratio is equal to 2. 83. Of any number of quantities, A, B, C, D, 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, and so on to the last. 84. Inverse ratio is, when the antecedent is made the consequent, and the consequent the antecedent.--Thus, if 1: 2:: 3: 6; then inversely, 2: 1:: 6: 3. 85. Alternate proportion is, when antecedent is compared with antecedent, and consequent with consequent.--As, if 1:2:: 3: 6; then, by alternation, or permutation, it will be 1: 3:: 2: 6. 86. Compound ratio is, when the sum of the antecedent and consequent is compared, either with the consequent, or "with the antecedent.--Thus, if 1: 2:: 3: 6, then by composition, 1+ 2: 1:: 3 + 6: 3, and 1 + 2: 2:: 3-f 6: 6. 87. Divided ratio, is when the difference of the antecedent and consequent is compared, either with the antecedent or with the consequent.--Thus, if 1: 2:: 8: 6, then, by division, 2--1:1:: 6--3: 3, and 2--1:2:: 6--3: 6. Note. The term Divided, or Division, here means subtract
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