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. 1897 Excerpt: ...Four quantities are said to be in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth. The four quantities are called proportionals, or the terms of the proportion. Thus, if-=-, then a, b, c, d are proportionals. This is b d expressed by saying that a is to b as c is to ...
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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. 1897 Excerpt: ...Four quantities are said to be in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth. The four quantities are called proportionals, or the terms of the proportion. Thus, if-=-, then a, b, c, d are proportionals. This is b d expressed by saying that a is to b as c is to d, and the proportion is written a: b:: c: d, or a: b = c: d. The terms a and d are called the extremes, b and c the means. 349. If four quantities are in proportion, the product of the extremes is equal to the product of the means. Let a, b, c, d be the proportionals. Then by definition-=-; b a whence ad = be. Hence if any three terms of a proportion are given, the fourth may be found. Thus if a, c, d are given, then b=--c Conversely, if there are any four quantities, a, b, c, d, such that ad = be, then a, b, c, d are proportionals; a and d being the extremes, b and c the means; or vice versa. 350. Continued Proportion. Quantities are said to be in continued proportion when the first is to the second, as the second is to the third, as the third to the fourth; and so on. Thus a, b, c, d, are in continued proportion when a_b_c_ _ bed If three quantities a, b, c are in continued proportion, then a: b = b: c;.-. ac = b2. (Art. 349.; In this case 6 is said to be a mean proportional between a and c; and c is said to be a third proportional to a and b. 351. If three quantities are proportionals, the first is to the third in the duplicate ratio of the first to the second. Let the three quantities be a, b, c; then 353. Transformations that may be made in a Proportion. If four quantities, a, b, c, d form a proportion, many other proportions may be deduced by the properties of fractions. The results of these operations are very useful, and some of them a
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