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. 1917 Excerpt: … the same ratio 2:4 exists between every pair of corresponding numbers: 1:2, 3:6, 42:84, 125:250, etc. Explain why this is true. This leads at once to the rule for finding the fourth term of a proportion, when the first three are given. We give this rule in diagrammatic form, as follows: To find the fourth term of a proportion: In this article we have followed to a considerable extent the treatment given in the Manual for the use of the Mannheim Slide Rule, published by the Keuffel and Esser Co., New York. This gives the solution of the equation a_c 6 x To find the product ab, solve the proportion a To find the quotient solve the proportion b a_x bl’ The following examples will make clear the procedure. Example 1. Solve the proportion: 13/24 = 32/x. Example 2. Solve the proportion: 13/24 = 75/x. Since the first two terms of the proportion are the same as in the preceding example, we set the slide as before. We now find, however, that 75 on C is. beyond the extremity of D. We accordingly set the runner on the left-hand 1 of C, and then set the right-hand 1 of C on the runner. We find under 75 the number 138.5, the required value of %. (Justify the above use of the runner.) The same example can be done on scales A and B with one setting, without using the runner. Example 3. Find the product: 23.2 x 5.3. Here we set the right-hand 1 on 23.2. Use whichever 1 serves. The decimal point, in this as in the other examples, is simply located by inspection and a brief mental estimate of the answer. Here we see readily that the answer is something over 100; hence we locate the decimal point at the place to give us 123.0. The.5 in this answer must be estimated. Usually, if more than three significant figures are obtained from the rule, the last is uncertain. Example 5. …
