# The Complete Arithmetic, Oral and Written; Second Part

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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. 1876 edition. Excerpt: ...Make the statement so that two of the given numbers which are of the same unit value, shall form the first couplet of the proportion, and have a ratio equal to the ratio of the third given term to the required term. II. Divide the product of the means by the given extreme, and the quotient will be the number required. CAUSE AND EFFECT. 768. The terms of a proportion have not only the relations of magnitude, but also the relations of cause and effect. Every problem in proportion may be considered as a comparison of two causes and two effects. Thus, if 4 tons as a cause will bring when sold, \$24 as an effect, 12 tons as a cause will bring \$72 as an effect. Or, if 6 horses as a cause draw 10 tons as an effect, 9 horses as a cause will draw 15 tons as an effect. 769. Since like causes produce like effects, the ratio of two like causes equals the ratio of two like effects produced by these causes. Hence, 1st cause: 2d cause:: 1st effect: 2d effect. WRITTEN EXERCISES. 770. 1. If 8 men earn \$32 in one week, how much will 15 men earn at the same rate, in the same time? STATEMENT. ANALYSIS.--In this BX let cause. 2d cause. 1st effect, 2d effect. ample an effect is required. 8 men: 15 men:: \$32: %x The first cause is 8 men, OPERATION. and since they are like \$x--15 x 3 2-H 8--\$60 causes they can be com pared. The effect of the first cause is \$32 earned, the effect of the second cause is \$z earned, or the required term. Since like effects have the same ratio as their causes (769), the causes may form the first couplet, and the effects the second couplet of the proportion. The required term is readily obtained by (763, 3). 2. If 20 bushels of wheat produce 6 barrels of flour, how many bushels will be required to produce 24 barrels? STATEMENT. ANALYSIS.--In.