The new system of practical arithmetic; whereby most of the various problems of that useful science are easily and expeditiously solved by one simple rule ... - Tapa blanda

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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. 1835 Excerpt: ... more requires less, or less requires more; as--If 3 men dig a certain number of yards in 14 hours, in how many hours will 6 men do the same work? Here, more requires less, for 6 men are more than three men, and will do the same work in less than 14 hours. Or, If 6 men do a certain work in 7 days, in how many days will 3 men do the same? Here, less requires more, for 3 men will require more than 7 days to perform the same work. Ratio is a name which is used to denote the relation of two numbers or quantities of the same kind. Thus the ratio of 6 to 3 is-J=2. The first or leading term is called the antecedent, and the latter the consequent. Proportion denotes an equality or similitude of ratio. Thus the ratio of 8 to 4 is f=2, and is therefore the same as the ratio of 6 to 3. Hence, 8, 4, 6, 3, are in proportion, which is denoted by placing the numbers thus, 8: 4:: 6: 3, and is read 8 is to 4, so is 6 to 3. The middle terms are called the mean terms, as 4 and 6, and the other two the extreme terms. When four numbers or quantities are proportional, the product of the two mean terms is always equal to the product of the two extremes:--thus, in the above, 8x3=4x6=24. Hence, from this property of a proportion, it follows that when three terms or numbers are given, the fourth may be easily found, as will be exemplified in the following questions. In all the questions which come under the rule of three, two of the given numbers contain a supposition, and the third a demand, thus:--If 3 men perform a certain work in 10 hours, in how many hours will 6 men do the same work? Here 3 men and 10 hours form part of the supposition; these numbers, therefore, are called the terms of supposition, and the terms of demand are how many hours, and 6 men. The two cases direct and...