Grammar of Arithmetic Or, an Analysis of the Language of Figures and Science of Numbers
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from ... Show synopsis 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. 1850 Excerpt: ... quotient of the second term divided by the first. Convenience, therefore, as well as general analogy, indicates this as the proper definition of the term ratio. 67. Again, all authors, so far as I have consulted them, are uniform in their definition of the ratio of a geometrical progression: viz. that it is the quotient which arises from dividing the second term by the first, or any other term by the preceding one. For example, in the progression 2: 4: 8: 16: 32: 64, &c, 66. How may every question in the Rule of Three be regarded? Which term is used as a divisor in all such questions? What simole rule may then be given for finding the fourth term? all concur, that the ratio is 2: that is, that it is the quotient which arises from dividing the second term by the first: or any other term by the preceding term. But a geometrical progression differs from a geometrical proportion only in this: in the former, the ratio of any two terms is the same; while in the latter, the ratio of the first and second is different from that of the second and third.. There is, therefore, no essential difference in the two proportions. Why, then, should we say that in the proportion 2: 4:: 6: 12, the ratio is the quotient of the first term divided by the second; while in the progression 2: 4: 8: 16: 32: 64, &c, the ratio is defined to be the second term divided by the first, or of any term divided by the preceding term? As far as I have examined, all the authors who have defined the ratio of two numbers to be the 67. In what definition are all authors uniform? What ia that definition? Give an example. In what respect does a geometrical progression differ from a proportion? Is there, therefore, any essential difference? quotient of the first divided by the second, have dep..