Difference between revisions of ".Mzcw.NzE5NA"
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| − | 78. From what has been said the | + | 78. From what has been said the analogy |
| + | between ratios & fractions is evident. The | ||
| + | exponent of a ratio may be considered as | ||
| + | a fraction: but instead of dividing ratios | ||
| + | into proper & improper, the may be distinguished | ||
| + | into ratios greater & less than than | ||
| + | of equality or of 1 to 1. Thus the ratio of | ||
| + | 3 to 2 is greater than that of equality; but | ||
| + | the ratio of 2 to 3 is less. The exponent of | ||
| + | the first will be an improper fraction | ||
| + | & that of the second will be a proper | ||
| + | one. And this analogy between ratios | ||
| + | & fractions has led some authors to call | ||
| + | the antecedant of a ratio its numerator, | ||
| + | & the consequent its denominator. But | ||
| + | these appellations are inconvenient | ||
| + | in geometry; because it is certain | ||
| + | that there are some ratios, such as | ||
Latest revision as of 18:43, 11 August 2018
(18) 78. From what has been said the analogy between ratios & fractions is evident. The exponent of a ratio may be considered as a fraction: but instead of dividing ratios into proper & improper, the may be distinguished into ratios greater & less than than of equality or of 1 to 1. Thus the ratio of 3 to 2 is greater than that of equality; but the ratio of 2 to 3 is less. The exponent of the first will be an improper fraction & that of the second will be a proper one. And this analogy between ratios & fractions has led some authors to call the antecedant of a ratio its numerator, & the consequent its denominator. But these appellations are inconvenient in geometry; because it is certain that there are some ratios, such as
