Difference between revisions of ".Mzcw.NzE4NA"
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(13) | (13) | ||
69. Hence [[unclear]] the exponent of a compound | 69. Hence [[unclear]] the exponent of a compound | ||
| + | [[unclear]] the product of the exponents of the | ||
| + | ratios of [[unclear] compounded. And 20. that any | ||
| + | ratios as ^ [[addition]] a [[/addition] [[unclear]] to g, being given, quantities | ||
| + | in a ratio compounded of these will be found | ||
| + | by multiplying the antecedents together and | ||
| + | the consequents together. Thus the exponents of the | ||
| + | ratio act to bdg [[unclear]] act/bdg which is the product of | ||
| + | the three [[unclear]] a/b x c/e x f/g. | ||
| + | |||
| + | 70. The doctrine of compound ratios is the | ||
| + | foundation of the compound rule of three | ||
| + | in arithmetic. For if any unknown quantity | ||
| + | q be to one known of the same kind, in a | ||
| + | ratio compounded of ever so many others as | ||
| + | q may easily be found. For instance, let | ||
| + | q be to m, in a ratio compounded of [[unclear]] | ||
| + | of d to c: then q/m = b/a x d/c = bd/ac. Multiply [[unclear]] | ||
| + | sides of the equation by m, & we have | ||
| + | q = bdm/ac. | ||
Latest revision as of 19:10, 10 August 2018
(13) 69. Hence unclear the exponent of a compound unclear the product of the exponents of the ratios of [[unclear] compounded. And 20. that any ratios as ^ addition a [[/addition] unclear to g, being given, quantities in a ratio compounded of these will be found by multiplying the antecedents together and the consequents together. Thus the exponents of the ratio act to bdg unclear act/bdg which is the product of the three unclear a/b x c/e x f/g.
70. The doctrine of compound ratios is the foundation of the compound rule of three in arithmetic. For if any unknown quantity q be to one known of the same kind, in a ratio compounded of ever so many others as q may easily be found. For instance, let q be to m, in a ratio compounded of unclear of d to c: then q/m = b/a x d/c = bd/ac. Multiply unclear sides of the equation by m, & we have q = bdm/ac.
