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(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.