Elements of Algebra

CHAP. X. OF ALGEBRA. 159 $(100 \cdot 30) : 1000 :: (2 \cdot 101 \cdot 119) : \frac{1000 \cdot 2 \cdot 101 \cdot 119}{100 \cdot 30} =$ $\frac{2 \cdot 101 \cdot 119}{3} = 8012\frac{2}{3}$ Polish florins. Ans. 487. We will propose another example, which may still farther illustrate this method. Ducats of Amsterdam are brought to Leipsic, having in the former city the value of 5 flor. 4 stivers current; that is to say, 1 ducat is worth 104 stivers, and 5 ducats are worth 26 Dutch florins. If, therefore, the agio of the bank at Amsterdam is 5 per cent.; that is, if 105 currency are equal to 100 banco; and if the exchange from Leipsic to Amsterdam, in bank money, is $133\frac{1}{4}$ per cent.; that is, if for 100 dollars we pay at Leipsic $133\frac{1}{4}$ dollars; and lastly, 2 Dutch dollars making 5 Dutch florins; it is required to determine how many dollars we must pay at Leipsic, according to these exchanges, for 1000 ducats? By the rule, $5 : 1000 :: 26$ flor. Dutch curr. $105$ --- $100$ flor. Dutch banco $400$ --- $533$ doll. of Leipsic $5$ --- $2$ doll. banco; therefore, As $(5 \cdot 105 \cdot 400 \cdot 5) : 1000 :: (26 \cdot 100 \cdot 533 \cdot 2) :$ $\frac{1000 \cdot 26 \cdot 100 \cdot 533 \cdot 2}{5 \cdot 105 \cdot 400 \cdot 5} = \frac{4 \cdot 26 \cdot 533}{21} = 2639\frac{11}{21}$ dollars, the number sought. *** CHAP. X. Of Compound Relations. 488. Compound Relations are obtained by multiplying the terms of two or more relations, the antecedents by the antecedents, and the consequents by the consequents; we then say, that the relation between those two products is compounded of the relations given. Thus the relations $a:b$, $c:d$, $e:f$, give the compound relation $ace:bdf$*. * Each of these three ratios is said to be one of the \textit{roots} of the compound ratio.