E<^ATION OF PAYMENTS BY DECIMALS. I99 



3. Divide the first number by the second, and call the 

 cjuotient the third number. 



4. Call 



But arx z:z — ■ by the question, from which equation ps 



i-{-tr — rx ^ 



h found = ititff;: + '•±1±'!!l\ ' _ if 



Let — ■ — ■ be put equal to «, and — = in. 



2ar ar 



Then it is e-vldent that n, or its equal «^j" is greater than 



«^ — m\^) and therefore x will have two affirmative values, the 



quantities «-|-»^ — m\ and n — n^ — m\ being both positive. 



3ut only one of those values will answer the conditions of the 

 question ; and, in all cases of this problem, x will be = » -*^ 



« - — jn\ 



Por suppose the contrary, and let .\* zz n -|-«* — ni\ . 



Then tsz::L — n — n ^ — wp= t — u 1 ^ | — « * — mV" =1 



e — 2/« + «M* — «* — m\ =«^4-r — 2tn\ — «^ — m\ 



Nov/, since a-\-h-^atr X — =«> acd It X — = ???> we ^hall 

 liavc from the first of tliesc equations /*— 2/«nr — ht-^at X — 



and consequently / — x = ?;^ — ^/— ^/ X — 



'_;,'-^/X— I 



Bir 



