2iO ARITHMETIC. 



5. A person bouglit a chaise, horse and harness, for 

 60I. ; the horse came to twice the price of the harness, 

 and the chaise to twice the price of the horse and harness ; 

 what did he give for each ? 



Ans. 13I. 6s. 8d. for the horse, 6L 13s. 4d. for the har- 

 ness, and 40I. for the chaise. 



6. A vessel has three cocksj A, B and C ; A can fill it 

 in I hour, B in 2, and C in 3 : in what time will they all 

 fill it together ? Ans. -^ hour. 



DOUBLE POSITION. 



Double Position teaches to resolve questions by making 

 two suppositions of false numbers. 



RULE.* 



I. Take any two convenient numbers, and proceed ^yith 

 each according to the conditions of the question. 



2. Find 



* The rule is founded on this supposition, that the first errgr, 

 is to the second, as the difference between the true and first sup- 

 posed number is to the difference between the true and second 

 supposed number : when that is not the case, the exact answer to 

 the question cannot be found by this rule. 



That the rule is true, according to the supposition, may be thus 

 demonstrated. 



Let A and B be any twp nurnbers, produced from a and b by 

 similar operations ; it is required to find the number, from wh^ich 

 JV" is produced by a like operation. 



Put X = number required, and let N — Azzr, and N—B:=:s, 

 Then, according to the supposition, on which the rule Is found- 

 ed, r IS : : x— •« : x — b, whence, by multiplying means and 



extremes. 



