RUL 



RUL 



Noti i. — If the firft and fiecond terms contain different de- 

 nominations, they mull both be reduced to the fame deno- 

 minations ; and if the third term be a compound number, it 

 is generally moft convenient to reduce it to the loweft deno- 

 mination contained in it. 



Note 2 The fame rule is applicable, whether the given 



quantities be integral, fractional, or decimal. 



Examples. 

 If an acre of land be worth 73/. is., how much land may 

 be bought for 250/. ior. ? 



Integral. 

 £ s. £ s. Acre. 



As 



73 

 20 



1461 



1461)5010(3 acres. 

 4383 



627 

 4 



1461)2508(1 rood. 

 1461 



1047 

 40 



1461)41880(28444 perches. 

 29.22 



12660 

 1 1688 



As 73, 



Or, as 



Whence 



By Decimals. 

 As 73.05 : 250.5 :: 1 



73.05)250.50(3.4291 = 3 ac. 1 r. 28.656P. 

 21915 



3 > 35° 

 29220 



21300 

 14610 



66900 

 65745 



11550 



7305 



4*45 



Example 2. If 3 pounds be bought for 17s. how many 

 will 170*. buy ? Since as 17/. are to 170J. fo are 3 pounds 

 to the pounds required ; the number will be found thus : 



17X. : 170X. :: 31b. 



3 



17)510(30^. 

 5 l 



00 



Example 3. If 3 pounds and 4 ounces coft zs. 4//. what 

 will 2 pounds coft ? The operation will be thus : 



3lb. 40Z. : 2 lb. :: zs. qd. 



16 16 12 



52 32 28 



28 



256 

 64 



52)896( i"]d.\4 of a penny. 

 52 



37<5 

 3 6 4 



12 



In many cafes of commerce and accompts, we have more 

 compendious ways of working queftions that come under 

 the rule of three than by the rule itfelf ; which, by reafon 

 of their expediting practice, are called prafiice, and confti- 

 tute a particular rule of themfelves. , 



According to the above rule, it will be obferved, that 

 the third term is of the fame kind or name as the fourth 

 term or anfwer, and the fecond of the fame name with the 

 firft ; fo that the analogy in both pair of terms is between 

 quantities of the fame kind ; which is, in faft, neceflary to 

 conftitute a proportion, according to Euclid's definition : 

 whereas, by fome ftrange overfight, it will be found that 

 moft of our writers on arithmetic, by making the middle 

 term like the anfwer, have neceffarily to confider the ratio 

 of incongruous quantities, or at leaft the ratio between the 

 abftraft numbers by which they are exprefled. 



Rule of Compound Proportion, or Double Rule of Three, 

 or, as it is otherwife called, the Rule of Five, is the method 

 of folving, at one operation, fuch queftions as would re- 

 quire two or more ftatings by the common or fimple rule 

 of three. 



Rule. — 1. Set down the terms expreffing the condition of 

 the queltion, in one line. 2. Under each conditional term 

 fet its correfponding one in another line. 3. Multiply the 

 producing terms of or^e line, and the produced term of the 

 other line continually, and take the refult for a dividend. 

 4. Multiply the remaining terms continually, and let the 

 produft of them be a divifor. 5. The quotient of this di- 

 vifion will be the term required. 



By producing terms here, are meant whatever neceffarily 

 and jointly produce any effeft ; as the caufe and the time ; 

 length, breadth, and depth ; buyer and his money ; feller 

 and his goods ; all neceffarily infeparable in producing their 

 feveral effe&6. 



In a queftion where a term is underftood, and not ex- 

 preffed, that term may be expreffed by unity. 



Example. — If 35©/. ferve fix perfons for nine months; 

 how long will loco/, ferve four perfons at the fame rate? 



j Here 



