U5 



A Demonstration oj orii of the HINDOO RULES of 

 ARITHMETIC. — By Mr. REUBEN BURROW. 



'HE Art of Invention' being- in a great meafure dependent on the doct- 

 rine of combinations ; every additional improvement in the laft mint 

 of confequence be ufeful in the former; and as the following ancient Rule 

 for " finding thefum of all the different permutations of a given numeral quan- 

 tity, confi/ling of a given number of places of figures" is not, I believe extant in 

 any European Author, and is befides very ingenious ; I take the liberty to 

 infert it, and alfo to add the demonftration. 



Rule. Place an Arithmetical progreffion over the figures beginning with 

 unity at the Units place and increasing by unity : divide the product of the 

 terms of this progreffion by the number of places of figures in the given 

 quantity : Multiply the fum of the figures in the given quantity by the 

 quotient, and fet down the product as often as there are places in. the given 

 quantity ; removing it each repetition one place to the right hand, and the 

 Sum of thefe lines is the Sum of all the permutations. 



EXAMPLE. Required the Sum of the different permutations of 893 



-L**2il= 35(8 + 9 + 3)3 = 403 893 



839 



40 983 



3^1 40 938 



8 9 3 40 389 



■ 398 



4440 



4440 



