1^2 ARITHMETIC. 



Now this division may be conveniently made by writing 

 a point over the place of units, and also over the last fig- 

 ure of every period on both sides of it ; that is, over every 

 second figure, if it be the second root 5 over every third, 

 if it be the third root, &c. 



Thus, to point tliis number 2io'^^^g6'i2'j2S > 



for the second root, it will be 21035896*127350 j 



but for the third root . 2 103 5 896* 12 73 50 ; 



and for the fourth 2 103 5 896" 1273 5000. 



Note. The root will contain just as many places of 

 figures, as there are periods or points in the given power ; 

 and they will be integers, or decimals respectively, as the 

 periods are so, from which they are found, or to which they 

 correspond ; that is, there will be as many integral or deci- 

 mal figures in the root, as there are periods of integers or 

 decimals in the given number. 



To EXTRACT THE SqUARE RoOT» 



I. Having distinguished the given number into periods, 

 find a square number by the table or trial, either equal to, 



or 



* In order to shew the reason of the rule, it will be proper to 

 premise the following 



Lemma. Th^e product of any two numbers can have at most 

 but as many places of figures, as are in both the factors,' and at 

 least but one less. 



Demonstration. Take two numbers consisting of any num- 

 ber of places, but let them be the least possible of those places, 

 viz. unity with cyphers, as 1000 and 100 ; then their product will 

 be I with as many cyphers annexed as are in both the numbers, 



viz. 



