SIMPLE ADDITIO>r. t^ 



i. Add up tl^e figures in the row of units, and find how 

 rnany tens are contained in their sum. 



3. Set down the remainder, and carry as many units 

 to the next row, as there are tens ; with which proceed 

 as before ; and so on till the whole is finished. 



Method 



hers, and carrying for the tens ; both which are evident from the 

 nature of notation : for any other disposition of tlie numbers 

 would entirely alter their value ; and carrying one for every ten, 

 from an inferior line to a superior, is evidently right, since an un^t 

 in the latter case is of the fame value as ten in the former. 



Beside the method here given, there is another very Ingenious 

 one of proving ad^dition by casting out the nines, thus : 



Rule r. Add the figures in the uppermost line together, and 

 £nd how many nines are contained in their sum. 



2. Reject the nines, and set down the remainder directly even 

 with the £gures in the line. , 



3. Do the same with each of the given numbers, and set^alF 

 these excesses of nine togetlier in a row, and find their sum ; 

 then if the excess of nines in this sum, found as before, is equal to 

 the excess of nines in the total sum, the question Is right. 



EX-AMPLE. 



3782 

 5766 



^755 

 18303 



.2 6 





This method depends upon a property of the number 9, which 

 belongs to no other digit whatever, except 3 ; viz. that any num- 

 bcx, divided by 9, will leave the same remainder as the sum of its 

 figures or digits divided by 9 ; which may be thus demonstrated. 



Demon* 



