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and distinctness; and this, in a form which subjects them 

 most conveniently to arithmetical compulaiinn. The im- 

 portant utility oF the contrivance it may be sufficient for 

 the present to illustrate by the /ollowing remark. Most 

 children oi' a very young a<re can with ease multiply or di- 

 vide the number 67,489 bv the number 508. But let the 

 same numbers be expressed by the Roman method of no- 

 tation, which prevailed in Europe before the introduction 

 of the Arabic, thus — Ixvii.cccclxxxix and dviii ; — a man 

 will be puzzled to perform either operation. The Greeks 

 employed a numeral notation similar to the Roman : and 

 it is truly wonderfid how their malhematicians (even with 

 the aid of some mechanical contrivances) surmounted the 

 difficulties which they had to encounter in their arithme- 

 tical calculations ; while we know that they were engaged 

 in some of a very long and complicated nature. 



" Yet when we examine the fundamental principle of 

 the Arabic notation, it becomes a matter of surprise that 

 the invention was not of earlier discovery: for it proceeds 

 on a principle extremely simple, and one that must have 

 been employed in all ages, whenever there was a practical 

 occasion of counting any very large number. We may 

 illustrate the principle by supposing that we had to count 

 a great heap of guineas. It is plain that unless we employ 

 some check on our numeration, we shall be very apt to 

 lose our reckoning, and get astray as we ad\'ance. What 

 then is the most obvious method of securing accuracy in 

 our reckoning? Is it not to count by tens, or some fixed 

 number beyond which we never shall proceed ? Thus, 

 when we have reckoned ten guineas, we may lay them 

 aside in one parcel, and proceed to count another parcel, 

 often. But to prevent the number of these parcels from 

 accumulating so as to lead us astray, whenever we have 

 counted ten such parcels we may make them up into a 

 rouleau, containing therefore ten times ten guineas, or one 

 hundred: and whenever we have ten such rouleaus, we 

 may combine them into one set, consisting of ten hun- 

 dred, or a thousand, guineas : and so on. And by this 

 simple contrivance it would never be necessary to reckon 

 beyond the number ten. Now it is precisely upon this 

 principle that we proceed in designating numbers by the 

 Arabic notation. The several columns of figures, from 

 the right hand column, are the compartments in which we 

 dispose the several combinations of ten. The first column 

 on the right hand is the place for all odd units, below ten ; 

 the next to it on the left hand, or second column, is the 



place 



