improvement. 



182 CONVERSION OF NUMBERS FROM ONE SCALE TO APfOTHEK. 



Comparison of Before we enter upon the subject of transformation, it 

 different scales i u • ^ i p i ^- i , 



of notation. ^^^ ^ amiss to make a lew observations on the nature 



of notation in general, and the comparative advantages and 

 disadvantages of particular systems with regard to the de- 

 cimal scale of notation, which is almost universally adopted 

 by all nations that have any knowledge of arithmetical com- 

 putations. 



Notation by This singular coincidence in the division of numbers into 



*"^''* periods of tens is a subject, that has been noticed by phi- 



losophers ever since the time of Aristotle, and is now gene- 

 rally attributed to the formation of man; that is to say, 



Its origin. ^"s having ten fingers, by the assistance of which, in all 

 probability, calculation, or at least numbering, was first ef- 

 fected. See Montucla's tlistoire da Malhematiques, vol. I. 



Its use a late Our present scale of notation, however, though founded 

 on this principle, was not the immediate consequence of 

 this division, but was an improvement introduced a long 

 time afterward; as is evident from the works of the Greeks, 

 who, notwithstandiag they divided numbers into periods of 

 tens, had no idea of the present system of arithmetic, the 

 great and important advantage of which is, the giving to 

 every digit a local, as well as a simple or natural value, and 

 by this means being able to express any number, however 

 large, by ten numerical characters ; and, for want of which, 

 the Greeks employed twenty-seven, we may say thirty-six, 

 different symbols, with which they could not for a long 

 time express a number above 10000; but they afterwards 

 extended it to the squares of thii' number. See an ingeni- 

 ous essay on this subject, by Dalembert, at the end of the 

 French translation of the works of Archimedes. 



I have already observed, that the advantage of our pre- 

 oifr'rnethod ° ^^"^ system of notation consists in giving to each character 

 a local value, by which they increase in a tenfold proportion 

 from the right hand towards the left; but in this I wish to 

 be understood as rnere'y speaking of the method, and not 

 of the number that is selected for the radix of the system ; 

 for there is no doubt, that either 6 or 12 would have better 

 Not the best gjj^^.j.red this purpose, particularly the latter. 



It would be extendmg this paper to too great a length to 

 eater into the peculiar advantages qf this or that system of 



notation : 



Greek nota- 

 tion. 



