6o2 THE POPULAR SCIENCE MONTHLY 



what is more numerous. Thus, three and one or three and two take the 

 place of four and five. This method was actually incorporated into the 

 systems of the Phenicians and the ancient Hindus. Indeed, the habit 

 persists in the minds of people later on, when they possess many num- 

 ber symbols and the ability to use them in calculation. While the more 

 acute nowadays can without great difficulty comprehend four and five, 

 yet five will frequently be apprehended better as a combination of two 

 and three, while almost inevitably six will be thought of as a combina- 

 tion of three and three, and seven as made of three and four. 



Nevertheless as the mind of man becomes more powerful, and the 

 need for calculation becomes more frequent, larger numbers are made 

 use of, even though they can only be comprehended as combinations of 

 smaller ones. The designation of these number ideas soon becomes 

 necessary, and it must be made both for the eye and for the ear. For 

 the eye this may be done by symbols ; for the ear by words. Thus, the 

 Greeks may write 9' (90) and call it ivevrjKovTa ; the Eomans XL, and 

 call it qvadraginta. 



The designation of these number ideas either by symbol or by sound 

 is exceedingly difficult for the reason that number ideas are necessarily 

 abstract. It is true that the lower, which represent a few objects, can 

 be designated by pictures. So, man may originate the symbols for his 

 lower numbers in the same manner that he first makes the symbols for 

 his words, by ideographs or picture-drawings. In old Chinese the rude 

 representation of a man designates man. Similarly the Chinaman 

 writes a simple stroke to represent a single object; two strokes to rep- 

 resent two objects; and three, to represent three: 



The Hindu once employed the same device, except that his strokes were 

 usually perpendicular : 



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These symbols were used wherever men began to write their numbers. 

 They were employed by the Latin peoples, and as the Eoman numerals 

 are still in common use. In cursive form they are the numerals which 

 we use to-day : 



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Such graphic designation of number cannot be carried very far, 

 however, and arbitrary symbols must soon be employed. Thus, for 

 four the Hindu wrote two strokes crossed : 



