6o 4 THE POPULAR SCIENCE MONTHLY 



confusion, denoted ten by drawing a tenth stroke over the nine parallel 

 ones, 



mm 



and that this was abbreviated to two strokes crossed, X. The upholders 

 of this theory assert that five, half of ten, was then denoted by V, half 

 of X. For fifty, L was used; for one hundred, C ; for five hundred, D; 

 for one thousand, M. The numbers in between were expressed by com- 

 bination: LX = 60, DCXV=615; or by addition to or subtraction 

 from the nearest one of the seven symbols: XII = 12, IX = 9. 



The advantage of this system lay in the fewness of the symbols 

 employed. Where the Hebrew had twenty-two characters and the 

 Greek twenty-seven, the Roman made use only of seven. Because of 

 this fewness the value of the characters could be easily remembered. 

 On the other hand the smaller number of characters employed made 

 necessary the greater use of combination. The Greeks had a symbol 

 for sixty or for ninety, but the Latins must place together several 

 numeral signs of smaller value so that the combination would equal 

 the total required In Greek 60 might be expressed by £, one char- 

 acter; in Latin by two, LX. The more complex the number the 

 greater became the relative cumbersomeness of the method. In Greek 

 1863 could be expressed by aw£/ ; in Latin it would be MDCCCLXIII. 

 The result of these cumbersome combinations was that with the Eoman 

 numerals it was virtually impossible to make calculations of any 

 intricacy, and exceedingly difficult to make even simple ones. They 

 might be employed for mere designation, as they are to this day used 

 to express dates and to distinguish the pages of a preface ; but for addi- 

 tion, subtraction, multiplication, division, and intricate arithmetical 

 work, the Roman mathematicians were driven to use the Greek symbols 

 nnd methods. 



Meanwhile in the east other systems of numeral notation had been 

 developed, some of which, in modified form, are in use there at the 

 present time. The Babylonians were expert calculators; and the 

 Chinese invented a notation which they still have. It was in India, 

 however, that a system arose destined to supersede all others among 

 civilized people. 



There were probably some numerals in use among the Hindus a 

 thousand or more years before our era, but no records exist earlier than 

 the time of Asoka, in the third century B.C. From this time on occur 

 inscriptions which contain some of the native number symbols. Two 

 systems may be discerned, which possess respectively the characteristics 

 of the Roman and the Greek. 



