THE DECIMAL SYSTEM OF NUMBERS 493 



1.21, 10 1 as 1.36, 20 2 as 6.40 — naturally all in cuneiform characters. 

 The only possible interpretation of this is that the 1 in the left hand 

 place stands for 60. The table of cubic numbers bears out this inter- 

 pretation as W — 27,000 is given as 7.30, meaning 7 X 3,600 or 7 X 

 60~ 2 + 30 X 60 = 25,200 -f 1,800 which makes the total of 27,000. Up 

 to date no documents have been found which show the presence of the 

 zero in this system. Even though a zero, and with it thus a full place 

 system, had existed the unwieldiness of the large base would have 

 operated against a universal adoption of the system; a number system 

 must be adapted to child mind. 



Our division of the day into 24 hours is probably a heritage from 

 the Babylonians; the division of the hour and minute into sixty parts 

 is certainly a survival from this hoary system. So also the division of 

 the arc of the circle into 360° and the further subdivisions have come 

 to us from this extinct civilization. Greek astronomers and through 

 them all European astronomers borrowed much from the same source, 

 and for over fifteen hundred years of the Christian era sexagesimal 

 fractions were used in all arithmetical computation. The first tables 

 of trigonometric functions were on the basis of a radius of 600,000, 

 later 6,000,000, finally to be discarded by Eegiomontanus in 1470 for 

 the base 10 5 , later for 10 15 , and then by the great Vieta, in 1579, for 

 the base one with decimal values. 



It is entirely within the bounds of possibility that the first develop- 

 ment of the Hindu, commonly called Arabic, place system was due to 

 some oriental scholar who was familiar with the writings of these an- 

 cient Babjdonians. Abundant testimony exists tending to prove the 

 communication between Europe and the east. Having special symbols, 

 such as existed in India for 1, 2, 3, 4, 5, 6, 7, 8 and 9 as early as the 

 second centur} r , acquaintance with this advancement of the Babylon- 

 ians may have suggested the step to a decimal place system and the in- 

 novation of a zero. The existence of a Babylonian zero symbol would 

 strengthen this hypothesis ; even a blank space may have been the first 

 symbol. 



The Egyptians were in possession of a complete decimal system, 

 with separate symbols for 1, 10, 100, 1,000, 10,000 and higher powers 

 of 10. The famous Papyrus Bhind of the British Museum gives us a 

 practically complete Egyptian arithmetic. The striking peculiarity of 

 their arithmetic consisted in the work in fractions which was confined 

 almost entirely to unit fractions. The Ahmes Papyrus of date about 

 1700 B.C. gives a table for a conversion of fractions from % to % 9 into 

 unit fractions. The tremendous inertia of even the clumsiest system 

 once established is seen in the fact that Greek manuscripts of date 700 

 a.d., at least 2,200 years later, contain this same bungling system of 

 fractions. Aside from this malign influence European arithmetic was 

 not affected by the Egyptian. 



