second tablet also illustrates this same system. It records the 

 magnitude of the illuminated portion of the moon's disc for every 

 day from new to full moon. The whole disc they assumed to be 

 equal to 240 parts and the result for the first 5 days is, 5, 10, 20, 40, 

 1.20, which is a geometrical progression. After that, the series 

 becomes an arithmetical progression. 



It was not until the seventh century B.C., long years after 

 the development outlined above, that the Greeks became interested 

 in mathematical studies. Very early in their work they seem 

 to have drawn a distinction between what Plato called XoTio-rt/cr; 

 and dpifl/iTjTiKT?. At first this distinction was not made, but it 

 certainly dates from an early period. Plato pronounced calcula- 

 tion, Xo-yio-TiKT?, a vulgar and childish art, but he devoted much 

 time to arithmetic itself. The study of the evoluton of calculation, 

 or the mode of counting, is intensely interesting. Our own system 

 of notation, generally credited in its origin to the Arabs, was borrow- 

 ed by them from the Hindoos, and was not used by the Arabs 

 themselves till after the time of Mohammed. That this Hindoo 

 system itself did not spring into existence at one time we may be 

 certain, but there is no record as to when it was invented nor as to 

 who was its inventor. The early Greeks, like other primitive peo- 

 ples, began only gradually to learn to count. They commenced 

 with groups of only two or three things and then later five. Fingers 

 or toes or possibly both were used as a ready means to aid them, 

 and the decimal scale, prevalent very early, was doubtless based on 

 this fact, though, to be sure, a quinary or vigesimal scale might 

 equally well have resulted. Pebbles also were used and in case of 

 large numbers the device became gradually customary to use 

 parallel, vertical lines, one line representing units, another tens, a 

 third hundreds, and so on. Later, frames came into use, string 

 and wires upon these taking the place of the rows of pebbles. This 

 was the origin of the abacus, used so much in early calculation. 

 The Greeks finally used alphabetic numerals but never possessed 

 the boon of a clear, comprehensive symbolism. 



In the other branch of the study, dpi^n/cry, arithmetic, as 

 it has been called, the Greeks were however greatly interested. The 

 Pythagoreans classified numbers into odd and even and knew that 

 the sum of the series of odd numbers from 1 to 2n -f 1 was always 



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