Page:A History Of Mathematical Notations Vol I (1928).djvu/45

Rh much as they contained fewer symbols. The following are the Greek alphabetic numerals and their respective values:

etc.

37. A horizontal line drawn over a number served to distinguish it more readily from words. The coefficient for was sometimes placed before or behind instead of over the. Thus 43,678 was written $\overline$. The horizontal line over the Greek numerals can hardly be considered an essential part of the notation; it does not seem to have been used except in manuscripts of the Byzantine period. For 10,000 or myriad one finds frequently the symbol or, sometimes simply the dot ·, as in  for 20,074. Often the coefficient of the myriad is found written above the symbol.

38. The paradox recurs, Why did the Greeks change from the Herodianic to the alphabet number system? Such a change would not be made if the new did not seem to offer some advantages over the old. And, indeed, in the new system numbers could be written in a more compact form. The Herodianic representation of 1,739 was ; the alphabetic was. A scribe might consider the latter a great innovation. The computer derived little aid from either. Some advantage lay, however, on the side of the Herodianic, as Cantor pointed out. Consider ; there is an analogy here in the addition of hundred's and of ten's. But no such analogy presents itself in the alphabetic numerals, where the corresponding steps are and ; adding the hundred's expressed in the newer notation affords no clew as to the sum of the corresponding ten's. But there was another still more important consideration which placed the Herodianic far above the alphabetical numerals. The former had only six symbols, yet they afforded an easy representation of numbers below 100,000; the latter demanded twenty-seven symbols for numbers below 1,000! The mental effort