314 On the Systems of Numerical Signs 



beginning of the sixteenth century ?) has the knowledge of the 

 decimal fractions been introduced into the countries of the 

 West, which the nations of the East had been taught long 

 ago by their palpable arithmetic ! The descending scale from 

 the unit downwards, was known to the Greeks only in the 

 sexagesimal system for degrees, minutes, and seconds ; but as 

 they had not n — 1, that is, 59 numerical figures, the value by 

 position could only be expressed by layers of two figures, ; 

 If we direct our attention to the origin of numbers, we findi^ 

 that they could be written and read with great exactness, when 

 they were indicated by heaps of pebbles, or by the balls on the 

 strings of the calculation-machines. The impression which 

 these proceedings left behind on the mind, has everywhere 

 affected the manner of writing numbers. In the historical, 

 ritual, and negromantic hieroglyphics of the Mexicans, pub- 

 lished by me, the units up to nineteen (the first simple figure 

 for a group is twenty) are exhibited as great round coloured 

 grains, and, what deserves to be mentioned, they are counted 

 from the right to the left hand, like the Semitic writings. 

 This is evident in 12, 15, 17, where the first row contains ten, 

 and the second is not quite filled up. In the most ancient 

 Greek monuments, and in the Tuscan sepulchral inscriptions, 

 the units are expressed by vertical lines ; the same custom 

 prevailed among the Romans and Egyptians (which, respect- 

 ing the last, has been proved by Thomas Young, Jomard, 

 and Champollion). The Chinese use horizontal lines up to 

 the number four ; and such lines are likewise found in some 

 Phoenician coins described by Eckhel (t. iii., p. 410). The 

 Romans sometimes omitted the quinary figure in inscriptions, 

 and, therefore, we find even eight lines as unities placed 

 together. Many instances of this kind are collected by Marini, 

 in his Monumenti del Fratelli Arvali^, a work which deserves 

 attention. The heads of the nails, which anciently were em- 

 ployed by the Romans to indicate the years (annales antea in 

 clavis fuerunt, quos ex lege vetusta figebat praetor maximus, 

 says the elder Phny, vii. 40.) could have led them to the 

 unity-points of the Mexicans, and, in fact, we find such points 



* T, i,; p, 31. J t, ix., 675— for instance in Octumvir, 



