320 On the Systems of Numerical Signs 



the Roman inscriptions, a horizontal line added over them, 

 increases their value a thousand times, and here it may be con- 

 sidered only as a means of abbreviating and of saving space. 



The method of Eutocius for expressing myriads is more im- 

 portant. In it we find among the Greeks the first trace of the 

 system of exponents, or rather indicators, which rose to such 

 a degree of importance in the East. M", M^, M^, indicate 

 10,000, 20,000, 30,000. Here we find these indicators used 

 only with the myriads. But the Chinese and the Japonese, 

 which last received their civilization from the first about 200 

 years before our aera, both use them for the multipla of all 

 groups. Three horizontal lines under the figure of ten, signify 

 thirteen, but if they are placed over it they express thirty. 

 According to this method, 3456 is written, (I use the Roman 

 figures as signs of groups, and the Indian as exponents) 



M« 



C* 



X* 



I' 

 Among the Egyptians the same kind of indicators are found. 

 Two or four unities placed over a curved line, which denotes 

 a thousand, are used to express 2000 or 4000 *. Among the 

 Aztekes, or Mexicans, I found for 312 years the sign of the 

 vinculum, with six unities as exponent (6x52=312), and I 

 have published it in my work of the American Monuments. 

 Among the Chinese, Aztekes, and Egyptians, the signs of 



5 



groups are always under the exponent, as if X were written 

 instead of 50 ; but in the Arabic Gobar figures the signs of the 

 groups are placed over the indicators. For in the Gobar sys- 

 tem the signs of the groups are points, consequently cyphers ; 

 for in India, in Thibet, and in Persia, cyphers and points are 

 identical. These Gobar signs, which, since 1818, have attracted 



matical works, but horizontal, and thus the mistaking of it for the sign of fraction 

 is obviated. Bast, de Usu Litterarum ad Numeros indicandos, in Gregorii 

 Corinthii Liber de Dialectis Linguae Graecse. 1811. p. 850. 



* Kosegarten, de hierogl. Aegyyt. p. 54. The assertion of Gatterer adopted 

 by him from Bianchini (Dec. 1, cap. iii., p. 3), from Goquet (vol. i. p. 226), and 

 from Debrosses (vol. i. p. 432), that among the Egyptians the figures received 

 value by their position in a perpendicular row, has not been confirmed by modern, 

 researches. Gatterer, Weltgeschichte bis Cyrus, p. 555, 586. 



