used by different Nations* 309 



quos numerafe solemusy as Ovid Bays> we probably should have 

 adopted a duodenary scale*, if our extremities had been 

 divided sixfoldly. Such a scale has the great advantage, that 

 its groups can be divided by 2, 3, 4 and 6 without leaving 

 a fraction, and for that reason it has been adopted by the 

 Chinese for their measures and weights, ^om^^ibd' earlksl 

 times. ' ^V{.«cvf» ^{)%t\)\ ^tt: 



I The preceding observations regard the relation betwe^df' 

 language and writing, between the numerals and their figuresl' 

 I shall proceed to consider the latter by themselves. I remind 

 the reader that this essay is only an extract from my larg^''' 

 and unfinished work, and that I shall not speak of the hete- 

 rogeneous forms of the simple elements (numerical) figures, 

 but of the spirit of the different methods of expressing 

 numeral quantities, which are adopted by different nations. 

 I, therefore, shall only take notice of the figure or form of the 

 numerical signs, whenever it affects my conclusions respecting 

 the identity or heterogeneousness of the methods themselves. 

 The mode of proceeding adopted for the purpose of expressing 

 the pure or mixed multipla of the denary fundamental groups 

 n (for instance 4«, 4m*, or 4/1+7, 4n^+6?i, 4?i*+6rt+5) is 

 very different in different nations. Sometimes it is effected by 

 forming a row (that is by giving different value to the figures 

 according to their position), after the manner of some nations 

 of the Hindoos; sometimes by mere juxtaposition, as among 

 the ancient Tuscans, the Romans, Mexicans, and Egyptians. 

 Some nations use for that purpose coefficients, as that tribe 

 of the Hindoos, inhabiting India within the Ganges, which uses 

 the Tamul language ; others use exponents or indicators, 

 placed over the figures of the groups, as the Chinese, Japanese, 

 and also the Greek in employing myriads ; others again, use 

 an inverted method. These place over the nine numerical 

 figures a number of cyphers or points, to indicate the relative 

 value of them, and in this system, the cyphers or points are 

 the signs of the groups placed over the unities. Thfe last 

 method is found in the Arabic Gobar writings, and in an 

 Indian numerical system, preserved and explained in a. schp- 



