306 On the Systems of Numerical Signs 



It is by no means a difficult task for me to give a still greater 

 number of remarkable instances of the analogy existing between 

 language and numerical hieroglyphics in juxtaposition, in the 

 subtraction of unities by prefixing them, in writing, before 

 the group, and in the intermediate landing-places of 5 and 15 

 in those nations who have adopted groups of 10 or 20. In 

 the languages of some very rude American tribes, for instance 

 in those of the Guarinis and Lulos, six, seven, and eight are 

 expressed by four with two, four with three, five with three. 

 The more civilized Muyscas say twenty (or house) with ten, 

 instead of thirty. The Cymri, in Wales, use in such a case 

 deg (ten), or ugain (with twenty) ; as the French use soixante 

 et dix, for seventy. We find addition effected by juxta- 

 position, chiefly among the old Tuscans, Romans, Mexicans, 

 and Egyptians ; subtractive or diminishing expressions among 

 the Indians in the Sanscrit *, where 19 is called unavinsati, 

 99 unasata ; among the Romans in undeviginti {units de 

 viginti), for 19 ; undeoctoginta, for 79 ; duodequadraginta, 

 for 38 : among the Greeks in zUoai "^covra. hos, 19 ; and 

 TTsvTsxovra '^voiv ^sovrotv, 48 ; that is, wanting two to make up 

 fifty. Such subtractive expressions have passed into the 

 writing of numbers, and in such a case the figures expressing 

 unities to be subtracted are prefixed to the signs of the groups 

 of five and ten, and even to their multiplicates, for instance, 

 to 50 or 100 (IV, and XI, and XL, and XT, for four-and- 

 forty among the Romans and ancient Tuscans | ; though in 

 the last nation the numerical figures probably were entirely 

 derived from the alphabet, according to the researches lately 

 made by Otfried Miiller) . In some rare Roman inscriptions 



1807, p. 55. In the Celtic or Kymrich dialect of Wales, 5 is called pump; 

 10 deff i 20 ugain; 30 cleg ar ugain; 40 deugain ; 60 trigain. (William 

 Owen's Dictionary of the Welsh Language, vol. i., p. 137.) The same system 

 of twenty unities is used in the language of the Biscayans : bi is 2 j lau, 4 ; 

 amar, 10; ogiiai, 20; birroguai, 40; lauroguai, 80 ; berrgotiai-tamar, 50, namely 

 forty and ten (amar). Larramendi^ urte della Lengua Bascongada, 1729, p. 38. 

 (The numeral figures of the Biscayan and Gaelic languages are not mixed toge- 

 ther in my Monum. vol. ii., p. 237, but they are placed near one another to facili- 

 tate the comparison ; by an error of print, however, les premiers is said instead of 

 les deux or lea uns et les autres.) 



* M. Bopp quotes even 95 (or hundred — 5) in the words pantschonam satam 

 — K:ontracted from pantcsha (five) and una (less). 



t Otfried MvUler, Etrusker, ii., p. 317—320. 



