310 On the Systems of Numerical Signs 



lion of the Greek monk Neophytus. These five different 

 methods are in no way dependent on the forms of the nu- 

 merical figures, and to prove this fact more evidently, I shall, 

 in this treatise^ employ no other signs than the arithmetical 

 and algebraical, which are in common use. In this way the 

 attention is more directed to the essential point, the spirit 

 of the method. I already have used such a mode of pasi- 

 graphic notations in another work, treating of a very hete- 

 rogeneous subject, the regular stratification and often peri- 

 odical filation of the minerals (in the appendix to the Essai 

 Geognostique sur le Gisement des Roches) *, and there I 

 have tried to shew, how by this method our abstract views 

 on an object can be rendered more general. Proceeding in 

 this way, all observations respecting the form and composition 

 of individuals, which in themselves may be very useful and 

 true, but would turn ofi* the attention, are suppressed, in 

 order to place in a purer and clearer light a phenomenon, 

 which we wish to investigate in preference to others. This 

 is an advantage which in some way may be justified by the 

 chilly insipidity of such abstractions. 



As regards the manner of writing numbers adopted by dif- 

 ferent nations, it is usual to distinguish the figures not c?e- 

 pending on alphabetical letters, from the alphabetical letters 

 which indicate numerical value, either by forming a certain 

 row, or by short lines or points added to them ; or lastly, by 

 the initials of the numerals (in reference to language) f. 



It is beyond all doubt, that the nations of Hellenic, Semitic, 

 and Aramaic origin (among the last even the Arabs, before 

 they received the numerical figures from the Persians, in the 

 fifth century of the Hegira J), used the same signs to express 



* Ed. 1823, p. 364—375. 



+ The Arabic figures called Diwani, are compounded of mere monograms or 

 abbreviations of the initial letters of the numerals, and are the most complicated 

 instance of such initials. Whether the C and M, used by the ancient Tuscans and 

 Romans, are, in fact, initials taken from the Tuscan and Koman languages, is much 

 more subject to doubt than is commonly believed. (Leslie, Philos. of Arith., p. 7 

 —9, 21 1. Debrosses, t. i., p. 436. Hervas, p. 32—35. Otfried Miiller, Etrusker, 

 p. 304 — 318.) The cross at right angles, used by the Greek, and quite similar to 

 the Chinese figure of ten, signifies in the most ancient inscriptions a thousand 

 (Boeckh, Corpus Inscript. Grace, vol. i., p. 23), and is only the oldest form of ch. 

 (Nouveau Traite de Diplom. par deux Religieux de St. Maur, vol. i., p. 678.) ^ 



X Silvestre 4e Sacy, Gramm, Arabe, 1810, t, i, p. 7 A, Note 6. 



