NUMERALS (ante). The only valuable essays on the introduction of our present nu. merals arc the works of Woepeke, in the Encycladia Mitropolitana, London, 1845, vol. i., p. 412; in the Journal Asiatigue, 6th series, vol. i., 1863, pp. 27, 234, 442; and his mono. graph, Sur Untroduction de l'Aritlanetigue Indian en Occident, Borne, 1859. His knowl edge of Sanskrit, Arabic, and the higher mathematics, may be seen in his reconstruction of that passage where the education of the infant Buddha is a kind of competition-wallah, on the basis of the logical figure of the "heap." But we are only just beginning to get reliable dates in Indian archaeology, and the edition of Prinsep by Thomas, 1863, the archeological part of the surveys of India, the labors of German scholars in the line of Shemitic influence on early Indian alphabets, all point to conclu sions at variance with those of the scholars of the last generation. There are three sets of figures in use among what may be called the mathematical nations, the Sanskrit (this name is used because it does not identify them with any particular alphabet), the Nesklii (as used with the present Arabic alphabet), and the European. None are now as they were in the year 1000 A.D., and none is an immediate borrowing from another. All seem to have been once used without notational place, that is, without the zero, Arab-Greek 41g3pcc, Sansk. suneja, both meanine. void. The earliest Sanskrit figures appear to be of A.D. 674. Bactrian numerals are used till B.C. 116, they are Shemilic, and without nota tion. The Pali numerals which accompany the series of inscriptions from the 3d c. B.C. to the 5th c. A.D., are partly tallies, partly alphabetic, partly Shemitic, and are also without notation. The Sanskrit figures must be traced back through a Devanagari 10ih c. type, through a still older Kashmir shape, to identifiable initials of their Pali (") names in characters which are not quite identical with either Pali, Allahabad, or Sindli multani. The resemblance of 1, 2, 3 to our own figures vanishes as we go back, and the only shadow of likeness is an accidental form of the old 7. Evidently, there remains at that point not the slightest resemblance to any modern Devanagari letters, nor are the letters those usually proposed, as the six, is spelled with chh. and, seven with t. The other two types are, as to a few of their figures, bound together by a common origin, though dissimilar in shape and derivation. It may be well to remind the reader that Alexandria, with the party-colored nationalities who traded there, serves as a great receptacle, not only of all the mysticism but of all the knowledge of the antique cut. What a jumble of perverted intelligence remained long after any practical instruction had vanished may be easily seen by studying any of the patristic compilations, or any of the early Arabic encyclopedists. The Arabs of n. Egypt and Barbary, Mughrabin, had
always certain heretical traditions, a different arrangement of the supplementary letters of the alphabet, and certain differences in the figures, which distinguished them from their fellows of the east. - Their, civilization seems .earlier and more practical. The oldest figures known (except Chines6 current taarks) are the Egyptian, and they go ill. 111I•, which in Demotic are changed to one long stroke, with the others reduced each to a short scrabble on its upper left side. The Hieratic changes the tallies to a series of vertical scrabbles, and from these conic the Demotic signs for months, 1, 2, 3, almost identical with our figures. These furnish the radical between Arabic and Gobar figures. The Arabic; at least the Neskhi, takes the first four Demotic figures, and, necessarily reversing them in its writing from right to left, adds to them others, of which only 9 bears a chance resemblance to an European figure. The Gobar takes the three Demotic month figures, adds the Demotic common 4, and the rest are identical with the old Muglimb, with the apices of Boethius, and with our modern figures. Variant types are old Arabic 4 like a Greek sigma, E, and 5 like our 8 with a tail; the Gobar and the Boethian signs have another 2, like a Saxon t; the 14th c. Eurci pean 4 is like a Greek lambda, A. The apices, occurring in an old manuscript of Boethius, but unfortunately not to be fixed in date, have every appearance of being Gnostic. The signs are strangely deformed, and their names, affixed, are from 4 to 9, Syrian, but 1 and 2 are Indo-German, and 3 unreadable. As the GObar seem older than the Neskhi, and as their first four figures are undoubtedly Egyptian, it may be that the rest, our figures of to-day, are also debased Demotic. They would be either alphabetical— bat of the sequence of the Demotic alphabet we are not entirely certain—or initial—but; if so, of Coptic numbers, or of Arabic numbers spelled in Coptic? It seems impossible to tell, and no guessing. or discovery of chance relation in appearance; is of the slightest value. A series of deductions would attribute the other Neskhi figures to either a Syriac alphabet becoming Kufic, or perhaps to some arrangement of Perso-Bactrian signs with which we are not yet acquainted. The manuscript of Washiyi will show with how many signs an inquisitive Arab of his time might be familiar, while without real knowl edge of a single alphabet, even, beside his own.