NUMERALS, the general name given to figures or symbols by means of which num bers are expressed (for PecRoTATIoN)Ctherdistinetive name of Arabic numerals being given to the tine figures Or digits and the zero that are now in almost universal use among civilized nations for this purpose. Both the origin of these figures and the period at which they became known in Europe have been made subjects of laborite s investigation; and it seems to be, now proved beyond a doubt that they are of Indian, not Arabic, origin, and were invented by the Brahmans some time n.c. But the more important inquiry as to the time of their introduction into Europe has hitherto battled all research. The simple and convenient theory that they were intro duced into Spain by the conquering Arabs, and from that country, then a great seat of learning, a knowledge of them was disseminated throughout Europe, is contradicted by the fact that the eastern Arabs themselves had no knowledge of them previous to the time of the caliph Al-Mamun (813-33), while a knowledge of them existed in Europe from a considerably earlier date. The most probable theory is that they were brought from India, probably by the Neo-Pythagoreans, and introduced into Italy, whence tdhey became known to a few of the learned men of eastern Europe. We lave, however, every reason to suppose that the figures then known were totally different in form from those now used. These latter, called gobar by the Arabs, may have been brought to Bair. dad during the reign of Al-Mansor (760), or his immediate successors, and certainly not later than the time of Al-Mamun. the latter reign we know the present system
of arithmetic was introduced into Persia During India, and most probably a knowledge of the gobar figures at the same time. Thence the system of arithmetic was brought to north-western Africa and Spain, and doubtless the figures along with it, about the end of the 10th or beginning of the 11th c., and from Spain a knowledge of both was speedily communicated to the rest of Europe, the gobar figures superseding those forms of eastern figures which had previously been employed. The knowledge of the figures, however, spread, as was natural, much more rapidly than the notation and arithmetic of which they were the foundation, and we consequently find in writings and inscriptions of the middle ages the gobar figures partly substituted for, and mixed up with, the Roman numerals; as, for instance, XXX2, for 32; X4, for 14, etc.; and occasionally such expressions as 302, 303, for 32 and 33. The earliest work on modern arithmetic was published in Germany in 1390; it explained the decimal notation and exemplified the elementary rules. The Arabic numerals were not generally introduced into England till the commencement of the 17th c., and it was long after that time before the decimal arithmetic became general. See a dissertation Sur les Chiffres Indiens, in the Asiatic journal.