258 



ARITHMETIC. 



stead of pebbles, nml smn 11 silver coins came \n 

 supply the place of counters. But the operations 

 with tin 1 alxiciis were rendered still more conmuxlious, 

 liy substituting, for such tali or counters, small 

 Ix-nds strung on parallel threads, and sometimes pegs 

 si nek along grooves. With such nn instrument, it is 

 not difficult to perceive how the simpler additions and 

 subtractions could be performed with tolerable ex- 

 pedition ; but to accomplish a process of multiplica- 

 tion or division, even on tin- smallest scale, must 

 h.i\ e IK en a work of tedious and most irksome labour. 

 Accountants by profession, among the Romans, were 

 stylet! calculatotes, or ralionarii. Various expedients 

 see-in to have been employed for shortening the 

 arithmetical operations. The different positions of 

 tlie. fingers were, for that purpose, used to a certain 

 extent. Hocthius treated largely of the subject; and 

 even the venerable Hcde has given very diffuse rules 

 for what was called digital arithmetic. When calcu- 

 lations with counters became more involved, the 

 table on which they were performed, being neces- 

 sarily of a very considerable size, was called the 

 bench or bank; and hence our term for an office 

 where money transactions are negotiated. The court 

 of exchequer, introduced into England by the Nor- 

 nuin conquest, and intended for auditing the revenue 

 of the crown, liad its name from scaccarium, which, 

 in modern Latin, signifies a chess-board. The ac- 

 counts were cast up oy the tellers, or computatores, 

 on a large table covered with black cloth, chequered 

 with white lines, on which were placed counters, or 

 small foreign coins, to denote successively pence, 

 shillings, and pounds ; proceeding afterwards, on the 

 several distinctures of the cloth, by units, tens, 

 hundreds, &c. Sums of money were also rudely 

 marked on tallies, so called because they consisted of 

 white sticks of hazel or willow, split up and cut 

 square at both ends ; a very fine notch on them 

 denoting a penny, one rather larger a shilling, and 

 one still larger a pound ; the notch next in size re- 

 presented twenty pounds, a larger one expressed a 

 hundred, and the largest of all a thousand. This 

 very strange practice has been handed down to our 

 own times ; a striking instance of the blind obstinacy 

 with which ancient usages, however absurd and 

 ridiculous they may through time have become, are 

 yet retained in public offices, and especially in our 

 courts of law. The introduction of the Arabic digits, 

 which produced a total revolution in the system of 

 modern arithmetic, is commonly ascribed to Gerbert, 

 a Benedictine monk of Fleury, who, at the commence- 

 ment of the eleventh century, was elevated to the 

 papal chair, by the name of Sylvester II. That 

 ardent ecclesiastic, in an age of darkness and rooted 

 prejudice, had yet the resolution to pass into Spain, 

 and study for several years the sciences there culti- 

 vated by the Moors. On his return to France from 

 this new pilgrimage, fraught with various and useful 

 information, he was esteemed a prodigy of learning 

 by the Christians of the West ; nor did the malice of 

 his rivals fail to represent him as a magician leagued 

 with the infernal powers. To the decimal system of 

 notation with which he had become acquainted, 

 Gerbert applied indifferently the old name abacus, or 

 the Arabic term algorismus, compounded of the 

 definite article al and the Greek word afdpes, and 

 signifying, therefore, the art of numbering. The 

 knowledge of that art was farther extended, from the 

 intercourse then opened with the East, by the crusa- 

 ders and the Italian merchants who frequented the 

 coasts of the Levant. Yet it must for some time 

 have made a very slow and obscure progress. The 

 characters themselves appear to have been long con- 

 sidered in Europe as dark and mysterious. Deriving 

 their whole force from the use made of the eero or 



cipher, so called from the Arabic word tsaphara, 

 denoting empty or void, this term can/c afterwards to 

 express, in general, any secret mark. While tin- 

 verb to cipher means to compute with figures, the 

 phrase tn irriti- in cipher still signifies the concealing 

 a communication under private and concerted sym- 

 bols. The Arabic characters occur in some arith- 

 metical tracts composed in England during the course 

 of the thirteenth and fourteenth century, |>nrticularly 

 in a work by John of Halifax, or Sacro-Hosco ; but 

 another century elapsed before they were generally 

 adopted. At first, they were used only partially, and 

 intermixed with the Saxon, or corrupted Roman, 

 numerals. Their form also was gradually improved, 

 and seems not to have been fully settled till iilnmt 

 the middle of the fifteenth century, the memorable 

 epoch of the invention of printing. The following 

 cut represents the progress of European numerals. 



1O OUrtt 



o, ' m 



6 ? 8 9 I </ 



123450 789 -10. 



But though our present minerals were certainly 

 derived from the Arabians, through the medium ot 

 the Saracen conquerors of Spain, tliat imitative people 

 laid no claim to the merit of the original discovery. 

 The various tribes which wandered with their herds 

 over tlie wide plains of Arabia, had continued for ages 

 in a state of rude independence, till the enjoyment 

 of ease and plenty, under the prosperous reigns of 

 the caliphs, tempted them to cultivate letters and the 

 physical sciences. Having once tasted the delight 

 which knowledge imparts, they applied, with ardour 

 and unremitting diligence, to procure information 

 from every quarter. They seldom, however, aspired 

 to original efforts, but contented themselves with 

 commenting on the writings of their admired instruc- 

 tors, or with slowly augmenting the stock of facts by 

 their own laborious observations. They adopted 

 with eagerness the geometry and astronomy of the 

 Greeks, and joined to these refined sciences the deci- 

 mal system of arithmetic, borrowed most probably 

 from the Persians, who had long been the undisputed 

 masters of India. According to Alsephadi, a learned 

 Arabian doctor, the people of India boasted of three 

 discoveries, the composition of the Golaila fl'adum- 

 na, or Pilpay's Fables the game of chess and the 

 numeral characters. Maximus Planudes, a Greek 

 author of the fourteenth century, bears the same 

 testimony in his arithmetic, expressly styling it \- 



rtxti ItSixv, or VnQofia, KO.-T IvSst/f, that is, Indian 

 computation, or Calculation after the Indians ; and 

 he moreover subjoins, that the figures themselves 

 were Indian. The characters given by Planudes 

 scarcely differ at all from the Arabic, which, again, 

 very nearly resemble the Persian, now universally 

 used through the lower provinces of India. Pla- 

 nudes, by an omicron, represents the cipher, which is 

 merely a full dot in the Persian, and a very small a 

 in the Arabic ; and his mark for five, which the 

 Arabians denoted by a large 0, resembles most nearly 

 the Sanscrit. But the Arabians likewise employed 

 occasionally, as we do, letters to signify numbers. In 

 the astronomical tables of Ulugh Beigh, the numbers 

 are set down in letters ; and this after the Arabian 



