ARITHMETIC. 



indeed, in his commentary on the first 

 book of Euclid, says that the Phoenicians, 

 by reason of their traffic and commerce, 

 were the first inventors of arithmetic ; 

 and Strabo also informs us, that in his 

 time it was attributed to the Phoenicians. 

 Others have traced the origin of this art 

 to Egypt ; and it has been a general opi- 

 nion, sanctioned by the authorities of So- 

 crates and Plato, that Theut or Thot was 

 the inventer of numbers; that from hence 

 the Greeks adopted the idea of ascribing 

 to their Mercury, corresponding to the 

 Egyptian Theut or Hermes, the superin- 

 tendance of commerce and arithmetic. 

 With the Egyptians we ought also to as- 

 sociate the Chaldeans, whose astronomi- 

 cal disquisitions and discoveries, in which 

 they took the lead, required a considera- 

 ble acquaintance with arithmetic. From 

 Asia it passed into Egypt, as Josephus 

 says, by means of Abraham. Here it was 

 greatly cultivated and improved ; inso- 

 much, that a large part of the Egyptian 

 philosophy and theology seems to have 

 turned altogether upon numbers. Kirch- 

 er shews, that the Egyptians explained 

 every thing by numbers ; Pythagoras 

 himself affirming, that the nature of num- 

 bers pervades the whole universe, and 

 that the knowledge of numbers is the 

 knowledge of the Deity. From Egypt 

 arithmetic was transmitted to the Greeks 

 by Pythagoras and his followers ; and 

 among them it was the subject of particu- 

 lar attention, as we perceive in the wri- 

 tings of Euclid, Archimedes, and others ; 

 with the improvements derived from 

 them, it passed to the Romans, and from 

 them it came to us. The ancient arith- 

 metic was very different from that of the 

 moderns in various respects, and particu- 

 larly in the method of notation. The In- 

 dians are at this time very expert in com- 

 puting, by means of their fingers, without 

 theuseofpen and ink ; and the natives 

 of Peru, by the different arrangements 

 of their grains of maze, surpass the Euro- 

 pean, aided by all his rules, with regard 

 both to accuracy and dispatch. The He- 

 brews and Greeks, however, at a very 

 early period, and after them also the Ro- 

 mans, had recourse to the letters of their 

 alphabet for the representation of num- 

 bers. The Greeks, in particular, had two 

 different methods : the first resembled 

 that of the Romans, which is sufficiently 

 known, as it is still used for distinguish- 

 ing the chapters and sections of books, 

 dates, &c. They afterwards had a better 

 met -if -. 'n which the first nine letters of 

 the ;.i,i'iibet represented the first num- 

 bers from 1 to 9, and the next nine let- 



ters represented any number of tens, 

 from 1 to 9, that is, 10, 20, &c. to 90. 

 Any number of hundreds they expressed 

 by other letters, supplying what they 

 wanted by some other marks, or charac- 

 ters : and in this order they proceeded, 

 using the same letters again, with differ- 

 ent marks to express thousands, tens of 

 thousands, hundreds of thousands, &c. ; 

 thus approaching very near to the more 

 perfect decuple scale of progression used 

 by the Arabians, who acknowledge, as 

 some have said, that they received i 1 from 

 the Indians. Archimedes, also, in his 

 " Arenarius," used a particular scale and 

 notation of his own. In the second cen- 

 tury of the Christian era, Ptolem) is sup- 

 posed to have invented the sexagesimal 

 numeration and notation, and this method 

 is still used by astronomers and others, 

 for the subdivisions of the degrees of cir- 

 cles. These several modes of notation, 

 above recited, were so operose and in- 

 convenient, that they limited the extent, 

 and restrained the progress of arithmetic, 

 so that it was applicable, with great diffi- 

 culty and embarrassment, to the other 

 sciences, which required its assistance. 

 The Greeks, if we except Euclid, who in 

 his elements furnished many plain and 

 useful properties of numbers, and Archi- 

 medes in his Arenarius, contributed little 

 to the advancement of this science to- 

 wards perfection. From Boethius we 

 learn, that some Pythagoreans had in- 

 vented and employed, in their calcula- 

 tions, nine particular characters, whilst 

 others used the ordinary signs, namely, 

 the letters of the alphabet. These cha- 

 racters he calls apices; and they are said 

 greatly to resemble the ancient Arabic 

 characters, which circumstance suggests 

 a suspicion of their authenticity. Indeed, 

 the MSS. of Boethius, in which these 

 characters, resembling those of the Ara- 

 bian arithmetic, are found, not being more 

 ancient than three or four centuries, con- 

 firm the opinion that they are the works 

 of a copyist. Upon the whole, this trea- 

 tise of Boethius does not warrant our re- 

 jecting the commonly received system 

 with regard to the origin of our arithme- 

 tic ; but if we suppose that the Arabians 

 derived their knowledge of it from the 

 Indians, it is more probable that it was 

 one of the inventions which Pythagoras 

 spread among the Indians, than that 

 those persons should have obtained it 

 from the Greeks. 



The introduction of the Arabian or In- 

 dian notation into Burope,about the tenth 

 century, made a material alteration in the 

 state of arithmetic; and this, indeed, was 



