ARITHMETIC. 
from hence the Greeks adopted the idea of 
ascribing to their Mercury, corresponding 
to the Egyptian Theut or Hermes, the su- 
perintendance of commerce and arithmetic. 
With the Egyptians we ought also to asso- 
ciate the Chaldeans, whose astronomical 
disquisitions and discoveries, in which they 
took the lead, required a considerable ac- 
quaintance with arithmetic. From Asia it 
passed into Egypt, as Josephus says, by 
means of Abraham. Here it was greatly 
cultivated and improved ; insomuch that a 
large part of the Egyptian philosophy and 
theology seems to have turned altogether 
upon numbers.- Kircher shews-, that the 
Egyptians explained every thing by num- 
bers ; Pythagoras himself affirming, that the 
nature of numbers pervades the whole uni- 
verse, 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 particular atten- 
tion, as we perceive in the writings of Eu- 
clid, Archimedes, and others ; with the im- 
provements derived from them, it passed to 
the Romans, and from them it came to us. 
The ancient arithmetic was very different 
from that of the moderns in various respects, 
and particularly in the method of notation. 
The Indians are at this time very expert in 
computing, by means of their fingers, with- 
out the use of pen and ink ; and the 
natives of Peru, by the different arrange- 
ments of their grains of maize, surpass the 
European, aided by all his rules, with re- 
gard both to accuracy and dispatch. The 
Hebrews and Greeks, however, at a very 
early period, and after them also the Ro- 
mans, had recourse to the letters of their al- 
phabet for the representation of numbers. 
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 distinguishing the chapters 
and sections of books, dates, &c. They af- 
terwards had a better method, in which the 
first nine letters of the alphabet represented 
the first numbers from 1 to 9, and the 
next nine letters represented any number 
of tens, from 1 to 9, that is, 10, 20, & c. 
to 90. Any number of hundreds they ex- 
pressed by other letters, supplying what they 
wanted by some other marks or characters : 
and in this order they proceeded, using the 
same letters again, with different marks to 
express thousands, tens of thousands, hun- 
dreds 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 it from the Indians. Archimedes 
also in his “Arenarius,” used a particular 
scale and notation of liis own. In the se- 
cond century of the Christian era, Ptolemy 
is supposed to have invented the sexagesi- 
mal numeration and notation, and this me- 
thod is still used by astronomers and others, 
for the subdivision of the degrees of circles. 
These several modes of notation above re- 
cited, were so operose and inconvenient, 
that they limited the extent, and restrained 
the progress of arithmetic, so that it was ap- 
plicable with great difficulty and embarrass- 
ment 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 Archimedes in his Arenarius, contri- 
buted little to the advancement of this sci- 
ence towards perfection. From Boethius 
we learn, that some Pythagoreans had in- 
vented and employed, in their calculations, 
nine particular characters, whilst others 
used the ordinary signs, namely, the letters 
of the alphabet. These characters he calls 
apices ; and they are said greatly to resem- 
ble 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 Arabian arithmetic, are found, not 
being more ancient than three or four cen- 
turies, confirm the opinion that they are the 
works of a copyist. Upon the whole, this 
treatise of Boethius does not warrant our re- 
jecting the commonly received system with 
regard to the origin of our arithmetic ; 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 inven- 
tions 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 Europe, about the tenth 
century, made a material alteration in the 
state of arithmetic ; and this, indeed, was 
one of the greatest improvements which 
this science had received since the first dis- 
covery ofit. This method of notation, now 
universally used, was probably derived ori- 
ginally from the Indians by the Arabians, 
and not, as some have supposed, from the 
Greeks ; and it was brought from the Ara- 
bians into Spain by the Moors or Saracens, 
in the tenth century. Gerbert, who was 
afterwards Pope, under the name of Silves- 
