K U M 
not, ill tbeiv original intention, ufe letters to exprefs num- 
hers at all; the moft natural account of the matter feems 
to be this. The Romans probably put down a fingle 
ftroke 1 for one, as is ftill the practice of thofe who fcore 
on a (late or with chalk; this ftroke they doubled, trebled, 
and quadrupled, to exprefs 2, 3, and 4 ■. thus 11 li! fill. 
So far they could eafily number the ftrokes with a glance 
of the eye. But they prefently found, that, if more were 
added, it would foon be neceft'ary to tell the ftrokes one 
by one; for this reafor., then, when they came to 5, they 
exprefled it by joining two ftrokes together in an acute 
angle thus, V ; which will appear the more probable, if 
it be conftdered that the progreflion of the Roman num¬ 
bers is from j to 5, i.e. from the fingers on one hand to 
the fingers on the other. Ovid has touched upon the ori¬ 
ginal of this in his Faftorum, lib. iii. and Vitruvius has 
made the fame remark. After they had made this acute 
angle V for five, they added the fingle ftrokes to it to the 
number of 4, thus, VI VII VI 11 VI 111 ; and then, as the 
ftrokes could not be further multiplied without confufion, 
they doubled their acute angle by prolonging the two 
lines beyond their interfeftion thus, X> to denote two 
fives, or ten. After this they doubled, trebled, and quadru¬ 
pled, this double acute angle thus, X X XXX XXXX; 
they then, for the fame reafon which induced themfirft to 
make a fingle I, qnd then to double it, joined two fingle 
ftrokes in another form; arid, inftead of an acute angle, 
made a right angle, L, to denote fifty. When this fifty 
was doubled, they then doubled the right angle thus E, 
to denote one hundred; and, having numbered this 
double right angle four times, thus EE EEE EEEE ; 
when they came to the fifth number, as before, they re-, 
verfed it, and put a fingle ftroke before it thus |j, to de¬ 
note five hundred ; and, when this five hundred was dou¬ 
bled, then they alfo doubled their double right angle, 
letting two double right angles oppofite to each other, 
with a fingle ftroke between them, thus EICI, to denote 
one thoufand. This was the limit of numeration among 
the early. Romans ; but, in the progrefs of refinement, 
they repeated the fymbols of a thoufand to denote the 
higher terms. Thus, cr. I a a was employed to reprefent 
ten thoufand, and LEEI333, to fignify an hundred thou¬ 
fand ; the letter I, inclofed between the E 3 , being, for 
the fake of greater diftindtnefs, elongated. Again, each 
of thefe being divided, gives 1 33 for five thoufand, and 
1 333 for fifty thoufand. Tliefe characters, however, were 
' often modified and abbreviated in monumental inferip- 
tions. By drawing a horizontal line over the letters, their 
value was augmented a thoufand times. 
That the Romans did not originally write M for 1000, 
and C for 100, but fquare characters, as they rfre printed 
above, weareexprefslyinformed by Paulus Manutius; but, 
the corners of the angles being cut ofr by the tranferibers 
for difpatch, thefe figures were gradually brought into 
what are now numeral letters. When the corners of E13 
were made round, it flood thus cio, which is fo near the 
Gothic CD, that it foon deviated into that letter; fo 13 
having the corner made round, it flood thus io, and then 
eafily deviated into D. r. alfo became a plain C by the 
fame means; the fingle redtangle which denoted 50, was, 
without alteration, a capital L; the double acute angle 
was an X ; the fingle acute angle a V confonant; and a 
plain fingle ftroke, the letter I; and thus thefe feven let¬ 
ters,. M, D, C, L, X, V, I, became numerals. 
Such a fyllem of notation might ferve laborioufly to 
regifter a number that was not very large ; but it could 
not afford the flighteft aid in performing an arithmetical 
computation. By what ingenuity, for inflance, could 
even fuch final] numbers as 48 and 34 be multiplied to¬ 
gether, if exprefled by the complicated fymbols XLVIII 
and XXXIV, where both the units and the tens are equally 
involved? and how unmanageable mull that notation be, 
where the fnm of 543,475,003 requires the following 
characters! looooooo. cccccIddodo. cccccIooddo. 
CCCCClODODD. ccccclooooo. CCCClOOOO, CCCClODOO. 
Vol. XVII. No. 1178. 
B E R; 2<M 
ccccloooo. ccclooo. cccloao. ceclaaa. ccclo.oo 
Idod. ccloo. ccloo. Im. III. 
The Romans were late in acquiring any t-afte for 
refinement; and remained, during the whole courfe of 
their hiftory, profoundly ignorant of fcience. Such a 
notation as wehave exhibited above could hardly be called 
an improvement upon numeration by counters, or palpable. 
arithmetic, though this laft no.doubt long preceded the 
invention and ufe of numeral characters. It was.retained 
in Europe for a very confiderable time after the adoption 
of figures, and. might even at prefent be employed in 
praClice to a certain extent with obvious advantage. The 
exhibition of numbers by counters, appears happily fitted 
for unfolding the principles of calculation. In thefchools 
of ancient Greece, the boys acquired the elements of 
knowledge by working on a frnooth board witli a narrow 
rim, the abax; fo named evidently from the combination 
of A, B, E, the firft letters of their alphabet, refembling, 
except perhaps in fize, the tablet, likewjfe called A, B, C, 
on which the children with us ufed to begin to learn the 
art of reading. The pupils, in thofe dillant ages, were 
inftruCled to compute, by forming progreftive rows of 
counters, which, according to the wealth or fancy of the 
individual, confifted of final! pebbles, of round bits of 
bone or ivory, or even of filver coins. From 1]/5;<po?, the 
Greek word fora pebble, comes the verb, to coin- 
pate. But the fame board ferved alfo for teaching the ru¬ 
diments of writing and the principles of geometry. The 
abax being ltrewed with green land, the pulvis eruditus of 
clafllc authors, it was eafy, with a radius, or fmall roe), 
to trace letters, draw lines, conllrnCl triangles, or deferibe 
circles. Beiides the original word the Greeks had 
the diminutive a^cr/.io-j ; and it feems very probable, that 
this linaller board was commonly ufed for calculations, 
while the larger one was referved among them for the pur- 
pofe of tracing geometrical diagrams. 
To their calculating-board the ancients make frequent 
allufions. It appears, from the relation of Diogenes Laer¬ 
tius, that the practice of bellowing on pebbles an artificial 
value, according to the rank or place which they occu¬ 
pied, mounts higher than the age of Solon, the great re¬ 
former and legillator of the Athenian commonwealth. 
This fagacious obferver and dilinterefted ftatefman, who 
was however no admirer of regal government, ufed to 
compare the pafiive minifters of kings or tyrants to the 
counters or pebbles of arithmeticians, which are fome- 
times mod important, and at other times quite infignifi- 
cant. FEfchines, in his oration for the Crown, fpeaking- 
of balanced accounts, lays, that the pebbles were cleared 
away, and none left.” His rival, Demofthenes, repeating 
his exprelfion, employs farther the verb, a-jiavthew, which 
means “ to take up as many counters as were laid down.” 
It is evident, therefore, that the ancients, in keeping 
their accounts, did not feparately draw together the cre¬ 
dits and the debts; but fet down pebbles lor the former, 
and took up pebbles for the latter. As foon as the board 
became cleared, the oppofite claims vvereexadlly balanced. 
We may obferve, that the phrafe “ to clear one’s fcores os- 
accounts,” meaning to fettle or adjull them, is ftill pre- 
ferved in the popular language of Europe, being fuggefted 
by the fame praflice of reckoning with counters, which 
prevailed indeed until a comparatively late period. 
The Romans borrowed their abacus from tlie Greeks, 
and never afpired higher in the purfuit of fcience. To 
each pebble or counter, required for that board, they gave 
the name of calculus, a diminutive formed from calx, a 
Hone ; and applied the verb calculare to fignify the one- 
ration of combining or fepa.rating-fuch pebbles or counters. 
Hence innumerable allufions by the Latin authors. Po- 
nere calculum, Jubducere ca/cuhwi, “ to put down a coun¬ 
ter, or to take it up ;” that is, to add or fub trail; vocare 
ulicjuid ad calculum, ut par Jit ratio acceptorum et datorum ; 
“ to fubmit any thing to calculation, fo that the balance 
of debtor and creditor may be ftruck.” The emperor 
Helvius Pertinax, who had been taught, while a boy, the 
