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rtrts of writing and cafting accounts, is faid, by Julius 
Capitolinus, to be litteris elrmentariis et calculo imbutus. 
ft. Auguftlne, whofe juvenile years were devoted to plea¬ 
sure and diffipation, acquaints us, in his extraordinary 
Confelfions, that to him no fong ever founded more odious 
than the repetition, or cantio, that one and one make two, 
and two and two make four. The ufe of the aitrciw, called 
Sometimes likewife the Msnja Pythagorica, formed an ef- 
fential part of the education of every noble Roman youth : 
Nec qui abaco numeros, et J'e£lo in pulvere me fas 
Scit riffle vafer.- Per/. Sat. i. 15.2. 
From Martianus Capella, we learn that, as refinement 
advanced, a coloured fand, generally of a greeniih hue, 
was employed to ftrew the fur face of the abacus: 
Sic abacum perflare jubet, fic tegmine glauco 
Pandere pulvereum formarum duCtibus aequor. Lib. vii. 
A.Small box or coffer, called a loculus, having compart¬ 
ments for-holding the calculi or counters, was a neceffary 
appendage of the abacus. Inltead of carrying a flate and 
Satchel, as in modern times, the Roman boy was accuf- 
tomed to trudge to School, loaded with his arithmetical 
hoard, and his box of counters : 
Quo pueri magnis e centurionibus orti, 
Lervo fij’peiiji tcculos tabulamque laccrto. Hor. Sat. i. 8. 
In the progrefs of luxury, tali, or dies, made of ivory, 
were tiled inltead of pebbles, and fmall lilver coins came 
to fupply the place of counters. Under the emperors, 
every patrician living in a fpacious marifion, and indulg¬ 
ing in all the pomp and Splendour of eaftern princes, ge¬ 
nerally entertained, for various functions, a numerous 
train of foreign Haves or freedmen in his palace. Of thefe, 
the librarius or miniculator, was employed in teaching the 
children tl\eir letters; but the notarius regiftered expenfes, 
tiie rationarivs adjufted and fettled accounts, and the ta- 
bularhis or calculator, working with his counters and 
board, performed what computations might be required. 
Sometimes thefe laborious combiners of numbers were 
termed reproachfully canculoms or calculoms. In the fer¬ 
vour of operation, their geftures muft often have appeared 
eonltrained and rifible: 
Com put at, ac cevet. Ponatur calculus adlint 
Cum tabula pueri. Juv. Sat. ix. 40. 
The nicety acquired in calculation by the Roman youth, 
was not quite agreeable to the carelefs and eafy temper of 
Horace: 
Romani pueri longis rationilus affem, 
Difcunt in parteis centum diducere : dicat 
Filius Albini, Si de quincunce remota eft 
Uncia, quid fuperat? poteras dixilfe Triens heu 
Rem poteris fervare tuam, redit uncia, quid fit ? 
Semis.- Epift. ad Pifonem. 
It was a praCtice among the ankients to keep a diary, 
by marking their fortunate days by a lapillus, or fmall 
white pebble, and their days of misfortune, by a black 
one. Hence the frequent allulions which occur in the 
dallies : O ! diem laetum, notandumque mihi candidijfimo 
calculo. Plin. Epift. vi. 11. 
-diefque nobis 
Signanda meliorihus lapillis - Mart. ix. 53. 
Hunc, Macrini, diem numera meliore lapillo, 
Qui tibi labentes apponit candidus annos. Pevf, Sat. ii. 
To facilitate the working by counters, the conftruCtion 
of the abacus was afterwards improved. Inftead of the 
perpendicular lines or bars, the board had its furfa.ee di¬ 
vided by fets of parallel grooves, by ftretched wires, or 
ev-en by fuccefiive rows of holes. It was ealy to move 
fmall counters in the grooves, to Aide perforated beads 
along the wires, or to Hick large knobs or round-headed 
nails in the different holes. See Abacus, vol. i. p. 4. 
But ftill the abacus, with its ftore of counters, wanted 
the valuable property of being portable, and was at all 
B E K. 
times evidently a clumfy -and moft incommodious imple¬ 
ment of calculation. In many cafes, it became indiipen- 
fable to adopt fome fure and ready method of exprefling 
at leaft the lower numbers. The ancients employed the 
varioufly-combined inflexions of thk/tno-ejis on both hands 
to fignify the numerical feries; and on this narrow bafts 
they framed a fyftem of confiderableextent. In allufion 
to the very ancient praCtice of numbering by the arbitrary 
play of the fingers, Orontes, the fon-in-law of Artax’- 
erxes, having incurred the weighty difpleafure of that 
monarch, is reported by Plutarch to have exclaimed in 
terms exactly of the fame import as tbofe before aferibed 
to Solon, that “ the favourites of kings refemble the fin¬ 
gers of the arithmetician, being fometimes at the top, and 
iometimes at the bottom, of the (bale, and are equivalent 
at one time to ten thoufand, and atanother to mere unit's/’ 
Among the Romans likewife, the allulions to the mode 
of exprelfing numbers by the varied inflexion of the fin¬ 
gers, are very frequent. Hence the ciaflical expreflions, 
computure digilis, and nmnerareper digitos; and hence the 
line of Aufonius, “ Quot ter luflatus cum pollice com- 
putatindex.” 
In this play of the fingers great dexterity was acquired ; 
and hence the phrafe which fo frequently occurs in the 
dailies, micare digitis. It was cultomary to begin with 
the left hand, and thence proceed to the right hand, on 
which the different combined inflexions indicated ex¬ 
actly one hundred times more. Hence the peculiar force 
of this pallage from Juvenal 1 
Rex Pylius, magno fi quicquam credis Homero, 
Exemplum vitae fit it a cornice fecundae-; 
Felix nimirum, qui tot per fascula mortem 
Diftulit, atque fuos jam dextra computat annos. Sal. x. 
Many fuch allulions to the mode of indicating numbers 
by the varied pofition of the fingers or the hands, occur 
in the writings of Cicero and Quintilian. The ancients, 
indeed, for want of better inftruments, were tempted to 
puflt that curious art to a very great extent. By a finde 
inflexion of the fingers of the-left hand, they proceeded^as 
far as ten ; and, by combining another inflexion with it 
they could advance to an hundred. The fame fig no on 
the right hand, being augmented, as we have feen, an hun¬ 
dred-fold, carried them as far as ten thoufand ; and, by a 
farther combination, thofe iigns, being referred fuccef- 
fively to different parts of the body, were again multiplied 
an hundred times, and therefore extended to a million. 
This kind of pantomime outlived the fubverfion of the 
Roman empire, and was particularly fitted for the iloth- 
ful religious orders who fattened on its ruins; and, relin- 
quilhing every manly purfuit, recommended filence as a 
virtue, or enjoined it as an obligation. Boethius treated 
largely of the fubjeCt; and even the venerable Bede has 
given very diffufe rules for what was called digital arith¬ 
metic. 
But the application of the abacus itfelf was not entirely 
forgotten at a much later period. We have feen a fmall 
volume of arithmetic, quaintly cornpofed in the form of 
dialogue, by Robert Recorde, teacher of mathematics and 
practitioner in phyfic at Cambridge, during the reign of 
Edward VI. in which round dots, placed on perpendicu¬ 
lar lines, and employed to exprefs the fucceflion of units, 
tens, hundreds, See. are made to perform fome of the Am¬ 
pler numerical operations. To the fame ingenious,man 
we are indebted for thenrft treatife of algebra, then named 
the coffic art, which appeared in the Englilh language; but 
his meritorious labours, like thole of the greateit bene¬ 
factors of our fpecies, feem to have been ill-requited, fince, 
having removed to the capital, he died under confinement 
for debt in the Fleet prifon. 
A fmall in Hr unseat, entirely refembling the abacus, has 
likewife at different times been recommended, for teach¬ 
ing the elements of ciphering, under the name of palpable 
arithmetic. Managed with proper dilcretion, fuch a con¬ 
trivance would no doubt be uleful in conveying juft no¬ 
tions. 
