), a word
probably of Eastern origin, which has been explained from two different
Semitic roots: (1) abaq,
“sand, dust,” a derivation propounded by several eminent French
scholars and accepted by Daremberg and Saglio (Dict. des
s. v.); or (2) abak,
“to raise or lift up,” recently suggested in
Wölfflin‘s Thesauri Latini
1884. According to the former, the oldest meaning is
that of the sanded board for calculations, rendered necessary at an early
period by the rise of commerce between the East and the West. The latter has
the merit of accounting more completely for the various usages of the word;
but neither derivation can be regarded as anything more than a more or less
Adopting, for the sake of classification, the primary meaning of
“anything raised,” we have:
I. A table, dresser, or stand for supporting vessels of any kind.
(1) The simplest kind was no doubt that enumerated by Cato among farm
requisites, and distinguished by him from mensa
10, 4; 11, 3). Of a more elaborate sort was--
(2) A table or sideboard, used for the display of plate, of a square form,
supported by a trapezophoron,
as the leg or
legs were sometimes called ; but the word trapezophoron
also signified the table itself. (Pollux, 10.69;
Cic. Fam. 7.2. 3
; Dig. 33
, tit. 3,
s. 3.) The abacus was supported sometimes by four legs, sometimes by one,
which were made of marble, ivory, bronze, or silver, highly ornamented. Cf.
Ornamentum abaci, nec non et parvulus infra Cantharus et recubans sub eodem
Here the “Chiron” was the trapezophoron;
and similar ones representing sphinxes and
griffins are found in museums. The use of abaci (mensae
) in private houses was first introduced at Rome (according
to Liv. 39.6
Plin. Nat. 34.14
) from Asia Minor
after the victories of Cn. Manlius Vulso, B.C. 187,
Abacus or Sidebord. (From a sarcophagus in the British
and their introduction was regarded as one of the marks of the
growing luxury of the age. (Varr. L. L.
9.46; Cic. Ver. 4.16, 35
5.21, 61; Juv.
; Plin. Nat. 37.14
73; Auson. Epigr.
8.2.) Sidenius Apollinaris
17.7) speaks of “per multiplices abaco
” These cavernae
were probably shelves under the abacus in which
ornaments were placed, some-what resembling cabinets in modern
drawing-rooms. Mensae Delphicae
appear to have
been a variety of abacus, but distinguished from it, as being round tables
with three legs, and taking their name from resemblance to the Delphic
tripod (Procop. B. Vand.
Ver. 4.59, 131
; Mart. 12.66
). The abacus or sideboard was used
also in temples and at the festivals of the gods, where offerings of food
were placed upon it, or sacred objects exposed to view
ii. p. 353;
Marquardt, [p. 1.2]Röm. Alterth.
p. 310; Tyrrell, Corresp. of Cicero,
ii. p. 239).
(3) A wooden tray, platter, or trencher, used for a variety of purposes in
domestic economy. It was, for instance, a name given to the mactra (μάκτρα
or trough for kneading dough (Cratin.
86, Meineke; Pollux, 6.86, 90, 10.105; Plin. Nat. 37.18
, ib. 21; Apul.
2.7; Hesych. sub voce
II. A board for playing a variety of games, either with dice or counters or
figures, called latrunculi,
and divided into
compartments like the abaci described below (Pollux, 10.150; Caryst. ap.
Ath. x. p. 435 d; joined with latrunculi,
). We may distinguish two kinds,
one more resembling a backgammon board [DUODECIM SCRIPTA
]; the other corresponding to the
chess or draught board [LATRUNCULI
]. The game of πεσσοὶ
being traditionally said to have been invented by Palamedes, we find the
board called τὸ Παλαμήδειον ἀβάκιον
(Eustath. in Od.
1.107). The abacus mentioned by Suetonius
was a kind of table, on which toy-chariots could be made to run ( “cum
eburneis quadrigis in abaco luderet,” Suet. Her.
III. A calculating table. This might be--
) A tablet with a frame or rim, covered with
sand, in which lines or figures could be drawn either with the finger or
some pointed instrument; and used in geometry, arithmetic, &c.
(Pers. 1.131; Apul. Apol.
100.16, p. 426; Sen.
74, 27; Plut. Cat. min.
70; eruditus pulvis,
Cic. N. D. 2.1. 8
, 48.) The
name Arenarius applied to the elementary teacher, qui
(Mart. Cap. vii. init.
), implies that this sort of abacus was used by
) A development of this simple form was the
abacus on which ψῆφοι,
pebbles or counters, were employed to
calculate with. It was a board marked off by ridges or grooves (along which
balls, counters, or buttons could be moved) into compartments, for the
several orders of numbers. We have examples of both Greek and Roman abaci:
of the former, one found by Rangabé at Salamis is figured here
(Rangabé, Letronne, and Vincent in Revue
année iii. p. 295 ff., p. 401
ff.). It is of marble, about 40 inches long by 28 broad. At a distance of 10
inches from one of the sides are
Greek Abacus or Calculating Table.
marked five parallel lines. At 20 inches' distance from the last
of these, eleven others are marked and bisected by a cross line, the point
of whose intersection with the third, sixth, and ninth lines is marked by a
star. Along three of the sides is arranged a series of characters in the
same order, and so as to be read with equal ease whichever way the abacus is
turned: the series on one side having two more characters than the others.
These characters ([drachma] being known as = drachma) give the following
scale, reckoned from the left of [drachma]:--
A short explanation of these characters, which are of great antiquity, will
facilitate the study of the numerous inscriptions in which public accounts
have been preserved. [drachm1] is a mutilated Ε,
initial of ἓν
[drachm5] an old form of Π
while of the three remaining
characters [drachm100] is for ΗΕΚΑΤΟΝ,
the old way of writing ἑκατόν,
[drachm50] is [drachm5] with [drachm10]
inscribed, [drachm500] [drachm5] with [drachm100]. The
characters on the right of [drachm1] are Ι
= obol, Ξ
= 1/2 obol,
= 1/4 obol, ZZZ = χαλκοῦς,
1/8 obol. The two additional characters
in the left-hand series are [drachm5000] = 5000 ([drachm5] with
[drachm1000] inscribed), and Τ
(of 6000 drachmas); so that the lowest and highest money units are at the
two ends of the scale. To understand the use of this abacus, the calculator
must be supposed sitting before one of its long sides, and putting counters
into the spaces between the marked lines. Each space represents an order of
numerals, the space on the right hand being intended for units, the next
space for tens, the next for hundreds, and so on. The numbers belonging to
the first four of each series are put on that side of the bisecting line
which is nearest the calculator; those over 5 are put beyond it. As five
spaces out of the ten would be enough for these purposes, it is conjectured
that after the progression of drachmas going up to 5000, a fresh progression
of talents began (Τ
= 6000 drachmas), going
up to the seventh place (1,000,000). Thus the Greek abacus, like the Roman,
which was no doubt derived from it, reckoned up to a million. The fractions
of the drachma were reckoned on the five lines at the other end of the slab.
It is to an abacus of this kind that Polybius refers, when he compares the
ups and downs of court favourites to the ψῆφοι
on an ἀβάκιον,
according to the line in which they are placed may signify either a talent
or a chalcus (Plb. 5.26.13
). This comparison
is elsewhere attributed to Solon (D. L. 1.59
The Roman abacus (figured here from the Kircherian Museum at Rome) was on the
Roman Abacus or Calculating Table.
system. It is divided into eight lower and eight higher (somewhat
shorter) groves: there is [p. 1.3]
also a ninth lower groove,
without an upper groove to correspond. Four sliding buttons are attached to
each lower groove except the eighth, which has five: each upper groove has
one button. Between the two sets of grooves the following numbers are
The units of any other number when not above 4 are marked by moving a
corresponding number of buttons along the lower groove upwards, the button
in the upper groove=5. The eighth row was used by reckoning fractions
) on the duodecimal system,
by ounces, or twelfth of the as,
and is accordingly
= uncia: each of its five lower buttons = 1 ounce, and the
upper one = 6. Fractions below an ounce were reckoned on the ninth groove,
||Z or 2
| 1/2 oz.
|| 1/2 oz.
|| 1/3 oz.
(Marquardt, vii. p. 97 seq.
ii. p. 100; Daremberg and Saglio,
s. v.) [LOGISTICA
IV. In architecture--
) A painted panel, coffer, or square
compartment in the wall or ceiling of a chamber. (Plin. Nat. 33.159
, 35. §
§ 3, 32; Vitr. 7.3.10
) The flat square tone which constituted the
highest member of a column, being placed immediately under the architrave
). The annexed figure is drawn from that in the British
Museum, which was taken from the Parthenon at Athens, and is a perfect
specimen of the capital of a Doric column. [COLUMNA
Abacus of a Column.