A Dictionary of Greek and Roman Antiquities/Abacus

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A Dictionary of Greek and Roman Antiquities  (1890) 
by Various Authors, edited by William Smith
Abacus

AB´ACUS (ἄβαξ), 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 Antiq. s. v.); or (2) abak, to raise or lift up, recently suggested in Wölfflin's Thesauri Latini specimen, 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 probable conjecture.

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 (R. R. 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, x. 69; Cic. Fam. vii. 2. 3, 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. Juv. iii. 203:

Urceoli sex,
Ornamentum abaci, nec non et parvulus infra Cantharus et recubans sub eodem marmore Chiron.

[Image missing. Caption: "Abacus or Sidebord. (From a sarcophagus in the British Museum.)"]

Here the Chiron was the trapezophoron; and similar ones representing sphinxes and griffins are found in museums. The use of abaci (mensae vasariae) in private houses was first introduced at Rome (according to Liv. xxxix. 6, 7; and Plin. H. N. xxxiv. § 14) from Asia Minor after the victories of Cn. Manlius Vulso, B.C. 187, and their introduction was regarded as one of the marks of the growing luxury of the age. (Varr. L. L. ix. § 46; Cic. Verr. iv. 1. 6, 35; Tusc. v. 21, 61; Juv. iii. 204; Plin. H. N. xxxvii. § 14; Petron. 73; Auson. Epigr. viii. 2.) Sidenius Apollinaris (Carm. xvii. 7) speaks of per multiplices abaco splendente cavernas. 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. i. 21; Cic. Verr. iv. 5. 9, 131; Mart. xii. 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 (Becker-Göll, Gallus, ii. p. 353; Marquardt, [p. 2] Röm. Alterth. vii. 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. Fragm. 86, Meineke; Pollux, vi. 86, 90, x. 105; Plin. H. N. xxxvii. § 18, ib. 21; Apul. Met. ii. 7; Hesych. s. v. μάκτρα).

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, x. 150; Caryst. ap. Ath. x. p. 435 d; joined with latrunculi, Macrob. Sat. i. 5, § 11). 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. i. 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. 22).

III. A calculating table. This might be—

(a) 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. i. 131; Apul. Apol. c. 16, p. 426; Sen. Ep. 74, 27; Plut. Cat. min. 70; eruditus pulvis, Cic. N. D. ii. 1. 8, 48.) The name Arenarius applied to the elementary teacher, qui calculare monstrabat (Mart. Cap. vii. init.), implies that this sort of abacus was used by school-children.

(b) A development of this simple form was the abacus on which ψη̂φοι, calculi, 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 Archéol. 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 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 ([drachm] being known as = drachma) give the following scale, reckoned from the left of [drachm]:—

[drachm1] [drachm5] [drachm10] [drachm50] [drachm100] [drachm500] [drachm1000]
1 5 10 50 100 500 1000

[Image missing. Caption: "Greek Abacus or Calculating Table."]

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 i. e. πέντε; [drachm10] obviously represents δέκα, and [drachm1000] χίλιολ: 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, Τ = 1/4 obol, ZZZ = χαλκου̂ς, 1/8 obol. The two additional characters in the left-hand series are [drachm5000] = 5000 ([drachm5] with [drachm1000] inscribed), and Τ = talent (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 ψη̂φοι on an ἀβάκιον, which according to the line in which they are placed may signify either a talent or a chalcus (Polyb. v. 26, § 13). This comparison is elsewhere attributed to Solon (Diog. Laërt. i. 59).

[Image missing. Caption: "Roman Abacus or Calculating Table."] The Roman abacus (figured here from the Kircherian Museum at Rome) was on the same system. It is divided into eight lower and eight higher (somewhat shorter) groves: there is [p. 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 marked:--

X ΞΞΞ|ↃↃↃ ΞΞ|ↃↃ Ξ|Ↄ Ξ Χ Ι
1,000,000 100,000 10,000 1,000 100 10 1

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 (aes recurrens) on the duodecimal system, by ounces, or twelfth of the as, and is accordingly marked Θ or Θ = uncia: each of its five lower buttons = 1 ounce, and the upper one = 6. Fractions below an ounce were reckoned on the ninth groove, marked:

S Z or 2
| \ \ \
semuncia. sicilicus. duella.
1/2 oz. 1/2 oz. 1/3 oz.

(Marquardt, vii. p. 97 seq.; Becker-Göll, Gallus, ii. p. 100; Daremberg and Saglio, s. v.) [Logistica]

IV. In architecture--

(a) A painted panel, coffer, or square compartment in the wall or ceiling of a chamber. (Plin. H. N. xxxiii. § 159, xxxv. § § 3, 32; Vitruv. vii. 3, § 10; Letronne, Peinture mur., p. 476.)

(b) The flat square tone which constituted the highest member of a column, being placed immediately under the architrave (Vitruv. iii. 5, § 5; iv. 1, § 11). 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] [A.G] [J.H.O]