GREEK AND ROMAN ANTIQUITIES.
AB'ACUS (ἄϐαξ) denoted generally and primarily a square tablet of any material. Hence we find it applied in the following special significations:—
I. In architecture it denoted the flat square stone, which constituted the highest member of a column, being placed immediately under the architrave. The annexed figure is drawn from the Parthenon at Athens, and is a perfect specimen of the capital of a Doric column.
In thee more ornamented orders of architecture, such as the Corinthian, the sides of the abacus were curved inwards, and a rose or some other decoration was frequently placed in the middle of each side; but the name Abacus was given to the stone thus diversified and enriched, as well as in its original form. (Vitruv. iii. 3; iv. 1. 7.)
Pliny, in his account of glass, says (H. N. xxxvi. 67), "It is artificially stained as in making the small times, which some persons call abaculi." Moschion says, that the magnificent ship built by Archimedes for Hiero, king of Syracuse, contained a pavement made of such tiles of various colours and materials. ((Greek characters). Apud Athen. v. 207.)
III. Abacus was also employed in Architecture to denote a panel, coffer, or square compartment in the wall or ceiling of a chamber. As panels are intended for variety and ornament, they were enriched with painting. (Plin. H. N. xxxiii. 56; xxxv. 13.) Pliny, in describing the progress of luxury with respect to the decoration of apartments, says, that the Romans were now no longer satisfied with panels (non placent jam abaci), and were beginning even to paint upon marble. (H. N. xxxv. 1.)
IV. Abacus further denoted a wooden tray, i. e. a square board surrounded by a raised border. This may have been the article intended by Cato, when in his enumeration of the things necessary in furnishing a farm (olivetum), he mentions "one abacus." (De Re Rust. 10.)
Such a tray would be useful for various purposes. (See Cratin. Frag. edit. Runkel, p. 27; Pollux, vi, 90; x. 105; Bekker, Anec. Gr. i. 27.) It might very well be used for making bread and confectionary; and hence the name of abacus ((Greek characters)) was given to the (Greek characters), i. e. the board or tray for kneading dought. (Hesych. sub (Greek characters): Schol. in Theoer. iv. 61.)
V. A tray of the same description, covered with sand or dust, was used by mathematicians for drawing diagrams, (Eustath. in Od. i. 107. p. 1397.)
VI. It is evident that this contrivance would be no less serviceable to the arithmetician: and to this application of it Persins (Sat. i. 131) alludes, when he censures the man who ridiculed "the numbers on the abacus and partitions in its divided dust." Abaco numeros, et secto in pulxere metas. In this instance the poet seems to have supposed perpendicular lines or channels to have been drawn in the sand upon the board; and the instrument might thus in the simplest and easiest manner be adapted for arithmetical computation.
It appears that the same purpose was answered by having a similar tray with perpendicular wooden divisions, the space on the right hand being intended for units, the next space for tens, the next for hundreds, and so on. Thus was constructed the (Greek characters), "the abacus on which they calculate," i. e. reckon by the use of stones (ψήφοι, calculi). (Eustath. in Od. iv. 249. p. 1494.) The figure following is designed to represent the probable form and appearance of such an abacus.
The reader will observe, that stone after stone might be put into the right-hand partition until they amounted to 10, when it would be necessary to take them all out as represented in the figure, and instead of them to put one stone into the next partition. The stones in this division might in like manner amount to 10, thus representing 10 × 10 = 100, when it would be necessary to take out the 10, and instead of them to put one stone into the third partition, and so on.