among the ancients, was a kind of cupboard or buffet. Livy, describing the luxury into which the Romans degenerated after the conquest of Asia, says, They had their abaci, beds, &c. plated over with gold.

among the ancient mathematicians, signified a table covered with dust, on which they drew their diagrams; the word in this sense being derived from the Phoenician abak, dust.

in architecture, signifies the superior part or member of the capital of a column, and serves as a kind of crowning to both. Vitruvius tells us the abacus was originally intended to represent a square tile laid over an urn, or rather over a basket. See Architecture, no. 15.—The form of the abacus is not the same in all orders: in the Tuscan, Doric, and Ionic, it is generally square; but in the Corinthian and Composite, its four sides are arched inwards, and embellished in the middle with some ornament, as a rose or other flower. Scamozzi uses abacus for a concave moulding on the capital of the Tuscan pediment; and Palladio calls the plinth above the echinus, or boulton, in the Tuscan and Doric orders, by the same name.

ABACUS is also the name of an ancient instrument for facilitating operations in arithmetic. It is variously contrived. That chiefly used in Europe is made by drawing any number of parallel lines at the distance of two diameters of one of the counters used in the calculation. A counter placed on the lowest line signifies 1; on the second, 10; on the third, 100; on the fourth, 1000, &c. In the intermediate spaces, the same counters are estimated at one half of the value of the line immediately superior, viz. between the first and second, 5; between the second and third, 50; &c. See the figure on Plate I., where the same number, 1788 for example, is represented under both divisions by different dispositions of the counters.

ABACUS is also used by modern writers for a table of numbers ready cast up, to expedite the operations of arithmetic. In this sense we have Abaci of addition, of multiplication, of division.

Chinese Abacus. See SWANPAN.

ABACUS Pythagoricus, the common multiplication-table, so called from its being invented by Pythagoras.

ABACUS Logificus is a rectangular triangle, whose sides, forming the right angle, contain the numbers from 1 to 60; and its area, the facts of each two of the numbers perpendicularly opposite. This is also called a canon of sexagesimals.

ABACUS & Palmule, in the ancient music, denote the machinery, whereby the strings of Polyplectra, or instrumets of many strings, were struck with a plectrum made of quills.

ABACUS Harmonicus, is used by Kircher for the structure and disposition of the keys of a musical instrument, whether to be touched with the hands or the feet.