ABACUS. —
1. In liturgy
From Gr. ἀβαξ = tablet, it is the small table which, according to the Caeremoniale Episcoporum, must be placed near the altar, on the side of the Epistle, away from the wall if possible, to hold what is needed for Mass, especially sung Mass: candlesticks, chalice, cruets, missal, basin with manutergium, etc. It must have no adornment, no steps, no cross, nor images, but shall be covered with a linen cloth reaching to the ground. In Requiem Masses and on Good Friday, it is without a cloth.2. In pedagogy
The abacus, in its most general definition, may be described as an instrument for calculating. At least this is the historical meaning of the word; for the modern bead-frame, though a customary teaching aid, is not the heir of the abacus in its original practical and commercial use, to which it was chiefly destined.In its most rudimentary and primitive form, the abacus was probably a type of writing tablet. A perfecting differentiation equipped it with grooves, in which pebbles (*calculi*) could be easily aligned, and later with rods (horizontal or vertical) for movable elements (beads, disks, counters) to slide along. These indicated units of different orders if in different rods, equal if in the same one. Often the unit value of the counters was inscribed on them, which further facilitated the use of the abacus. The very simple method allowed operations up to a million.
Though its origin is shrouded in obscurity, the abacus is known to us through its historical and geographical expansion, so that we can confidently affirm its existence and use in the ancient Chinese and Assyro-Babylonian civilizations, as well as—through richer documentation—among the Greeks and Romans. Famous among others is the Greek abacus known as the Salaminian abacus, and the Roman one from the former Kircherian museum. The Middle Ages saw a new flourishing in the use of the abacus, although the term tended to assume a richer and different meaning from the original. Thus Gerbert (Pope Sylvester II), in his *De numerorum divisione* (PL 139, 84-92), though asserting his intention to explain the *rationes numerorum abaci*, actually discusses a new and different method of computation. Likewise, Leonardo Fibonacci of Pisa’s *Liber abaci* (1202) deals with the introduction, value, etc., of Arabic numerals. In this way, progressively, both in scientific terminology and in common usage, the word *abacus* came to be almost identified with that of arithmetic, and was sometimes used as a synonym for the first classes of elementary school.
Indeed, *abacus* is also the name given to the small booklet of a few pages that teaches the first calculations; now generally replaced by books compiled with more modern methods, which also use intuitive drawings to better represent and impress numbering and operations.
**ABACUS** (Architecture): see **ORDINI ARCHITETTONICI**.