ABACO. -
1. IN THE LITURGY
From the Greek ἄβαξ = tablet, it is the small table which, according to the Caeremoniale Episcoporum, must be placed near the altar, on the Epistle side, set apart, if possible, from the wall, for placing upon it what is needed for Mass, especially sung Mass: candlesticks, chalice, cruets, missal, basin with lavabo towel, etc. It must have no ornament, steps, cross, or images, but is to be covered with a linen cloth hanging down to the floor. At Requiem Masses and during the Good Friday service, it is without a cloth.2. IN PEDAGOGY
The a., in the most general formulation, may be defined as an instrument for calculation. At least, this is so in the meaning that may be called historical for the term; in fact, although the modern abacus constitutes a didactic aid in customary practical use, it is not the heir of the a. in the useful and commercial use for which the latter was originally intended above all.In its most rudimentary and primitive form, the a. was probably a variety of writing tablet. A subsequent differentiation provided it with grooves, in which small stones (calculi) could easily be aligned, and then with rods (horizontal or vertical), along which movable elements (balls, disks, counters) could slide. These indicated units of different orders when placed on different rods, and equal units when placed on the same rod. Often the unit value of the counters was engraved on them, which further facilitated the use of the a. This very simple method allowed operations up to one million.
Although its origin is shrouded in obscurity, the a. is known to us in its historical and geographical expansion, so that its existence and use can be confidently affirmed in the ancient Chinese and Assyro-Babylonian civilizations, as well as, through richer documentation, among the Greeks and Romans. Famous, among others, are the Greek a. known as that of Salamis, and the Roman one from the former Kircherian Museum. The Middle Ages marked a new flowering in the use of the a., 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), while asserting that he wished rationes numerorum abaci explicare, in reality 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 ordinary usage, the word a. came almost to be identified with arithmetic, and at times it was also used as a synonym for the first classes of elementary school.
A., in fact, is also the name given to the small book of a few pages that teaches how to perform the first calculations; it has now generally been replaced by books compiled according to more modern methods, which also make use of illustrative drawings in order better to represent and impress upon the mind numeration and operations.
ABACO (Architecture): V. ORDINI ARCHITETTONICI.