ABACUS. - 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 away from the wall if possible, on which to place what is needed for Mass, especially a sung Mass: candlesticks, chalice, cruets, missal, basin with the manuterge, etc. It must have no ornament, no steps, no cross, no images, but shall be covered with a linen cloth hanging down to the floor. At Requiem Masses, and in the service of Good Friday, it is without a cloth.
Bibliography
Enrico Dante
2. IN PEDAGOGY
The abacus, in the most general formula, can be defined as an instrument for calculating. At least this is the sense that may be called the historical one of the word; in fact the modern counting frame, although it constitutes a didactic aid in habitual practice, is not the heir of the abacus in useful and commercial use, for which the latter was principally intended in origin.
In its most rudimentary and primitive realization the abacus is probably a variety of writing tablets. A differentiation earned it the qualities of grooves, in which pebbles (calculi) could easily be aligned, and then of rods (horizontal or vertical), suited to the sliding of movable elements (balls, discs, counters). These indicated units of a different order if on different rods, equal if on the same one. Many times the unit value of the counters was engraved on the counters themselves, which further facilitated the use of the abacus. The very simple method allowed operations up to a million.
Even if wrapped in obscurity as to its origin, the abacus is known to us in its historical-geographical expansion, so that we can confidently affirm its existence and use in the ancient Chinese and Assyro-Babylonian civilizations, as well as, through a richer documentation, among the Greeks and Romans. Famous, among others, are the Greek abacus said to be of Salamis, and the Roman one of the former Kircherian museum. The Middle Ages marked a new flowering in the use of the abacus, although the word tends to assume a richer and different meaning than the original. Thus Gerbert (Pope Sylvester II), in his De numerorum divisione (PL 139, 84-92), while asserting that he wishes rationes numerorum abaci explicare, in reality discourses on a new and different method of computation. Thus also the Liber abaci (1202) of Leonardo Fibonacci plainly treats of the introduction, value, etc. of Arabic numerals. In this way there came about, progressively, both in scientific and in ordinary terminology, almost an identification of the word abacus with that of arithmetic, and at times it was even used as a synonym for the first classes of elementary school.
Abacus, in fact, is also the name of the small book of few pages that teaches how to do the first calculations; now generally replaced by books compiled with more modern methods, which also resort to intuitive drawings to better represent and impress numeration and operations.
Bibliography2 works
Felicissimo Tinivella
ABACUS (Architecture): v. ORDINI ARCHITETTONICI.