Abăcus
(Gr. ἄβαξ, ἀβάκιον).
1.
A square plate, especially the stone slab that covers the capital of a column.
2.
A dice-board. See Duodecim Scripta; Latrunculi.
3.
A mathematician's table strewn with fine sand, on which figures were drawn with a stilus.
4.
A counting-board, on which sums were worked for private and public accounts. This might be:- A tablet with a frame or rim, covered with sand, in which lines or figures could be drawn either with the finger or some pointed instrument; and used in geometry, arithmetic, etc. (Pers. i.131; eruditus pulvis, Cic. N. D. ii. 18, 48). The name arenarius, applied to the elementary teacher, implies that this sort of abacus was used by school-children.
- A development of this simple form was the abacus on which ψῆφοι, calculi, pebbles or counters, were employed in
calculations. It was a board marked off by ridges or grooves (along which balls, counters,
or buttons could be moved) into compartments, for the several orders of numbers. We have
examples of both Greek and Roman abaci. The Greek abacus figured here is from Salamis, and
is of marble, about forty inches long by twentyeight broad. At a distance of ten inches
from one of the sides are marked five parallel lines. At twenty inches' distance from the
last of these, eleven others are marked and bisected by a cross
line, the point of whose intersection with the third, sixth, and ninth lines is marked by a star. Along three of the sides is arranged a series of characters in the same order, and so as to be read with equal ease whichever way the abacus is turned: the series on one side having two more characters than the others. These characters ( being known as = drachma) gives the following scale, reckoned from the left of :Greek Abacus, or Calculating Table.
These characters are of great antiquity. is a mutilated , initial of ἓν; an old form of , i. e. πέντε; Δ obviously represents δέκα, and χίλιοι; while of the three remaining characters, is for , the old way of writing ἑκατόν, is with Δ inscribed, with The characters on the right of are =obol, =1/2 obol, =1/4 obol, =χαλκοῦς, 1/8 obol. The two additional characters in the left-hand series are =5000 ( with inscribed), and =talent (of 6000 drachmas); so that the lowest and highest money units are at the two ends of the scale.
To understand the use of this abacus, the calculator must be supposed sitting before one of its long sides, and putting counters into the spaces between the marked lines. Each space represents an order of numerals, the space on the right hand being intended for units, the next space for tens, the next for hundreds, and so on. The numbers belonging to the first four of each series are put on that side of the bisecting line which is nearest the calculator; those over five are put beyond it. As five spaces out of the ten would be enough for these purposes, it is conjectured that after the progression of drachmas going up to 5000, a fresh progression of talents began (=6000 drachmas), going up to the seventh place (1,000,000). Thus the Greek abacus, like the Roman, which was no doubt derived from it, reckoned up to a million. The fractions of the drachma were reckoned on the five lines at the other end of the slab. It is to an abacus of this kind that Polybius refers, when he compares the ups and downs of court favorites to the ψῆφοι on an ἀβάκιον, which, according to the line in which they are placed, may signify either a talent or a chalcus (Polyb. v. 26.13). This comparison is elsewhere attributed to Solon (Diog. Laert. i. 59).
The Roman abacus (figured here from the Kircherian Museum at Rome) was on the same system.
 |
| Roman Abacus, or Calculating Table. |
The units of any other number when not above 4 are marked by moving a corresponding number of buttons along the lower groove upwards, the button in the upper groove=5. The eighth row was used by reckoning fractions (aes recurrens) on the duodecimal system, by ounces, or twelfth of the as, and is accordingly marked or = uncia: each of its five lower buttons=1 ounce, and the upper one=6. Fractions below an ounce were reckoned on the ninth groove, marked:
See the article Logistica.
5.
The name is also used of a wooden tray or platter employed in domestic economy. Cf. Plin. H. N. xxxvii. 18 and 21; Ov. Met. ii. 7.
6.
A sideboard for vessels, and for offerings to the gods (Boetticher, Tektonik der Hellenen, iii. p. 46). |
| Abacus, sideboard. (Relief in British Museum.) |