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 p1  Abacus

Article by James Yates, M.A., F.R.S.,
on pp1‑2 of

William Smith, D.C.L., LL.D.:
A Dictionary of Greek and Roman Antiquities, John Murray, London, 1875.

AB′ACUS (ἄβαξ) denoted primarily a square tablet of any material; and was hence applied in the following significations:—

  1. In Architecture it denoted the flat square stone, which constituted the highest member of a column, being placed immediately under the architrave. The annexed figure is drawn from that in the British Museum, which was taken from the Parthenon at Athens, and is a perfect specimen of the capital of a Doric column.

[image ALT: An engraving of a square slab of stone on the Tuscan capital of a column. It is a representation of the architectural element known as an 'abacus'.]

    In the more ornamented orders of architecture, such as the Corinthian, the sides of the abacus were curved downwards, and a rose or some other decoration was frequently placed in the middle of each side; but the name Abacus was given to the stone thus diversified and enriched, as well as in its original form (Vitruv. III.3, IV.1 §7).

  2. A painted panel, coffer, or square compartment in the wall or ceiling of a chamber (Plin. H. N. XXXIII.56, XXXV.1, 13; Vitruv. VII.3 §10; Letronne, Peintur. mur. p476).

  3. A wooden tray, used for a variety of purposes in domestic economy. It was, for instance, the name given to the mactra (μάκτρα), or tray for kneading dough (Cratin. Frag. p27, ed. Runkel; Pollux, VI.90, X.105; Cato, R. R. 10; Hesych. s.v. μάκτρα; Schol. in Theocr. IV.61).

  4. A board, covered with sand or dust, used by mathematicians for drawing diagrams (Eustath. in Od. I.107), and by arithmeticians for the purposes of calculation (Pers. Sat. I.131). For the latter purpose perpendicular lines or channels seem to have been drawn in the sand upon the board; but sometimes the board had perpendicular wooden divisions,​a the space on the right hand being intended for units, the next space for tens, the next for hundreds, and so on. Thus was constructed the ἀβάκιον, ἐφ’ οὗ ψηφίζουσιν, "the abacus on which they calculate," i.e. reckon by the use of stones (ψήφοι, calculi). (Cf. Pol. V.26). The figure following represents the probable form and appearance of such an abacus. The reader will observe, that stone after stone might be put into the right-hand partition until they amounted to 10, when it would be necessary to take them all out as represented in the figure, and instead of them to put one stone into the next partition. The stones in this division might in like manner amount to 10, thus representing 10 × 10 = 100, when it would be necessary to take out the 10, and instead of them to put one stone into the third partition, and so on. On this principle the stones in the abacus, as delineated in the figure, would be equivalent to 359,310.​b

[image ALT: An engraving of something like a backgammon board. It is a Graeco-Roman gameboard of the type called 'abacus'.]
  5. A board adapted for playing with dice or counters, resembling a draught-board or backgammon-board (Caryst. ap. Ath. X p435 D; Suet. Ner. 22; Macrob. Sat. I.5). The Greeks had a tradition ascribing this contrivance to Palamedes, hence they called it "the abacus of Palamedes" (Τὸ Παλαμήδειον ἀβάκιον, Eustath. in Od. I.107). [Latrunculi].

  6. A table or sideboard, chiefly used for the display (exponere) of gold and silver cups. The tops of such tables were sometimes made of silver, but more usually of marble,​c and appear in some cases to have had numerous cells or partitions beneath, in which the plate was likewise placed. The use of abaci was first introduced at Rome from Asia Minor after the victories of Cn. Manlius Vulso, B.C. 187, and their introduction was regarded as one of the marks of the growing luxury of the age  p2 (Cic. Verr. IV.16, Tusc. V.21; Liv. XXXIX.6; Plin. H. N. XXXVII.6; Petron. 73; Sid. Apoll. XVII.7, 8). These abaci are sometimes called mensae Delphicae (Cic. Verr. IV.59; Mart. XII.67; Becker, Gallus, vol. 1 p140).

  7. A part of the theatre on or near the stage.

  8. The diminutive Abaculus (ἀβακίσκος) denoted a tile of marble, glass, or any other substance used for making ornamental pavements. They were of various colours (Plin. H. N. XXXVI.67;​d Moschion, ap. Ath. V.207D).

Thayer's Notes:

a The Graeco-Roman abacus was what we now call a counting-board. The device is pretty inconvenient and not really portable; as far as we know, it never occurred to the ancients to attach the calculi to rods rather than let them slide around loose in grooves or channels, and it was in medieval China that this improved design led to what we think of today as an abacus, for which see among many others this interesting page.

b The article sidesteps the nitty-gritty of just how the operations of addition, subtraction, multiplication, division were performed on the abacus.

The gentle reader may be surprised to note that we don't absolutely know, even though the various modern types of abacus, most of them Asian, give us an idea; but no surviving ancient writer explains the procedure and very few Roman abaci have come down to us, so that their specific use is a matter of some uncertainty, and, as usual, the whole subject is far more complicated than one might expect. This section of J. Hilton Turner's "Roman Elementary Mathematics" (Classical Journal, Vol. 47, 1951) will be helpful to the advanced student.

c If you're like me, you've been wondering how the word abacus came to have so many meanings, not all of which appear to be related, even if our author contends that the connection is simple, all the items the word denotes being square. But how do you get from a sand-box or a plaster panel to a sideboard?

Vitruvius (VII.3.10) may give us the key. Speaking of how you must beat plaster very thoroughly with wooden mallets to make it hard, he goes on to say that some people took to salvaging the painted plaster panels from old houses and reusing them as table tops, or even mirrors! The sheen of very smooth beaten plaster, painted a dark color, would be reflective: and in fact, in VII.4.4 Vitruvius mentions polished black panels (abaci), and early Spanish explorers found the technique, or something very like it, in use among the native peoples of what is now the southwestern United States (Bolton, The Spanish Borderlands, p196). Marble, mind you, and silver, if you could afford it — and the slaves to keep it polished constantly — would be even shinier.

Now this reflective quality is exactly what you want in a sideboard to display beautiful dishes and bowls. By their nature, especially before glazed porcelain was known in Europe, they would be undecorated on the very visible inside; the outer surfaces would be the more attractive, but you can't see them well without a mirror. Even today, china hutches often have mirrors and lights.

d Neither abacus nor abaculus appear in that section. Pliny very tangentially refers to the little cubes used in mosaic, today as in Roman times normally called tesserae. He is discussing his main point, the versatility of glass and the variety of colors it affords, and in passing says this:

neque est alia nunc sequacior materia aut etiam picturae accommodatior.

(The Loeb translator renders this "There is no other material nowadays that is more pliable or more adaptable, even to painting". I know of no ancient painting that employed glass — powdered?? — and I think pictura here does in fact mean mosaic, often referred to in Antiquity as pictura de musivo. I'm siding with our dictionary.)

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