Hutton, Charles A Mathematical and Philosphical Dictionary

 ABACUS
ABACUS

, in Arithmetic, an ancient instrument used by most nations for casting up accounts, or performing arithmetical calculations: it is by some derived from the Greek a<*>ac, which signifies a cupboard or beaufet, perhaps from the similarity of the form of this instrument; and by others it is derived from the Phœnician abak, which signifies dust or powder, because it was said that this instrument was sometimes made of a square board or tablet, which was powdered over with fine sand or dust, in which were traced the figures or characters used in making calculations, which could thence be easily defaced, and the abacus refitted for use. But Lucas Paciolus, in the sirst part of his second distinction, thinks it is a corruption of Arabicus, by which he meant their Algorism, or the method of numeral computation received from them.

We find this instrument for computation in use, under some variations, with most nations, as the Greeks, Romans, Germans, French, Chinese, &c.

The Grecian abacus was an oblong frame, over which were stretched several brass wires, strung with little ivory balls, like the beads of a necklace; by the various arrangements of which all kinds of computa- tions were easily made. Mahudel, in Hist. Acad. R. Inscr. t. 3. p. 390.

The Roman Abacus was a little varied from the Grecian, having pins sliding in grooves, instead of strings or wires and beads. Philos. Trans. No. 180.

The Chinese Abacus, or Shwan-pan, like the Grecian, consists of several series of beads strung on brass wires, stretched from the top to the bottom of the instrument, and divided in the middle by a cross piece from side to side. In the upper space every string has two beads, which are each counted for 5; and in the lower space every string has five beads, of different values, the first being counted as 1, the second as 10, the third as 100, and so on, as with us. See SHWANPAN.

The Abacus chiefly used in European countries, is nearly upon the same principles, though the use of it is here more limited, because of the arbitrary and unequal divisions of money, weights, and measures, which, in China, are all divided in a tenfold proportion, like our scale of common numbers. This is made by drawing any number of parallel lines, like paper ruled for music, at such a distance as may be at least equal to twice the diameter of a calculus, or counter. Then the value of these lines, and of the spaces between them, increases, from the lowest to the highest, in a tenfold proportion. Thus, counters placed upon the first line, signify so many units or ones; on the second line 10's, on the third line 100's, on the fourth line 1000's, and so on: in like manner a counter placed in the first space, between the first and second line, denotes 5, in the second space 50, in the third space 500, in the fourth space 5000, and so on. So that there are never more than four counters placed on any line, nor more than one placed in any space, this being of the same value as five counters on the next line below. So the counters on the Abacus, in the figure here below, express the number or sum 47382.

Besides the above instruments of computation, there have been several others invented by different persons; as Napier's rods or bones, deseribed in his Rabdologia, which see under the word Napier; also the Abacus Rhabdologicus, a variation of Napier's, which is described in the first vol. of Machines et Inventions approuvées par l'Academie Royale des Sciences. An ingenious and general one was also invented by Mr. Gamaliel Smethurst, and is described in the Philosophical Transactions, vol. 46; where the inventor remarks that computations by it are much quicker and easier than by the pen, are less burthensome to the memory, and can be performed by blind persons, or in the dark as well as in the light. A very comprehensive instrument of this kind was also contrived by the late learned Dr. Nicholas Saunderson, by which he performed very intricate calculations: an account of it is prefixed to the first volume of his Algebra, and it is there by the editor called Palpable Arithmetic: which see.

Abacus

, Pythagorean, so denominated from its inventor, Pythagoras; a table of numbers, contrived for readily learning the principles of arithmetic; and was probably what we now call the multiplication-table.

Abacus

, or Abaciscus, in Architecture, the upper part or member of the capital of a column; serving as a crowning both to the capital and to the whole column. Vitruvius informs us that the Abacus was originally intended to represent a square flat tile laid over an urn, or a basket; and the invention is ascribed to Calimachus, an ingenious statuary of Athens, who, it is said, adopted it on observing a small basket, covered with a tile, over the root of an Acanthus plant, which grew on the grave of a young lady; the plant shooting up, encompassed the basket all around, till meeting with the tile, it curled back in the form of scrolls: Calimachus passing by, took the hint, and immediately executed a capital on this plan; representing the tile by the Abacus, the leaves of the acanthus by the volutes or scrolls, and the basket by the vase or body of the capital. See Acanthus.

Abacus is also used by Scamozzi for a concave moulding in the capital of the Tuscan pedestal. And the word is used by Palladio for other members which he describes. Also, in the ancient architecture, the same term is used to denote certain compartments in the incrustation or lining of the walls of state-rooms, mosaicpavements, and the like. There were Abaci of marble, porphyry, jasper, alabaster, and even glass; variously shaped, as square, triangular, and such-like.

Abacus Logisticus is a right angled triangle, whose sides, about the right angle, contain all the numbers from 1 to 60; and its area the products of each two of the opposite numbers. This is also called a canon of sexagesimals, and is no other than a multiplication-table carried to 60 both ways.

Abacus & Palmulæ, in the Ancient Music, denote the machinery by which the strings of the polyplectra, or instruments of many strings, were struck, with a plectrum made of quills.

Abacus Harmonicus is used by Kircher for the structure and disposition of the keys of a musical instrument, either to be touched with the hands or feet.

Abacus, in Geometry

, a table or slate upon which schemes or diagrams are drawn.