abacus

plural abaci · plural abacuses

1. historicalobsoleteA table or tray scattered with sand which was used for calculating or drawing.First known use attested from c. 1387

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   He [Gerebertus] was þe firste þat took abacus of Sarsyns, and ȝaf rules þerynne, þat mowe unneþe be understonde of þe kunnyngeste men of þe craft, þe whiche craftes men beþ cleped abaciste. Marianus. Abacus is a table wiþ þhe whiche schappes be portrayed and i-peynt in powdre, and abacus is a craft of geometrie.

   He [Gerebertus] was the first who took the abacus of the Saracens and gave rules for it, which can be barely understood by the most learned men of the craft, whose craftsmen are called abacists. Marianus. The abacus is a table with which shapes are portrayed and painted in powder, and abacus is [also] a branch of geometry.

   [a. 1387, Ranulphi Higden [i.e., Ranulf Higden], chapter X, in John Trevisa, transl., edited by Joseph Rawson Lumby, Polychronicon Ranulphi Higden Monachi Cestrensis; together with the English Translations of John Trevisa and of an Unknown Writer of the Fifteenth Century. […] (Rerum Britannicarum Medii Aevi Scriptores, or Chronicles and Memorials of Great Britain and Ireland during the Middle Ages), volume VII (in Middle English), London: Longman & Co., […]; Trübner & Co., […], published 1879, →OCLC, book VI, page 69

   [H]e set fondly and furiously to work upon [Thomas] Simpson's Euclid, [...] The smooth grassy sod answered all the purposes of the abacus, and the cows generously supplied him in a substitute for sand. Spreading and smoothing that substitute with his bear foot, he engraved upon it with his finger the mystic lines and letters; and, with book in hand, proceeded to establish the elementary principles of geometry, [...]

   1825, “a modern Greek” [pseudonym; Robert Mudie], “Education of the Athens”, in The Modern Athens: A Dissection and Demonstration of Men and Things in the Scotch Capital, 2nd edition, London: Printed for Knight and Lacey, […], →OCLC, page 269

2. A device used for performing arithmetical calculations; (rare) a table on which loose counters are placed, or (more commonly) an instrument with beads sliding on rods, or counters in grooves, with one row of beads or counters representing units, the next tens, etc.First known use late 17th c.

   I’ve heard merchants still use an abacus for adding things up in China.

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   Before leaving the question of early arithmetic I should mention that for practical purposes the almost universal use of the abacus or swan-pan rendered it easy to add or subtract, or even to multiply and divide, without any knowledge of theoretical mathematics. [...] [I]t will be sufficient here to say that they afford a concrete way of representing a number in the decimal scale, and enable the results of addition and subtraction to be obtained by a merely mechanical process.

   1888, Walter W[illiam] Rouse Ball, “Egyptian and Phœnecian Mathematics”, in A Short Account of the History of Mathematics, London; New York, N.Y.: Macmillan and Co., →OCLC, page 6

   The computer is but another vehicle to employ in helping people learn, a cousin of books, films, blackboards, chalk, gerbils, abacuses. Like each of these devices, it can be well used or misused.

   1974, Theodore R[yland] Sizer, “Foreword”, in Allan B. Ellis, The Use & Misuse of Computers in Education, New York, N.Y.: McGraw-Hill Book Company, →ISBN, page ix

   Take another look at the abacus to see how useful it is. Each row represents a successively higher counting group, or register, by 10 times. Thus, with only 6 rows you can count to one million (actually, up to 999,999, which is 1 short of one million).

   1999, Stan Gibilisco, Norman Crowhurst, “From Counting to Addition”, in Mastering Technical Mathematics, 2nd edition, New York, N.Y.: McGraw-Hill, →ISBN, part 1 (Arithmetic as an Outgrowth of Learning to Count), page 10

   Before Pythagoras it was necessary to see the thing before counting it, like children who learn on abacuses, with balls sliding along rods: children learn to add and subtract by sliding stones.

   2001, Augusto Boal, “The Impossible Return and the Strangeness of the Familiar”, in Adrian Jackson, Candida Blaker, transl., Hamlet and the Baker’s Son: My Life in Theatre and Politics, London; New York, N.Y.: Routledge, →ISBN, page 342

   Each rod in the bottom deck of an abacus has 5 beads. The value of each bead depends on which rod it is on. Each bead on the ones rod in the bottom deck equals 1. Each bead on the tens rod in the bottom deck equals 10. Each bead on the hundreds rod in the bottom deck equals 100.

   2004, Patricia J. Murphy, “The Bottom Deck”, in Counting with an Abacus: Learning the Place Values of Ones, Tens, and Hundreds, New York, N.Y.: The Rosen Publishing Group, →ISBN, page 8

3. architectureThe uppermost portion of the capital of a column immediately under the architrave, in some cases a flat oblong or square slab, in others more decorated.First known use mid 16th c.

   The shafts carry the usual cubical capitals—surmounted by plain heavy impost stones in place of moulded abaci—the one on the right being the better preserved.

   1942, Theodore Fyfe, Architecture in Cambridge: Examples of English Architectural Styles from Saxon to Modern Times, Cambridge, Cambridgeshire: At the University Press, →OCLC, page 49

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   The only mouldings uſed, both by the Saxon and Norman architects, were the torus, the ſcotia or reverſed torus, the cavetto or hollow moulding, and a kind of chamfered faſcia, which latter was generally uſed for impoſts or abacuſes to their capitals.

   1795 June 11, 18, 25, William Wilkins, “XIV. An Essay towards the History of the Venta Icenorum of the Romans, and of Norwich Castle; with Remarks on the Architecture of the Anglo-Saxons and Normans. [On the Architecture of NORWICH Castle.]”, in Archaeologia: Or, Miscellaneous Tracts Relating to Antiquity, volume XII, London: Published by the Society of Antiquaries of London; printed by J[ohn] Nichols, printer to the Society; […], published 1796, →OCLC, page 160

   At Amiens, the square form of the abaci, and the volutes of the capitals, afford a decisive proof that the Norman fashion had not yet been superseded. On the other hand, at Salisbury, the abaci are mostly round, and where foliage is used in the capitals, their graceful and luxurious design clearly shews an advancement in that department of the art.

   1829 June, “Cathedrals of Salisbury and Amiens Compared, by the Late Rev. G. D. Whittington, in the Sixth Chapter of His ‘Survey of the Ecclesiastical Antiquities of France.’ 1811.”, in The Crypt, or Receptacle for Things Past, and West of England Magazine, volume I, part I, number VI (New Series), Winchester, Hampshire: Published by Charles Henry Wheeler, […], →OCLC, page 245

   The stones of the cornice, hitherto called X and Y, receive, now that they form the capital, each a separate name; the sloping stone is called the Bell of the capital, and that laid above it, the Abacus. Abacus means a board or tile: I wish there were an English word for it, but I fear there is no substitution possible, the term having been long fixed, and the reader will find it convenient to familiarise himself with the Latin one.

   1851, John Ruskin, “The Capital”, in The Stones of Venice, volume I (The Foundations), London: Smith, Elder, and Co., […], →OCLC, § III, pages 102–103

   The dentil course of the pedimental cornice takes the form of a peculiar reeded H pattern which is repeated in much finer scale on the edge of the corona, the abacus of the capitals and its continuation across the lintel of the door.

   1920, Frank Cousins, Phil M. Riley, The Colonial Architecture of Philadelphia, Boston: Little, Brown, and Company

   The Hathor abaci above the Mammisi capitals were only decorated on the east flank. Perhaps the decoration of the abacus was not regarded as important as the capital and although it is above the capital, its decoration was executed only when time constraints did not prevail.

   1989, Eleni Vassilika, “The Work Methods of the Artisan at Philae”, in Ptolemaic Philae (Orientalia Lovaniensia Analecta; 34), Leuven, Belgium: Departement Oriëntalistiek, Uitgeverij Peeters, →ISBN, pages 187–188

4. Ancient RomehistoricalAncient GreeceA board, tray, or table, divided into perforated compartments for holding bottles, cups, or the like; a kind of buffet, cupboard, or sideboard.First known use late 18th c.

   ABACUS, among the ancients, was a kind of cupboard or buffet. Livy, deſcribing the luxury into which the Romans degenerated after the conqueſt of Aſia, ſays they had their abaci, beds, &c. plated over with gold.

   1817, “ABACUS”, in Encyclopaedia Britannica: Or, A Dictionary of Arts, Sciences, and Miscellaneous Literature, 5th enlarged and improved edition, volume I, Edinburgh: Printed at the Encyclopædia Press, for Archibald Constable and Company, […]; London: Gale and Fenner; York, Yorkshire: Thomas Wilson and Sons, →OCLC, page 4, column 1

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   The plate and nicknacks, always found in elegant Roman houses, were displayed on small one or three legged tables (trapezophoron), the slabs of which (abacus, a word which, like trapezophoron, is sometimes used for the whole table) had raised edges round them: several richly ornamented specimens of such tables have been found at Pompeii. Fig. 446 shows a small abacus resting on three marble legs, which has been found in the house of the "Little Mosaic-Fountain" at Pompeii.

   1875, E[rnst Karl] Guhl, W[ilhelm David] Koner, “The Romans”, in F[rancis] Hueffer, transl., The Life of the Greeks and Romans, Described from Antique Monuments: Translated from the Third German Edition, London: Chapman and Hall, […], →OCLC, § 89 (Tables.—Tripods), pages 446–447