See also:

• ABACUS (Gr. 15t(34, a slab; Fr. abaque, tailloir)

ABACUS (Gr. 15t(34, a slab; Fr. abaque, tailloir)  , in See also:

• ARCHITECTURE (Lat. architectura, from the Gr. ap)(LTEKrwv, a master-builder)

architecture, the upper member of the See also:

• CAPITAL (i.e. capital stock or fund)
• CAPITAL (Lat. caput, head)

capital of a See also:

• COLUMN (Lat. columna)

column . Its See also:

• CHIEF (from Fr. chef, head, Lat. caput)

chief See also:

• FUNCTION

function is to provide a larger supporting See also:

• SURFACE

surface for the See also:

• ARCHITRAVE (from Lat. arcus, an arch, and trabs, trabem, a beam)

architrave or See also:

• ARCH
• ARCH, JOSEPH (1826– )

arch it has to carry . In the See also:

• GREEK
• GREEK, ETRUSCAN AND

Greek Doric See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

order the See also:

• ABACUS (Gr. 15t(34, a slab; Fr. abaque, tailloir)

abacus is a See also:

• PLAIN (O. Fr. plain, from Lat. plenum)

plain square slab . In the See also:

• ROMAN

Roman and See also:

• RENAISSANCE, THE

Renaissance Doric orders it is crowned by a moulding . In the Archaic-Greek Ionic order, owing to the greater width of the capital, the abacus is rectangular in See also:

• PLAN
• PLAN (from Lat. planes, flat)

plan, and consists of a carved See also:

• OVOLO (adapted from Ital. uovolo, diminutive of uovo, an egg; other foreign equivalents are Fr. ore, echine, quart de rond; Lat. echinus)

ovolo moulding . In later examples the abacus is square, except where there are See also:

• ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle volutes, when it is slightly curved over the same, In the Roman and Renaissance Ionic capital, the abacus is square with a See also:

• FILLET (through Fr. filet, from the med. Lat. filettum, diminutive of filum, a thread)

fillet, on the See also:

• TOP (cf. Dan. top, Ger. Topf, also meaning pot)

top of an See also:

• OGEE (probably an English corruption of Fr. ogive, a diagonal groin rib, being a moulding commonly employed; equivalents in other languages are Lat. cyma-reversa, Ital. gola, Fr. cymaise, Ger. Kehlleisten)

ogee moulding, but curved over angle volutes . In the Greek Corinthian order the abacus is moulded, its sides are See also:

• CONCAVE

concave and its angles canted (except in one or two exceptional Greek capitals, where it is brought to a See also:

• SHARP, GRANVILLE (1735-1813)
• SHARP, JAMES (1618-1679)
• SHARP, JOHN (1645-1714)
• SHARP, RICHARD (1759-1835)
• SHARP, WILLIAM (1749-1824)
• SHARP, WILLIAM (1856-1905)

sharp angle); and the same shape is adopted in the Roman and Renaissance Coring thian and Composite capitals, in some cases with the ovolo moulding carved . In Romanesque architecture the abacus is square with the See also:

• LOWER

lower edge splayed off and moulded or carved, and the same was retained in See also:

• FRANCE
• FRANCE, ANATOLE (1844– )

France during the See also:

• MEDIEVAL

medieval See also:

• PERIOD
• PERIOD (Gr. irepioSos, a going or way round, circuit, aepi, round, and &Sis, way, road)

period; but in See also:

• ENGLAND
• ENGLAND, THE CHURCH OF

England, in See also:

• EARLY
• EARLY, JUBAL ANDERSON (1816-1894)

Early See also:

• ENGLISH

English See also:

• WORK

work, a circular deeply moulded abacus was introduced, which in the 14th and 15th centuries was transformed into an octagonal one . The diminutive of Abacus, ABACISCUS, is applied in architecture to the chequers or squares of a See also:

• TESSELLATED (Lat. tessellatus,)

tessellated See also:

• PAVEMENT (Lat. pavimentu;n, a floor beaten or rammed hard, from pavire, to beat)

pavement . " Abacus " is also the name of an See also:

• INSTRUMENT (Lat. instrumentum, from insincere, to build up, furnish, arrange, prepare)

instrument employed by the ancients for arithmetical calculations; pebbles, bits of See also:

• BONE (a word common in various forms to Teutonic languages, in many of which it is confined to the shank of the leg, as in the German Bein)
• BONE, HENRY (1755-1834)

bone or coins being used as counters . Fig . 1 shows a Roman abacus taken from an See also:

• ANCIENT
• ANCIENT (also spelt ANTIENT; derived, through the Fr. ancien, old, from the late Lat. antianum, from ante, before)

ancient See also:

• MONUMENT (Lat. monumentum or monumentum; from monere, to advise, bring to mind, remind; the German equivalent is Denkmal)

monument .

It contains seven See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long and seven shorter rods or bars, the former having four perforated beads See also:

• RUNNING

running on them and the latter one . The See also:

• BAR
• BAR (0. Fr. barre, Late Lat. barra, origin unknown)
• BAR, CONFEDERATION OF
• BAR, FRANCOIS DE (1538-1606)
• BAR, THE

bar marked I indicates See also:

• UNITS, DIMENSIONS OF
• UNITS, PHYSICAL

units, X tens, and so on up to millions . The beads on the shorter bars denote See also:

• FIVES

fives,—five units, five tens, &c . The See also:

• ROD (O.E. rodd, probably related to Norw. rudda, stick, rodda, stake)
• ROD, EDOUARD (1857-1910)

rod 0 and corresponding See also:

• SHORT, FRANCIS JOB (1857– )

short rod are for marking ounces ; and the short See also:

• QUARTER (through Fr. from Lat. quartarius, fourth part)

quarter rods for fractions of an See also:

• OUNCE

ounce . The See also:

• SWAN (A. S. swan and swan, Icel. svanr, Du. zwaart, Ger. Schwan)
• SWAN, J
• SWAN, JOHN MACALLAN (1847-1910)
• SWAN, SIR JOSEPH WILSON (1828– )

Swan-See also:

• PAN (" pasturer ")
• PAN (common in various forms to many Teutonic languages, cf. Ger. Pfanne; it is generally taken to be an early adaptation in a shortened form of Lat. patina, shallow bowl or dish, from patere, to lie open)

Pan of the See also:

• CHINESE, JAPANESE AND

Chinese (fig . 2) closely resembles the Roman abacus in its construction and use . Computations are made with it by means of balls of bone or See also:

• IVORY (Fr. ivoire, Lat. ebur)
• IVORY, SIR JAMES (1765-1842)

ivory running on slender See also:

• BAMBOO

bamboo rods, similar to the simpler See also:

• BOARD (O. Eng. bord)

board, fitted up with beads strung on wires; which is employed in teaching the rudiments of See also:

• ARITHMETIC (Gr. apeOµ7run7, sc. TEXVn, the art of counting, from (ipLBµos, number)

arithmetic in English See also:

• SCHOOLS

schools . The name of " abacus " is also given, in See also:

• LOGIC (Xoy1K7, sc. rixvrt, the art of reasoning)

logic, to an instrument, often called the " logical See also:

• MACHINE
• MACHINE (through Fr. from Lat. form machina of Gr. µnxavil)

machine," analogous to the mathematical abacus . It is constructed to show all the possible combinations of a set of logical terms with their negatives, and, further, the way in which these combinations are affected by the addition of attributes or other limiting words, i.e. to simplify mechanically the See also:

• SOLUTION (from Lat. solvere, to loosen, dissolve)

solution of logical problems . These See also:

• INSTRUMENTS

instruments are all more or less elaborate developments of the " logical See also:

• SLATE (properly CLAY SLATE; in M. Eng. slat or sclat, from O. Fr. esclat, a small piece of wood used as a tile; esclater, to break into pieces, whence modern Fr. eclat, the root being seen also in Ger. schleissen, to split)

slate," on which were written in See also:

• VERTICAL (from Lat. vertex, highest point)

vertical columns all the combinations of symbols or letters which could be made logically out of a definite number of terms . These were compared with any given premises, and those which were incompatible were crossed off . In the abacus the combinations are inscribed each on a single slip of See also:

• WOOD, ANTHONY A2 (1632-1695)
• WOOD, JOHN GEORGE (1827—1889)
• WOOD, MRS HENRY [ELLEN] (1814—1887)
• WOOD, SEARLES VALENTINE (1798—188o)

wood or similar substance, which is moved by a See also:

• KEY
• KEY (in O. Eng. tang; the ultimate origin of the word is unknown; it appears only in Old Frisian kei of other Teutonic languages; until the end of the 17th century the pronunciation was kay, as in other words in O. Eng. ending in aeg; cf. daeg, day; clang
• KEY (the phraseograms being indicated by hyphens)
• KEY, SIR ASTLEY COOPER (1821-1888)
• KEY, THOMAS HEWITT (1799-1875)

key; incompatible combinations can thus be mechanically removed at will, in accordance with any given See also:

• SERIES (a Latin word from serere, to join)

series of premises .

The See also:

• PRINCIPAL

principal examples of such See also:

• MACHINES

machines are those of W . S . See also:

• JEVONS, WILLIAM STANLEY (1835-1882)

Jevons (See also:

• ELEMENT (Lat. elementum)

Element . Lessons in Logic, c. See also:

• XXIII

xxiii.), See also:

• JOHN
• JOHN (1167–1216)
• JOHN (1290-c. 1320)
• JOHN (1296-1346)
• JOHN (1371–1419)
• JOHN (1468-1532)
• JOHN (1801-1873)
• JOHN (Heb. llni')
• JOHN (ZAPOLYA) (1487-1540)
• JOHN, 4TH MARQUESS OF TWEEDDALE (c. 1695-1762)
• JOHN, DON (1545-1578)
• JOHN, DON (1629–1679)
• JOHN, GOSPEL OF ST
• JOHN, or HAYS (1513–1571)
• JOHN, THE APOSTLE
• JOHN, THE EPISTLES OF

John See also:

• VENN, HENRY (1725–1797)

Venn (see his Symbolic Logic, 2nd ed., 1894, p . 135), and See also:

• ALLAN, DAVID (1744–1796)
• ALLAN, SIR HUGH (1810–1882)
• ALLAN, SIR WILLIAM (1782–1850)

Allan See also:

• MARQUAND, HENRY GURDON (1819-1902)

Marquand (see See also:

• AMERICAN

American See also:

• ACADEMY, GREEK
• ACADEMY, ROYAL

Academy of Arts and Sciences, 1885, pp . 303-7, and Johns See also:

• HOPKINS, EDWARD WASHBURN (1857— )
• HOPKINS, ESEK (1718-18oz)
• HOPKINS, MARK (1802—1887)
• HOPKINS, SAMUEL (1721–1803)
• HOPKINS, WILLIAM (1793–1866)

Hopkins University Studies in Logic, 1883) .