FEAST OF See also:

• FEAST OF TABERNACLES

TABERNACLES  , the autumn festival of the Israelites, beginning on the 15th of Tishri and celebrated by residing for the seven succeeding days in rustic booths (Heb . Sukkoth, in the See also:

• VULGATE (from Lat. vulgus, the common people)

Vulgate Tabernacula, whence the See also:

• ENGLISH

English name of the feast) . Among the See also:

• HEBREWS, EPISTLE TO THE

Hebrews it was the third and See also:

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

chief of the three See also:

• ANNUAL

annual See also:

• PILGRIMAGE (Fr. pelerinage, Lat. peregrinatio)

pilgrimage festivals connected respectively with the harvesting ofthebarley (See also:

• PASSOVER

Passover), of See also:

• WHEAT
• WHEAT (Triticum)

wheat (See also:

• PENTECOST

Pentecost), and of the See also:

• VINE

vine (See also:

• TABERNACLES, FEAST OF

Tabernacles) . Hence it is referred to as " the Feast " See also:

• PAR (Lat. par, equal)

par excellence (Heb . Hehag, cf . Arab . See also:

• HAJJ

Hajj) even as See also:

• LATE

late as 2 Chron. vii . 9 . Being of the nature of a pilgrimage feast the booths were temporary erections for the See also:

• ACCOMMODATION (Lat. accommodare, to make fit, from ad, to, cum, with, and modus, measure)

accommodation of the pilgrims . But in See also:

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

early Jewish tradition, in both Yahvist and Elohist See also:

• SOURCES

sources of the See also:

• PENTATEUCH

Pentateuch (Exod. xxxiv . 22, See also:

• XXIII

xxiii . 16) it is called simply the See also:

• HARVEST (A.S. hcerfest " autumn," O.H. Ger. herbist, possibly through an old Teutonic root representing Lat. car pere, " to pluck ")

Harvest Feast (A.V .

" Feast of Ingathering ") and is to be observed " at the end of the See also:

• YEAR

year," i.e. of the agricultural year . In Deut. xvi . 13 seq., it is termed the Feast of Tabernacles and is to be kept seven days after the produce of the threshing-See also:

• FLOOR (from O. Eng. flor, a word common to many Teutonic languages, cf. Dutch vloer, and Ger. Flur, a field, in the feminine, and a floor, masculine)

floor and winepress has been gathered in . In the Holiness See also:

• CODE (Lat. codex)

Code (Lev. xxiii . 39) it is to be kept for seven days after the first, the first of which is to be " a See also:

• SABBATH

sabbath," and the eighth " a sabbath " (possibly originally a lunar See also:

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

quarter-See also:

• DAY (O. Eng. dreg, Ger. Tag; according to the New English Dictionary, " in no way related to the Lat. dies")
• DAY, JOHN (1574-1640?)
• DAY, THOMAS (1748-1789)

day): branches of four trees are to be taken . In the Priestly Code (Lev. xxiii . 33 seq.; Num. See also:

• XXIX

xxix . 12–38) the first and eighth day are to be days of See also:

• HOLY

holy See also:

• ASSEMBLY, UNLAWFUL

assembly, and in the latter passage elaborate details are given of the sacrifices to be presented, including a See also:

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

series of bullocks, thirteen on the first day, twelve on the next, and so on down to seven on the seventh day . Only one is to be sacrificed on the concluding feast (Heb. rt1yereth) of the eighth day . The higher See also:

• CRITICISM
• CRITICISM (from the Gr. KpiTrlS, a judge, Kpivew, to decide, to give an authoritative opinion)

criticism See also:

• SEES

sees, in these successive enactments of the various codes included in the Pentateuch (q.v.), a development in the See also:

• CHARACTER (Gr. xapareri7p, from xap&crew, to scratch)

character of the festival . At first held at any of the See also:

• LOCAL

local shrines, such as See also:

• GILGAL (Heb. for " circle " of sacred stones)

Gilgal, See also:

• BETHEL (Heb. " House of God ")

Bethel, See also:

• SHILOH
• SHILOH, BATTLE OF

Shiloh, as well as See also:

• JERUSALEM (Heb. ^S0-r, Yerushalaim, pronounced as a dual)
• JERUSALEM, SYNOD OF (1672)

Jerusalem, it was held at an indefinite date during the harvest in the fall of the year . Then with the concentration of the cultus at Jerusalem represented by See also:

• DEUTERONOMY

Deuteronomy, the celebration was restricted to the Judean See also:

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

capital, and its duration fixed at seven days, though its date was still See also:

• LEFT

left indeterminate .

This was fixed in the Priestly Code at the 15th of the seventh See also:

• MONTH
• MONTH (a common Teutonic word, cf. Ger. Mond, Du. maand, Dan. maaned, &c., and cognate with Lat. mensis, Gr. µi7v, &c., in other branches of the Indo-Germanic family; all ultimately from the root seen in the word for the moon in nearly all those languages

month, and an eighth day of See also:

• SOLEMN (Lat. sollemnis, sollemnis, less correctly solennis, yearly, annual; from sollus = totus, whole, entire, Gr. Mos., and annus, year)

solemn assembly added after the return from the See also:

• EXILE (Lat. exsilium or exilium, from exsul or exul, which is derived from ex, out of, and the root sal, to go, seen in salire, to leap, consul, &c.; the connexion with solum, soil, country is now generally considered wrong)

exile . Against this hypothetical reconstruction is the fact that See also:

• SOLOMON, ODES OF
• SOLOMON, PSALMS OF

Solomon appears to have selected the occasion of the feast for the See also:

• DEDICATION (Lat. dedicatio, from dedicare, to proclaim, to announce)

dedication of the See also:

• TEMPLE
• TEMPLE, FREDERICK (1821-1902)
• TEMPLE, RICHARD
• TEMPLE, SIR RICHARD, BART
• TEMPLE, SIR WILLIAM, BART

temple, and that it lasted, even in histime, seven days (1 See also:

• KINGS, FIRST AND SECOND BOOKS OF

Kings viii . 2, 65) . See also:

• JEROBOAM (Heb. ydrob`dm, apparently " Am ['the clan,' here perhaps a divine name] contends "; LXX. iepof3oaµ)

Jeroboam arranged for a similar feast in the See also:

• NORTHERN

northern See also:

• KINGDOM

kingdom on the 15th day of the eighth month, " like unto the feast in See also:

• JUDAH

Judah" (ibid. xii . 32) . The determination of a fixed date must therefore have been much earlier than Deuteronomy or the alleged See also:

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

period of the Priestly Code . A pilgrimage feast must be fixed in date to ensure the simultaneous presence of the pilgrims . There are, besides, seeming references to the feast in the early prophets, as See also:

• HOSEA

Hosea xii . 9, See also:

• AMOS
• AMOS, SHELDON (1835–1886)

Amos v . 21, as well as in See also:

• ISAIAH
• ISAIAH, ASCENSION OF

Isaiah ix . 2 (Heb.) . The concluding feast does not seem to refer to tabernacles per se, but to be distinct from it, as is shown by the break in the descending series of the sacrifices of bullocks as given in See also:

• NUMBERS, BOOK OF
• NUMBERS, PARTITION OF

Numbers .

In Jewish practice the concluding feast is not held in booths, and See also:

• MAIMONIDES

Maimonides (Moreh, 42) suggests that its See also:

• OBJECT

object was to give opportunity for final proceedings in assembly halls . The existence, therefore, of much variation in the practice of the festival in historic times is scarcely proved by the seeming See also:

• VARIATIONS
• VARIATIONS, CALCULUS
• VARIATIONS, CALCULUS OF

variations of the enactments concerning it in the Pentateuch . It is possible, however, that there may have been See also:

• DIFFERENCES, CALCULUS OF (Theory of Finite Differences)

differences of See also:

• CUSTOM (from O. Fr. costume, costume or coustume; Low Lat. costuma, a shortened form of consuetudo)

custom in the carrying out of the feast . In Neh. xiii . 15 the trees whose branches were used for making the booths appear to differ from those mentioned in Lev. xxiii . 40, though in Jewish tradition the latter passage was taken to refer to the Lulab, or a See also:

• COMBINATION (Lat. combinare, to combine)

combination of twigs of See also:

• WILLOW (Salix)

willow and See also:

• MYRTLE

myrtle, with a See also:

• PALM (Lat. palma, Gr. iraX6.jn )
• PALM, JOHANN PHILIPP (1768-1806)

palm See also:

• BRANCH (from the Fr. branche, late Lat. branca, an animal's paw)

branch, which, together with a citron, are held in the See also:

• HAND
• HAND (a word common to Teutonic languages; cf. Ger. Hand, Goth. handus)
• HAND, FERDINAND GOTTHELF (1786-185r)

hand during processions in the See also:

• SYNAGOGUE (avvaywyii)
• SYNAGOGUE, UNITED

synagogue . The See also:

• SADDUCEES

Sadducees and Karaites did not carry these in their hand, but used them as decorations of the booths . In the second temple there was a See also:

• WATER

water See also:

• LIBATION (Lat. libatio, from libare, to take a portion of something, to taste, hence to pour out as an offering to a deity, &c.; cf. Gr. Aeid3ew)

libation every See also:

• MORNING

morning of the festival, and on the evening of the first day the See also:

• GREAT

great See also:

• GOLDEN

golden See also:

• CANDELABRUM (from Lat. candela, a taper or candle)

candelabrum was lit up and the men danced a See also:

• TORCH (O. Fr. torche, from Med. Lat. tortia, derived from tortus, twisted, torquere, to twist)

torch See also:

• DANCE
• DANCE (Fr. danse; of obscure origin, connected with Old High Ger. danson, to stretch)

dance around it (Mishnah, Sukkah, v . 2–4) . It is reported by See also:

• JOSEPHUS, FLAVIUS (c. 37-C. 95?)

Josephus that, when See also:

• ALEXANDER
• ALEXANDER (1461-1506)
• ALEXANDER (ALEXANDER OF BATTENBERG) (1857-1893)
• ALEXANDER (ALEXANDER OsxENOVici) (1876-1903)
• ALEXANDER, ARCHIBALD (1772—1851)
• ALEXANDER, FRANCIS (1800—1881)
• ALEXANDER, GEORGE (1858— )
• ALEXANDER, JOHN WHITE (1856- )
• ALEXANDER, JOSEPH ADDISON (18o9—186o)
• ALEXANDER, SIR JAMES EDWARD (1803—1885)
• ALEXANDER, WILLIAM (1824— )
• ALEXANDER, WILLIAM LINDSAY (1808—1884)

Alexander Jannaeus, in the year 95 B.C., was acting as high-See also:

• PRIEST (Ger. Priester, Fr. pretre)

priest in the temple on the Feast of Tabernacles, instead of pouring the water libation on the See also:

• ALTAR (Lat. altare, from alias, high; some ancient etymological guesses are recorded by St Isidore of Seville in Etymologiae xv. 4)

altar, according to the Pharisaic custom, he poured it at his feet, giving rise to a See also:

• RIOT (0. Fr. riote, of uncertain etymology)

riot in which 6000 men are said to have lost their lives (See also:

• ANT
• ANT (O. Eng. aemete, from Teutonic a, privative, and maitan, cut or bite off, i.e. " the biter off "; aemete in Middle English became differentiated in dialect use to (mete, then amte, and so ant, and also to emete, whence the synonym " emmet," now only u

Ant. xii., xiii., 5; See also:

• TALMUD

Talmud, Sukkah, 48 b) . The festival is certainly an agricultural one, and is so termed in the Pentateuch . Whether it was derived from the Canaanites, who had similar festivals (See also:

• JUDGES, THE BOOK OF

Judges xxix .

27), is uncertain . All nations have similar harvest homes, especially with reference to the vintage feasts; as, for instance, the Athenian Oschophoria . The Syrians celebrated every three years a " See also:

• BOOTH (connected with a Teutonic root meaning to dwell, whence also " bower ")
• BOOTH, BARTON (1681–1933)
• BOOTH, CHARLES (184o– )
• BOOTH, EDWIN [THOMAS] (1833–1893)

Booth Festival." At the See also:

• HINDU

Hindu Festival of Dasara, which lasted nine days from the new See also:

• MOON (a common Teutonic word, cf. Ger. Mond, Du. maan, Dan. maane, &c., and cognate with such Indo-Germanic forms as Gr. µlip, Sans. ma's, Irish mi, &c.; Lat. uses luna, i.e. lucna, the shining one, lucere, to shine, for the moon, but preserves the word i
• MOON, SIR RICHARD, 1ST BARONET (1814-1899)

moon of See also:

• OCTOBER

October, tents made of See also:

• CANVAS

canvas or booths made of branches were erected in front of the temples . The Spartans had a nine days' festival termed See also:

• CARNEA

Carnea, during which they dwelt in pavilions and tents in memory of their old See also:

• CAMP (from Lat. campus, field)

camp See also:

• LIFE

life (See also:

• ATHENAEUS

Athenaeus, iv . 19) . The Feast of Tabernacles is one of the few Jewish festivals described in classical writers . See also:

• PLUTARCH
• PLUTARCH (Gr. llXoi rapxos) (c. A.D. 46–120)

Plutarch (See also:

• SYMPOSIUM (Gr. avyr6cnov, a drinking party, from avµirivecv, to drink together, abv, with, and 7rivecv, to drink, root 7ro, cf. Lat. potare, to drink, poculum, cup)

Symposium iv., vi . 2) compares Tabernacles with the Bacchic See also:

• RITES

rites . It was pre-eminently the period of exultation in See also:

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

ancient Jewish rite, and the Mishnah declares that " He who has not seen the joy of the libations of Tabernacles has never in his life witnessed joy." So much importance was attributed to this festival that it was chosen as the occasion on which the See also:

• LAW
• LAW (0. Eng. lagu, M. Eng. lawe; from an old Teutonic root lag, " lie," what lies fixed or evenly; cf. Lat. lex, Fr. loi)
• LAW, JOHN (1671—1729)
• LAW, WILLIAM (1686-1761)

Law should be recited during the sabbatical year (Deut. xxxi . 9–12), and the Messianic See also:

• VISION (from Lat. videre, to see), or SIGHT

vision of See also:

• ZECHARIAH

Zechariah xiv . 16 sees the remnant of all the nations coming up to Jerusalem to See also:

• WORSHIP (i.e. " worth-ship," O. Eng. weor8scipe)

worship the See also:

• LORD
• LORD (O. Eng. hldford, i.e. hldfweard, the warder or keeper of bread, hlIf, loaf; the word is not represented in any other Teutonic language)
• LORD, JOHN (1810-1894)

Lord of Hosts, and to keep the Feast of Tabernacles . In later Jewish custom the one-year See also:

• CYCLE
• CYCLE (Gr. KUK)^os, a circle)

cycle of See also:

• READING

reading of sections from the Pentateuch ends on the concluding day of Tabernacles, which is therefore known as the Rejoicing of the Law (Simltat Torah) .

The custom of dwelling, for See also:

• PART

part of the day at least, in booths, is still kept up by orthodox See also:

• JEWS
• JEWS (Heb. Y8hudi, man of Judah; Gr. 'Iovbaiot; Lat. Judaei)

Jews, who have temporary huts covered with branches erected in their courtyards, and those who are not in See also:

• POSSESSION
• POSSESSION (Lat. possessio, possidere, to possess)

possession of a See also:

• HOUSE
• HOUSE (O. Eng. hiss, a word common to Teutonic languages, cf. Dut. huis, Ger. Haus; in Gothic it is only found in gudhiss, a temple; it may be ultimately connected with the root of " hide," conceal)

house with a backyard often go to pathetic extremes in 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 to fulfil the law by making holes in See also:

• ROOFS

roofs, across which branches are placed . U . JA.) When the table became a fixed and permanent piece of See also:

• FURNITURE (from " furnish," Fr. fournir)

furniture the word " See also:

• BOARD (O. Eng. bord)

board, " which had See also:

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

long connoted it, See also:

• FELL
• FELL, JOHN (1625-1686)

fell into disuse See also:

• SAVE, or SAVA (Ger. Sau; Hungarian Szdva; Lat. Savus)

save in an allusive sense, and its See also:

• PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place was taken by such phrases as " joyned table " and " framed table"—that is, jointed or framed together by a joiner; sometimes See also:

• PEOPLE

people spoke of a " See also:

• STANDING

standing " or " dormant " table . They were most frequently oblong, some two feet or two feet six inches wide, and the guests sat with their backs to the See also:

• WALL (O. Eng. weal, weall, Mid. Eng. wal, wane, adapted from Lat. vallum, rampart; the original O. Eng. word for a wall was wag or tenth)
• WALL, RICHARD (1694-1778)

wall, the other See also:

• SIDE
• SIDE (mod. Eski Adalia)

side of the table being left See also:

• FREE

free for service . Sometimes they were used as side-tables, or furnished with a See also:

• CUPBOARD

cupboard beneath the board; they were supported on quadrangular legs or massive ends and feet full of See also:

• GOTHIC

Gothic feeling, and were. several inches higher than the dining-table of the loth See also:

• CENTURY (from Lat. centuria, a division of a hundred men)

century . Heavy stretchers or See also:

• FOOT

foot-rails were fixed See also:

• CLOSE
• CLOSE (from Lat. clausum, shut)
• CLOSE, MAXWELL HENRY (1822-1903)

close to the floor—for the avoidance, no doubt, of See also:

• DRAUGHTS (from AS. dragan, to draw)

draughts . See also:

• OAK (O. Eng., (lc)

Oak was the usual material, but See also:

• ELM

elm, See also:

• CHERRY

cherry and other See also:

• WOODS, LEONARD (1774-1854)
• WOODS, SIR ALBERT (1816-1904)

woods were sometimes used . Soon the legs became bulbous, and were gadrooned or otherwise ornamented, and the See also:

• FRAME

frame began to be carved . The introduction, before the 16th century closed, of the "See also:

• DRAWING

drawing table" marked the rapidity with which this piece of furniture was See also:

• DEVELOPED

developed . This was the forerunner of the " extending dining-table." Of the three leaves of which these tables were composed two were below the other; they See also:

• DREW
• DREW, SAMUEL (1765-1833)

drew out and were supported by brackets, while the slab proper dropped to the same level . Somewhat later legs became excessively bulbous; 1 For mathematical tables see next See also:

• ARTICLE (from Lat. articulus, a joint)

article . This use of the word comes from the See also:

• ANALOGY (Gr. avaXo-yLa, proportion)

analogy of the laying out of See also:

• OBJECTS

objects on an See also:

• ORDINARY (med. Lat. ordinarius, Fr. ordinaire)

ordinary table.this ugly See also:

• FORM (Lat. forma)

form gave place soon after the See also:

• MIDDLE

middle of the 17th century to See also:

• BALUSTER (through the Fr. from the Ital. balaustro, so-called from a supposed likeness to the flower of the OaX ab inov, or wild pomegranate; the word has been corrupted in English into " banister ")

baluster-shaped legs .

Hitherto tables had, generally speaking, been large and massive—little in the nature of what is now called the " occasional table " seems to have been provided until some years after the Restoration . About that See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

time small tables of varying sizes and shapes, but still of substantial See also:

• WEIGHT

weight, began to be made; many of them were flap-tables, which took up little See also:

• ROOM

room when they were not in use . These, however, had been known at an earlier date . See also:

• CHARLES
• CHARLES (1270-1325)
• CHARLES (1421-1461)
• CHARLES (1525-1574)
• CHARLES (c. 1319-1364)
• CHARLES (Fr. Charles; Span. Carlos; Ital. Carlo; Ger. Karl; derived from O.H.G. Charal,latinized as Carolus, meaning originally " man ": cf. Mod.Ger., Kerl," fellow," A.S. ceorl, Mod. Eng. " churl ")
• CHARLES (KARL EITEL ZEPHYRIN LUDWIG; in Rum. CAROL)
• CHARLES [KARL ALEXANDER] (1712-1780)
• CHARLES, ELIZABETH (1828-1896)
• CHARLES, JACQUES ALEXANDRE CESAR (1746-1823)
• CHARLES, THOMAS (1755-1814)

Charles II. had not long been on the See also:

• THRONE

throne when the See also:

• IDEA (Gr. Ibia, connected with i&eiv, to see; cf. Lat. species from specere, to look at)

idea of the flap-table was amplified in a peculiarly graceful See also:

• FASHION (adapted from Fr. facon, agon, Lat. factio, making, facere, to do or make)

fashion . Two flaps were provided instead of one, the result being the rather large See also:

• OVAL (Lat. ovum, egg)

oval table of the " See also:

• GATE

gate-See also:

• LEG
• LEG (a word of Scandinavian origin, from the Old Norwegian leggr, cf. Swed. lagg, Dan. laeg; the O. Eng. word was sceanca, shank)

leg " variety that has remained in use ever since, in which the open " gate " supports the flap . Towards the end of the reign tables began to have the graceful See also:

• TWISTED

twisted legs joined to the See also:

• FLAT (a modification of O. Eng. flet, an obsolete word of Teutonic origin, meaning the ground beneath the feet)

flat See also:

• SERPENTINE

serpentine stretchers, which produced, almost for the first time in English furniture, a sense of lightness and gaiety . The See also:

• WALNUT (Juglans)

walnut tables of the end of the See also:

• STUART, ARABELLA (1575-1615)
• STUART, GILBERT (1755-x828)
• STUART, JAMES EWELL BROWN (1833-1864)
• STUART, JOHN
• STUART, MOSES (1780-1852)
• STUART, SIR JOHN, COUNT

Stuart period were often inlaid with See also:

• MARQUETRY (Fr. marqueterie, from marqueter, to inlay, literally to mark, marquee)

marquetry of great excellence . The number and variety of the tables in well-to-do households were now increasing rapidly, and the See also:

• CONSOLE (a French form, supposed to be an abbreviation of consolide, from Lat. consolidare, to strengthen)

console-table was imported from the See also:

• CONTINENT (from Lat. continere, "to hold together "; hence " connected," " continuous ")

Continent contemporaneously with the See also:

• COMMON

common use of the See also:

• MAHOGANY

mahogany side-table . As mahogany came into See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

general use, about the beginning of the second quarter of the 18th century, an enormous number of card-tables were made with See also:

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

plain or cabriole legs and See also:

• SPADE

spade or claw and See also:

• BALL (in Mid. Eng. bal; the word is probably cognate with " bale," Teutonic in origin, cf. also Lat. falls, and Gr. 7raXXa)
• BALL, JOHN (1585-1640)
• BALL, JOHN (1818-1889)
• BALL, JOHN (d. 1381)
• BALL, SIR ALEXANDER JOHN, BART
• BALL, THOMAS (1819- )

ball feet, often with lions' heads carved upon the knees; the See also:

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

top folded up to See also:

• HALF

half its See also:

• SIZE

size when open . The See also:

• CHIPPENDALE, THOMAS (d. 1979)

Chippendale school introduced small tables with carved open-See also:

• WORK

work " galleries " See also:

• ROUND (O. Fr. rond, Lat. rotundus, the Fr. is the source also of Du. rond; Ger., Swed., Dan. and Nor. rond)

round the edges (to protect See also:

• CHINA

china and other small objects), and clustered legs; Gothic forms and See also:

• CHINESE, JAPANESE AND

Chinese frets were for a time fashionable . Later in this century, so prolific in new forms of furniture, tables were frequently made of See also:

• ROSEWOOD

rosewood and satinwood; side-tables, often highly elaborate, adorned with swags and festoons and other classical motives, supported by termini or richly carved legs, were gilded and topped with See also:

• MARBLE (from Lat. marmor, Gr. pApµapos, shining stone)

marble slabs or inlaid See also:

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

wood . The See also:

• PEMBROKE
• PEMBROKE (Penfro)
• PEMBROKE, EARLS OF

Pembroke table, of oblong form, with two semi-circular or oblong leaves, with edgings of marquetry, was a characteristic feature of late 18th-century English furniture, and still retains its popularity .

Then came the See also:

• EMPIRE

Empire period; the See also:

• TAPER (probably of Celtic origin, cf. Irish tapar, Welsh tampr, taper, torch)

taper was replaced by the round leg, rosewood See also:

• GREW, NEHEMIAH (1641-1712)

grew commoner, and See also:

• BRASS
• BRASS (O. Eng. braes)

brass mountings the See also:

• RULE

rule . For illustrations see FURNITURE . to form a table of See also:

• PRIME, PRIMER AND PRIMING

prime numbers the See also:

• PROCESS

process is theoretically See also:

• SIMPLE

simple and rapid, for we have only to range all the numbers in a See also:

• LINE

line and strike out every second number beginning from 2, every third beginning from 3, and so on, those that remain being primes . Even when the See also:

• TABULAR

tabular results are constructed separately, the method of differences or other methods connecting together different tabular results may afford valuable verifications . By having recourse to tables not only does the computer save time and labour, but he also obtains the certainty of accuracy . The invention of logarithms in 1614, followed immediately by the calculation of logarithmic tables, revolutionized all the methods of calculation; and the See also:

• ORIGINAL

original work performed by See also:

• HENRY
• HENRY (1129-1195)
• HENRY (c. 1108-1139)
• HENRY (c. 1174–1216)
• HENRY (Fr. Henri; Span. Enrique; Ger. Heinrich; Mid. H. Ger. Heinrich and Heimrich; O.H.G. Haimi- or Heimirih, i.e. " prince, or chief of the house," from O.H.G. heim, the Eng. home, and rih, Goth. reiks; compare Lat. rex " king "—" rich," therefore " mig
• HENRY, EDWARD LAMSON (1841– )
• HENRY, JAMES (1798-1876)
• HENRY, JOSEPH (1797-1878)
• HENRY, MATTHEW (1662-1714)
• HENRY, PATRICK (1736–1799)
• HENRY, PRINCE OF BATTENBERG (1858-1896)
• HENRY, ROBERT (1718-1790)
• HENRY, VICTOR (1850– )
• HENRY, WILLIAM (1795-1836)

Henry See also:

• BRIGGS, CHARLES AUGUSTUS (1841– )
• BRIGGS, HENRY (1556–1630)

Briggs and See also:

• ADRIAN
• ADRIAN, SAINT

Adrian Vlacq in calculating logarithms in the early part of the 17th century has in effect. formed a portion of every arithmetical operation that has since been carried out by means of logarithms . And not only has an incredible amount of labour been saved, 1 but a vast number of calculations and researches have been rendered practicable which otherwise would have been beyond human reach . The mathematical process that underlies the tabular method of obtaining a result may be indirect and complicated; for example, the logarithmic method would be quite unsuitable for the multiplication of two numbers if the logarithms had to be calculated specially for the purpose and were not already tabulated for use . The arrangement of a table on the See also:

• PAGE
• PAGE, THOMAS NELSON (1853- )
• PAGE, WILLIAM (1811-1885)

page and all typographical details—such as the shape of the figures, their spacing, the thickness and placing of the rules, the See also:

• COLOUR (Lat. color, connected with celare, to hide, the root meaning, therefore, being that of a covering)

colour and quality of the See also:

• PAPER
• PAPER (Fr. papier, from Lat. papyrus)

paper, &c.—are of the highest importance, as the computer has to spend See also:

• HOURS, CANONICAL

hours with his eyes fixed upon the See also:

• BOOK

book; and the efforts of See also:

• EYE
• EYE (O. Eng. edge, Ger. Auge; derived from an Indo-European root also seen in Lat. oc-ulus, the organ of vision (q.v.)

eye and See also:

• BRAIN (A.S. braegen)

brain required in finding the right numbers amidst a See also:

• MASS (O.E. maesse; Fr. messe; Ger. Messe; Ital. messa; from eccl. Lat. missa)
• MASS, IN

mass of figures on a page and in taking them out accurately, when the computer is tired as well as when he is fresh, are far more trying than the See also:

• MECHANICAL

mechanical See also:

• ACTION

action of simple reading . Moreover, the trouble required by the computer to learn the use of a table need scarcely be considered; the important See also:

• MATTER

matter is the time and labour saved by it after he has learned its use . In the following descriptions of tables an See also:

• ATTEMPT (Lat. adtemptare, attentare, to try)

attempt is made to give an See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account of all those that a computer of the See also:

• PRESENT

present day is likely to use in carrying out arithmetical calculations . Tables See also:

• RELATING

relating to ordinary arithmetical operations are first described, and afterwards an account is given of the most useful and least technical of the more strictly mathematical tables, such as factorials, See also:

• GAMMA

gamma functions, integrals, See also:

• BESSEL, FRIEDRICH WILHELM (1784-1846)

Bessel's functions, &c .

Nearly all See also:

• MODERN

modern tables are stereotyped, and in giving their titles the accompanying date is either that of the original stereotyping or of the lirage in question . In tables that have passed through many See also:

• EDITIONS

editions the date given is that of the edition described . A much See also:

• FULLER, ANDREW (1954-1815)
• FULLER, GEORGE (1822—1884)
• FULLER, M
• FULLER, MARGARET, MARCHIONESS
• FULLER, MELVILLE WESTON (1833-1910)
• FULLER, THOMAS (16o8-1661)
• FULLER, WILLIAM (1670--c. 1717)

fuller account of general tables published previously to 1872, by the present writer, is contained in the See also:

• BRITISH

British Association See also:

• REPORT (O.Fr. report or raport, modern rapport, from O.Fr. reporter, mod. rap porter, Lat. reportare, to bring back, in poetical use only, of bringing back an account, news, &c.)

Report for 1873, pp . 1-175 . Tables of Divisors (See also:

• FACTOR (from Lat. facere, to make or do)

Factor Tables) and Tables of Primes.—The existing factor tables extend to 10,000,000 . In 1811 L . Chernac published at See also:

• DEVENTER

Deventer his Cribrum arithmeticum, which gives all the prime divisors of every number not divisible by 2, 3, or 5 up to 1,020,000 . In 1814–1817 J . C . See also:

• BURCKHARDT, JAKOB (1818–1897)
• BURCKHARDT, JOHN LEWIS [JOHANN LUDWIG] (1784-1817)

Burckhardt published at See also:

• PARIS
• PARIS (also called ALEXANDROS)
• PARIS, ALEXIS PAULIN (1800-x881)
• PARIS, BRUNO PAULIN GASTON (1839-1903)
• PARIS, FRANCOIS DE (169o-1727)
• PARIS, LOUIS PHILIPPE ALBERT
• PARIS, TREATIES OF (1814-1815)

Paris his Tables See also:

• DES

des diviseurs, giving the least divisor of every number not divisible by 2, 3, or 5 up to 3,036,000 . The second million was issued in 1814, the third in 1816, and the first in 1817 . The corresponding tables for the seventh, eighth, and ninth millions were calculated by Z .

Dase and issued at See also:

• HAMBURG

Hamburg in 1862, 1863, and 1865 . Dase died suddenly in 1861 during the progress of the work, and it was completed by H . Rosenberg . Dase's calculation was performed at the instigation of See also:

• GAUSS, KARL FRIEDRICH (1777-1855)

Gauss, and he began at 6,00o,000 because the See also:

• BERLIN
• BERLIN, CONGRESS AND TREATY OF
• BERLIN, ISAIAH (1725–1799)

Berlin See also:

• ACADEMY, GREEK
• ACADEMY, ROYAL

Academy was in possession of a See also:

• MANUSCRIPT

manuscript presented by Crelle extending Burckhardt's tables from 3,000,000 to 6,000,000 . This manuscript was found on examination to be so inaccurate that the publication was not desirable, and accordingly the three intervening millions were calculated and published by See also:

• JAMES
• JAMES (Gr. 'IlrKw,l3or, the Heb. Ya`akob or Jacob)
• JAMES (JAMES FRANCIS EDWARD STUART) (1688-1766)
• JAMES, 2ND EARL OF DOUGLAS AND MAR(c. 1358–1388)
• JAMES, DAVID (1839-1893)
• JAMES, EPISTLE OF
• JAMES, GEORGE PAYNE RAINSFOP
• JAMES, HENRY (1843— )
• JAMES, JOHN ANGELL (1785-1859)
• JAMES, THOMAS (c. 1573–1629)
• JAMES, WILLIAM (1842–1910)
• JAMES, WILLIAM (d. 1827)

James See also:

• GLAISHER, JAMES (1809-1903)

Glaisher, the Factor Table for the See also:

• FOURTH

Fourth i Referring to factor tables, J . H . See also:

• LAMBERT [alias NICHOLSON], JOHN (d. 1538)
• LAMBERT, DANIEL (1770-1809)
• LAMBERT, FRANCIS (c 1486-153o)
• LAMBERT, JOHANN HEINRICH (1728–1777)
• LAMBERT, JOHN (1619-1694)

Lambert wrote (Supplementa tabularum, 1798, p. xv.): " Universalis finis talium tabularum est ut semel See also:

• PRO

pro See also:

• SEMPER, GOTTFRIED (1803–1879)

semper computetur quod saepius de novo computandum foret, et ut pro omni casu computetur quod in futurum pro quovis casu computatum desiderabitur." This applies ti all tables . Million appearing at See also:

• LONDON

London in 1879, and those for the fifth and See also:

• SIXTH

sixth millions in 188o and 1883 respectively (all three millions stereotyped) . The tenth million, though calculated by Dase and Rosenberg, has not been published . The nine See also:

• QUARTO

quarto volumes (Tables des diviseurs, Paris, 1814–1817; Factor Tables, London, 1879–1883; Factoren-Tafeln, Hamburg, 1862–1865) thus form one See also:

• UNIFORM

uniform table, giving the least divisor of every number not divisible by 2, 3, or 5, from unity to nine millions . The arrangement of the results on the page, which is due to Burckhardt, is admirable for its clearness and condensation, the least factors for 9000 numbers being given on each page . The tabular portion of each million occupies 112 pages .

The first three millions were issued separately, and also See also:

• BOUND, or BOUNDARY (from O. Fr. bonde, Med. Lat. bodena or butina, a frontier line)

bound in one See also:

• VOLUME

volume, but the other six millions are all See also:

• SEPARATE

separate . Burckhardt began the publication of his tables with the second million instead of the first, as Chernac's factor table for the first million was already in existence . Burckhardt's first million does not supersede Chernac's, as the latter gives all the prime divisors of numbers not divisible by 2, 3, or 5 up to 1,020,000 . It occupies 1020 pages, and Burckhardt found it very accurate; he detected only See also:

• THIRTY

thirty-eight errors, of which nine were due to the author, the remaining twenty-nine having been caused by the slipping of type in the See also:

• PRINTING (from Lat. imprimere, O. Fr. empreindre)

printing . The errata thus discovered are given in Burckhardt's first million . Other errata are contained in See also:

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

Allan See also:

• CUNNINGHAM, ALEXANDER (c.1655-173o)
• CUNNINGHAM, ALLAN (1784-1842)
• CUNNINGHAM, WILLIAM (1805-1861)

Cunningham's paper referred to below . Burckhardt gives but a very brief account of the method by which he constructed his table; and the introduction to Dase's millions merely consists of Gauss's See also:

• LETTER (through Fr. lettre from Lat. littera or litera, letter of the alphabet; the origin of the Latin word is obscure; it has probably no connexion with the root of linere, to smear, i.e. with wax, for an inscription with a stilus)

letter suggesting their construction . The Introduction to the Fourth Million (pp . 52) contains a full account of the method of construction and a See also:

• HISTORY

history of factor tables, with a bibliography of writings on the subject . The Introduction (pp . 103) to the Sixth Million contains an enumeration of primes and a great number of tables relating to the See also:

• DISTRIBUTION (Lat. distribuere, to deal out)

distribution of primes in the whole nine millions, portions of which had been published in the See also:

• CAMBRIDGE
• CAMBRIDGE, EARLS AND DUKES OF
• CAMBRIDGE, RICHARD OWEN (1717-1802)

Cambridge Philosophical Proceedings and elsewhere . A See also:

• COMPLETE

complete See also:

• LIST (O.E. lisle, a Teutonic word, cf. Dut. lust, Ger. Leiste, adapted in Ital. lista and Fr. lisle)
• LIST, FRIEDRICH (1789-1846)

list of errors in the nine millions was published by J .

P . See also:

• GRAM

Gram (Acta mathematica, 1893, 17, p . 310) . These errors, 141 in number, and which affect principally the second, third, eighth, and ninth millions, should be carefully corrected in all the tables . In 1909 the See also:

• CARNEGIE
• CARNEGIE, ANDREW (1837– )

Carnegie Institution of See also:

• WASHINGTON
• WASHINGTON (or WASHINGTON COURT HOUSE)
• WASHINGTON, BOOKER TALIAFERRO (c. 1859– )
• WASHINGTON, BUSHROD (1762-1829)
• WASHINGTON, GEORGE (1732-1799)

Washington published a factor table by Prof . D . N . Lehmer which gives the least factor of all numbers not divisible by 2, 3, 5, or 7, up to ten millions . This table which covers a range of 21,000 numbers on a single page, was reproduced by See also:

• PHOTOGRAPHY (Gr. bias, light, and ypa w, to write)
• PHOTOGRAPHY, CELESTIAL

photography from a type-written copy of the author's original manuscript . The introduction contains a list of errata in the nine millions previously published, completely confirming Gram's list . The factor tables which have just been described greatly exceed both in extent and accuracy any others of the same See also:

• KIND (O. E. ge-cynde, from the same root as is seen in " kin," supra)

kind, the largest of which only reaches 408,000 . This is the limit of Anton Felkel's Tafel alter einfachen Factoren (See also:

• VIENNA (Ger. Wien; Lat. Vindobona)
• VIENNA, CONGRESS OF (1814-1815)

Vienna, 1776), a remark-able and extremely rare book,' nearly all the copies having been destroyed .

Georg See also:

• VEGA, GARCILASO DE LA
• VEGA, GARCILASO DE LA (1503-1536)

Vega (Tabulae, 1797) gave a table showing all the divisors of numbers not divisible by 2, 3, or 5 up to 102,000, followed by a list of primes from 102,000 to 400,313 . In the earlier editions of this work there are several errors in the list, but these are no doubt corrected in J . A . Hiilsse's edition (184o) . J . Salomon (Vienna, 1827) gives the least divisor of all numbers not divisible by 2, 3, or 5, up to 102,011, and B . See also:

• GOLDBERG

Goldberg (Primzahlen and Factoren-Tafeln, See also:

• LEIPZIG

Leipzig, 1862) gives all factors of numbers not divisible by 2, 3, or 5 up to 251,650 . H . G . Kohler (Logarithmisch-trigonometrisches Handbuch, 1848 and subsequent editions) gives all factors of numbers not prime or divisible by 2, 3, 5, or 11 up to 21,525 . See also:

• PETER
• PETER (Lat. Petrus from Gr. irfpos, a rock, Ital. Pietro, Piero, Pier, Fr. Pierre, Span. Pedro, Ger. Peter, Russ. Petr)
• PETER (PEDRO)
• PETER, EPISTLES OF
• PETER, ST

Peter See also:

• BARLOW, JOEL (1754-1812)
• BARLOW, PETER (1776-1862)
• BARLOW, SIR GEORGE HILARO (1762-1847)

Barlow (Tables, 1814) and F . Schaller (Primzahlen-Tafel, See also:

• WEIMAR

Weimar, 1855) give all factors of all numbers up to so,000 .

Barlow's work also contains a list of primes up to 100,103 . Both the factor table and the list of primes are omitted in the stereotyped (1840) reprint . Full lists of errata in Chernac (1811), Barlow (1814), Hiilsse's Vega (1840), Kohler (1848), Schaller (1855), and Goldberg (1862) are contained in a paper by Allan Cunningham (See also:

• MESS (an adaptation of O. Fr. mes, mod. mets; Ital. messo; derived from the Late Lat. missum, past participle of mittere " to send or place in position ")

Mess. of Math., 1904, 34, p . 24; 1905, 35, p . 24) . V . A . Le Besgue (Tables diverses pour la decomposition des nombres, Paris, 1864) gives in a table of twenty pages, the least factor of numbers not divisible by 2, 3, or 5 up to 115,500 . In See also:

• REES, THOMAS (1777–1864)

Rees's Cyclopaedia (1819), article " Prime Numbers," there is a list of primes to 217,219 arranged in decades . The Fourth Million (1879) contains a list of primes up to 30,341 . The fourth edition of the Logarithmic Tables (London, and See also:

• ITHACA
• ITHACA ('IeaK77)

Ithaca, N.Y., 1893) of G . W .

See also:

• JONES
• JONES, ALFRED GILPIN (1824-1906)
• JONES, EBENEZER (182o-186o)
• JONES, ERNEST CHARLES (1819-1869)
• JONES, HENRY (1831-1899)
• JONES, HENRY ARTHUR (1851- )
• JONES, INIGO (1573-1651)
• JONES, JOHN (c. 1800-1882)
• JONES, MICHAEL (d. 1649)
• JONES, OWEN (1741-1814)
• JONES, OWEN (1809-1874)
• JONES, RICHARD (179o-1855)
• JONES, SIR ALFRED LEWIS (1845-1909)
• JONES, SIR WILLIAM (1746-1794)
• JONES, THOMAS RUPERT (1819– )
• JONES, WILLIAM (1726-1800)

Jones of Cornell University contains a table of all the factors of numbers not divisible by 2 or 5 up to 20,000 . In the See also:

• CASE
• CASE, JOHN (d. 1600)

case of primes the ten-place See also:

• LOGARITHM (from Gr. Abyos, word, ratio, and apx0µos, number)

logarithm is given . This table does not occur in the third edition (Ithaca, N.Y., 1891) . On the first page of the Second Million Burckhardt gives the first nine multiples of the primes to 1423; and a smaller table of the same kind, extending only to 313, occurs in Lambert's Supplementa (1798) . Several papers contain lists of high primes (i.e. beyond the range of the For See also:

• INFORMATION (from Lat. informare, to give shape or form to, to represent, describe)

information about it, see a paper on " Factor Tables," in Camb . Phil . Proc . (1878), iii . 99–138, or the Introduction to the Fourth Million . factor tables) . Among these may be mentioned two, by Allan Cunningham and H . J .

Woodall jointly, in the Mess. of Math., 1902, 31, p . X65; 1905, 34, p . 72 . See also the papers on factorizations of high numbers referred to under Tables relating to the Theory of Number; . The Vienna Academy possesses the manuscript of an immense factor table extending to 100,000,000, constructed many years ago by J . P . Kulik (1793–1863) (see Ency. math . Wiss., 1900-1904, i . 952, and Lehmer's Factor Table, p. ix.) . Multiplication Tables.—A multiplication table is usually of See also:

• DOUBLE
• DOUBLE (from the Mid. Eng. duble, the form which gives the present pronunciation, through the Old Er. duble, from Lat. duplus, twice as much)

double entry, the two arguments being the two factors; when so arranged it is frequently called a See also:

• PYTHAGOREAN

Pythagorean table . The largest and most useful work is A . L .

Crelle's Rechentafeln (Bremiker's edition, 1857, stereotyped; many subsequent editions with See also:

• GERMAN
• GERMAN, DUTCH AND SCANDINAVIAN

German, See also:

• FRENCH
• FRENCH, DANIEL CHESTER (1850– )
• FRENCH, NICHOLAS (1604-1678)

French, and English See also:

• TITLE (0. Fr. title, mod. titre, from Lat. titulus)

title-pages), which gives in one volume all the products up to I000Xwoo, so arranged that all the multiples of any one number appear on the same page . The original edition was publishect in 1820 and consisted of two thick See also:

• OCTAVO

octavo volumes . The second (stereotyped) edition is a convenient See also:

• FOLIO (properly the ablative case of the Lat. folium, leaf, but also frequently an adaptation of the Ital. foglio)

folio volume of 450 pages.' In 1908 an entirely new edition, edited by O . Seeliger, was published in which the multiples of to, 20, ..., 990 (omitted in previous editions) are included . This adds 5o pages to the volume, but removes what has been a great See also:

• DRAWBACK

drawback to the use of the tables . Other improvements are that the tables are divided off horizontally and vertically by lines and spaces, and that, for calculations in which the last two figures are rejected, a See also:

• MARK
• MARK, CARL (1858– )
• MARK, GOSPEL OF ST
• MARK, ST

mark has been placed to show when the last figure retained should be increased . Two other tables of the same extent (woo X woo), but more condensed in arrangement, are H . C . See also:

• SCHMIDT, H
• SCHMIDT, HEINRICH JULIAN (1818-1886)
• SCHMIDT, KARL VON (1817-1875)
• SCHMIDT, WILHELM ADOLF (1812-1887)

Schmidt's Zahlenbuch (See also:

• ASCHERSLEBEN

Aschersleben, 1896), and A . Henselin's Rechentafel (Berlin, 1897) . An See also:

• ANONYMOUS

anonymous table, published at See also:

• OLDENBURG

Oldenburg in 1860, gives products up to 500X509, and M . Cordier, Le Multiplicateur de trois cents carres (Paris, 1872), gives a multiplication table to 300X300 (intended for commercial use) .

In both these See also:

• WORKS

works the product is printed in full . The four following tables are for the multiplication of a number by a single See also:

• DIGIT (Lat. digit us, finger)

digit . (I) A . L . Crelle, Erleichterungstafel fiir jeden, der zu rechnen See also:

• HAT

hat (Berlin, 1836), a work extending to woo pages, gives the product of a number of seven figures by a single digit, by means of a double operation of entry . Each page is divided into two tables: for example, to multiply 9382477 by 7 we turn to page 825, and enter the right-hand table at line 77, See also:

• COLUMN (Lat. columna)

column 7, where we find 77339; we then enter the left-hand table on the same page at line 93, column 7, and find 656, so that the product required is 65677339 . (2) C . A . See also:

• BRETSCHNEIDER, KARL GOTTLIEB (1776—1848)

Bretschneider, Produktentafel (Hamburg and See also:

• GOTHA

Gotha, 1841), is somewhat similar to Crelle's table, but smaller, the number of figures in the multiplicand being five instead of seven . (3) In S . L . Laundy, A Table of Products (London, 1865), the product of any five-figure number by a single digit is given by a double arrangement .

The extent of the table is the same as that of Bretschneider's, as also is the principle, but the arrangement is different, Laundy's table occupying only to pages and Bretschneider's 99 pages . (4) G . Diakow's Multiplikations-Tabelle (St See also:

• PETERSBURG

Petersburg, 1897) is of the same extent as Bretschneider's table but occupies woo pages . Among tables extending to IooXl000 (i.e. giving the products of two figures by three) may he mentioned C . A . Mailer's Multiplications-Tabellen (See also:

• KARLSRUHE, or CARLSRUHE

Karlsruhe, 1891) . The tables of L . See also:

• ZIMMERMANN, JOHANN GEORG, RITTER VON

Zimmermann (Rechentafeln, Liebenwerda, 1896) and J . Riem (Rechentabellen fiir Multiplication, See also:

• BASEL (Fr. Bale)
• BASEL (Fr. Belle, but Basle is a wholly erroneous form; Ital. Basilea)
• BASEL, CONFESSION OF
• BASEL, COUNCIL OF

Basel, 1897) extend to IooXio,000 . In a folio volume of 500 pages J . See also:

• PETERS (or PETER), HUGH (1598–166o)
• PETERS, KARL (1856– )

Peters (Rechentafeln See also:

• FUR (connected with O. Fr. forre, a sheath or case; so " an outer covering ")

fur Multiplikation and See also:

• DIVISION (from Lat. dividere, to break up into parts, separate)

Division mit e'n- bis viersteliigen Zahlen, Berlin, 1909) gives products of four figures by two . The entry is by the last three figures of the multiplicand, and there are 2000 products on each page .

Among earlier tables, the See also:

• INTEREST

interest of which is mainly See also:

• HISTORICAL

historical, mention may be made of C . See also:

• HUTTON, CHARLES (1737-1823)
• HUTTON, JAMES (1726-1797)
• HUTTON, RICHARD HOLT (1826-1897)

Hutton's Table of Products and See also:

• POWERS, HIRAM (1805-1873)

Powers of Numbers (London, 1781), which contains a table up to IooXl000, and J . P . Gruson's Grosses Einmaleins von Eins bis Hunderttausend (Berlin, 1799)—a table of products up to 9 X10,000 . The author's intention was to extend it to 100,000, but only the first part was published . In this book there is no condensation or double arrangement; the pages are very large, each containing 125 lines . Quarter-Squares.—Multiplication may be performed by means of a table of single entry in the manner indicated by the See also:

• FORMULA
• FORMULA (Lat. diminutive of forma, shape, pattern, &c., especially used of rules of judicial procedure)

formula- ab = 1(a +b)2-4 (a-b)2 . Only one other multiplication table of the same extent as Crelle's had appeared previously, viz . Herwart von Hohenburg's Tabulae arithmeticaa irporGacaipsos n universales (See also:

• MUNICH (Ger. Munchen)

Munich, 1610), a huge folio volume of more than a thousand pages . It appears from a See also:

• CORRESPONDENCE
• CORRESPONDENCE (from med. scholastic Lat. correspondentia, corrcspondere, compounded of Lat. cum, with, and respond ere, to answer; cf. Fr. correspondance)

correspondence between See also:

• KEPLER, JOHANN (1571-1630)

Kepler and von Hohenburg, which took place at the end of 1608, that the latter used his table when in manuscript for the performance of multiplications in general, and that the occurrence of the word prosthaphaeresis on the title is due to Kepler, who pointed out that by means of the table spherical triangles could be solved more easily than by Wittich's prosthaphaeresis . The invention of logarithms four years later afforded another means of performing multiplications, and von Hohenburg's work never became generally known . On the method of prosthaphaeresis, see See also:

• NAPIER
• NAPIER, JOHN (1550-1617)
• NAPIER, SIR CHARLES (1786-1860)
• NAPIER, SIR CHARLES JAMES (1782-1853)
• NAPIER, SIR WILLIAM FRANCIS PATRICK (1785-1860)

NAPIER, 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