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:

• JOHN WALLIS (1616-1703)

WALLIS (1616-1703)  , See also:

• ENGLISH

English mathematician, logician and grammarian, was See also:

• BORN, IGNAZ, EDLER VON (1742–1791)

born on the 23rd of See also:

• NOVEMBER (Lat. novem, nine)

November 1616 at See also:

• ASHFORD

Ashford, in See also:

• KENT
• KENT, EARLS AND DUKES OF
• KENT, JAMES (1763-1847)
• KENT, WILLIAM (1685-1748)

Kent, of which See also:

• PARISH (Gr. irapouda, district, neighbourhood; 7r&poucos, one dwelling near or beside, from crap&, OtKOS, house; Lat. paroecur, Late Lat. parochia; cf. Fr. paroisse)

parish his See also:

• FATHER

father, Rev . 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:

• WALLIS, JOHN (1616-1703)

Wallis (1567-1622), was See also:

• INCUMBENT (from Lat. incumbere, to lean, lie upon)

incumbent . After being at school at Ashford, See also:

• TENTERDEN
• TENTERDEN, CHARLES ABBOTT

Tenterden and See also:

• FELSTED, or FELSTEAD

Felsted, and being instructed in Latin, See also:

• GREEK
• GREEK, ETRUSCAN AND

Greek and See also:

• HEBREW

Hebrew, he was in 1632 sent to See also:

• EMMANUEL, or IMMANUEL

Emmanuel See also:

• COLLEGE (Collegium)

College, See also:

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

Cambridge, and afterwards was chosen See also:

• FELLOW

fellow of Queens' College . Having been admitted to See also:

• HOLY

holy orders, he See also:

• LEFT

left the university in 1641 to See also:

• ACT (Lat. actus, actum)

act as See also:

• CHAPLAIN

chaplain to See also:

• SIR

Sir See also:

• WILLIAM
• WILLIAM (1143-1214)
• WILLIAM (1227-1256)
• WILLIAM (1J33-1584)
• WILLIAM (A.S. Wilhelm, O. Norse Vilhidlmr; O. H. Ger. Willahelm, Willahalm, M. H. Ger. Willehelm, Willehalm, Mod.Ger. Wilhelm; Du. Willem; O. Fr. Villalme, Mod. Fr. Guillaume; from " will," Goth. vilja, and " helm," Goth. hilms, Old Norse hidlmr, meaning
• WILLIAM (c. 1130-C. 1190)
• WILLIAM, 13TH

William See also:

• DARLEY, GEORGE (1795-1846)

Darley, and in the following See also:

• YEAR

year accepted a similar See also:

• APPOINTMENT, POWER OF

appointment from the widow of Sir Horatio See also:

• VERE
• VERE, SIR FRANCIS (1560-1609)

Vere . It was about this See also:

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

period that he displayed surprising talents in deciphering the intercepted letters and papers of the Royalists . His adherence to the See also:

• PARLIAMENTARY

parliamentary party was in 1643 rewarded by the living of St See also:

• GABRIEL (Heb. SKns, man of God)

Gabriel, Fen-See also:

• CHURCH
• CHURCH (according to most authorities derived from the Gr. Kvpcaxov [&wµa], " the Lord's [house]," and common to many Teutonic, Slavonic and other languages under various forms—Scottish kirk, Ger. Kirche, Swed. kirka, Dan. kirke, Russ. tserkov, Buig. cerk
• CHURCH, FREDERICK EDWIN (1826-1900)
• CHURCH, GEORGE EARL (1835–1910)
• CHURCH, RICHARD WILLIAM (1815–189o)
• CHURCH, SIR RICHARD (1784–1873)

church See also:

• STREET
• STREET, GEORGE EDMUND (1824-1881)

Street, See also:

• LONDON

London . In 1644 he was appointed one of the See also:

• SCRIBES

scribes or secretaries of the See also:

• ASSEMBLY, UNLAWFUL

Assembly of Divines at See also:

• WESTMINSTER
• WESTMINSTER, MARQUESSES AND DUKES OF
• WESTMINSTER, STATUTES OF
• WESTMINSTER, SYNODS OF

Westminster . During the same year he married Susanna Glyde, and thus vacated his fellowship; but the See also:

• DEATH

death of his See also:

• MOTHER

mother had left him in See also:

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

possession of a handsome See also:

• FORTUNE, ROBERT (1813-188o)

fortune . In 1645 he attended those scientific meetings which led to the See also:

• ESTABLISHMENT (0. Fr. establissement, Fr. etablissement, late Norm. Fr. establishement, from O. Fr. establir, Fr. etablir, Lat. stabilire, to make stable)

establishment of the Royal Society . When the See also:

• INDEPENDENTS

Independents obtained the superiority Wallis adhered to the See also:

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

Solemn See also:

• LEAGUE

League and See also:

• COVENANT
• COVENANT (an O. Fr. form, later convenant, from convenir, to agree, Lat. convenire)

Covenant . The living of St . Gabriel he exchanged for that of St See also:

• MARTIN (Martinus)
• MARTIN, BON LOUIS HENRI (1810-1883)
• MARTIN, CLAUD (1735-1800)
• MARTIN, FRANCOIS XAVIER (1762-1846)
• MARTIN, HOMER DODGE (1836-1897)
• MARTIN, JOHN (1789-1854)
• MARTIN, LUTHER (1748-1826)
• MARTIN, SIR THEODORE (1816-1909)
• MARTIN, SIR WILLIAM FANSHAWE (1801–1895)
• MARTIN, ST (c. 316-400)
• MARTIN, WILLIAM (1767-1810)

Martin, See also:

• IRON [symbol Fe, atomic weight 55.85 (0=16)]

Iron-monger See also:

• LANE, EDWARD WILLIAM (1801–1876)
• LANE, JAMES HENRY (1814–1866)

Lane; and, as See also:

• RECTOR (Lat. for " ruler," " guide," &c., from regere, " rule ")

rector of that parish, he in 1648 sub-scribed the Remonstrance against putting 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 I. to death .

Notwithstanding this act of opposition, he was in See also:

• JUNE

June 1649 appointed Savilian See also:

• PROFESSOR (the Latin noun formed from the verb profiteri, to declare publicly, to acknowledge, profess)

professor of See also:

• GEOMETRY

geometry at See also:

• OXFORD
• OXFORD, EARLS OF
• OXFORD, EDWARD DE VERE, 17TH EARL
• OXFORD, JOHN DE VERE, 13TH EARL OF (1443-1513)
• OXFORD, PROVISIONS OF
• OXFORD, ROBERT DE VERE, 9TH EARL OF (1362-1392)
• OXFORD, ROBERT HARLEY, 1ST

Oxford . In 1654 he there took the degree of D.D., and four years later succeeded See also:

• GERARD (c. 1040-1120)
• GERARD (d. I1o8)
• GERARD, ETIENNE MAURICE, COUNT (1773–1852)
• GERARD, FRANCOIS, BARON (1770-1837)
• GERARD, JEAN IGNACE ISIDORE (1803-1847)
• GERARD, JOHN (1545-1612)
• GERARD, or GIRARD, AUDRAN

Gerard Langbaine (1609-1658) as keeper of the archives . After the restoration he was named one of the See also:

• KING
• KING (O. Eng. cyning, abbreviated into cyng, cing; cf. O. H. G. chun- kuning, chun- kunig, M.H.G. kiinic, kiinec, kiinc, Mod. Ger. Konig, O. Norse konungr, kongr, Swed. konung, kung)
• KING [OF OCKHAM], PETER KING, 1ST BARON (1669-1734)
• KING, CHARLES WILLIAM (1818-1888)
• KING, CLARENCE (1842–1901)
• KING, EDWARD (1612–1637)
• KING, EDWARD (1829–1910)
• KING, HENRY (1591-1669)
• KING, RUFUS (1755–1827)
• KING, THOMAS (1730–1805)
• KING, WILLIAM (1650-1729)
• KING, WILLIAM (1663–1712)

king's chaplains in See also:

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

ordinary . While complying with the terms of the Act of Uniformity, Wallis seems always to have retained moderate and rational notions of ecclesiastical polity . He died at Oxford on the 28th of See also:

• OCTOBER

October 1703 . The See also:

• WORKS

works of Wallis are numerous, and relate to a multiplicity of subjects . His Institutio logicae, published in 1687, was very popular, and in his Grammatica linguae Anglicanae we find indications of an acute and philosophic See also:

• INTELLECT (Lat. intellectus, from intelligere, to understand)

intellect . The mathematical works are published, some of them in a small 4to See also:

• VOLUME

volume (Oxford, 1657) and a See also:

• COMPLETE

complete collection in three thick See also:

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

folio volumes (Oxford, 1693-1699) . The third volume includes, however, some theological See also:

• TREATISES

treatises, and the first See also:

• PART

part of it is occupied with See also:

• EDITIONS

editions of treatises on harmonics and other works of Greek geometers, some of them first editions from the See also:

• MSS

MSS., and in See also:

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

general with Latin versions and notes (See also:

• PTOLEMY (CLAUDIUS PTOLEMAEUS)

Ptolemy, Porphyrius, Briennius, See also:

• ARCHIMEDES (c. 287–212 B.C.)
• ARCHIMEDES, SCREW OF

Archimedes, Eutocius, See also:

• ARISTARCHUS

Aristarchus and Pappas) . The second and third volumes include also his See also:

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

correspondence with his contemporaries; and there is a See also:

• TRACT (from Lat. tractare, to treat of a matter, through Provencal tractat and Ital. trattato)

tract on See also:

• TRIGONOMETRY (from Gr. rpiywvov, a triangle, /ATpov, measure)

trigonometry by Caswell . Excluding all these, the mathematical works contained in the first and second volumes occupy about 1800 pages . The titles in the 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 adopted, but with date of publication, are as follows: " Oratio inauguralis," on his appointment (1649) as Savilian professor (1657) ; " Mathesis universalis, seu See also:

• OPUS ('O7rois)

opus arithmeticum philologice et mathematice traditurn, arithmeticum numerosam et speciosam aliaque continens " (1657) ; " Adversus Meibomium, de proportionibus dialogus " (1657) ; " De sectionibus conicis nova methodo expositis " (1655) ; Arithmetica infinitorum, sive nova methodus inquirendi in curvilineoruin quadraturam aliaque difficiliora matheseos problemata " (1655); " Eclipsis solaris observatio Oxonii habita 2° Aug .

16544 ' (1655); " Tractatus duo, See also:

• PRIOR (from Lat. prior—former, and hence superior, through O. Fr. priour)
• PRIOR, MATTHEW (1664-1721)

prior de cycloide, posterior de cissoide et de curvarum turn linearum € lmost turn superficierum nXaruaµca" (1659); " Mechanica, sive de motu tractatus geometricus " (three parts, 1669–1670—1671); " De See also:

• ALGEBRA (from the Arab. al-jebr wa'l-mugabala, transposition and removal [of terms of an equation], the name of a treatise by Mahommed ben Musa al-Khwarizmi)

algebra tractatus historicus et practicus, ejusdem originem et progressus varios ostendens " (English, 1685) ; " De combinationibus alternationibus et partibus aliquotis tractatus " (English, 1685) " De sectionibus angularibus tractatus " (English, 1685); " De angulo contactus et semicirculi tractatus " (1656) ; " Ejusdem tractatus defensio " (1685); " De postulato quinto. et quinta definitione, See also:

• LIB

lib . VI . Euclidis, disceptatio geometra " ( ? 1663); "cunocuneus, seu corpus partim conum partim cuneum repres('ntans geometrice consideratum " (English, 1685) ; " De gravitate et gravitatione disquisitio geometrica " (1662; English, 1674); " De aestu marls See also:

• HYPOTHESIS (from Gr. inrorcOivat, to put under; cf. Lat. suppositio, from sub-ponere)

hypothesis nova " (1666–1669) . The Arithmetica infinitorum relates chiefly to the See also:

• QUADRATURE (from Lat. quadratura, a making square)

quadrature of curves by the so-called method of indivisibles established by See also:

• BONAVENTURA, SAINT (JOHN OF FIDANZA)

Bonaventura Cavalieri in 1629 (see INFINITESIMAL CALCULUS) . He extended 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 of continuity " as stated by Johannes See also:

• KEPLER, JOHANN (1571-1630)

Kepler; regarded the denominators of fractions as See also:

• POWERS, HIRAM (1805-1873)

powers with negative exponents; and deduced from the quadrature of the See also:

• PARABOLA

parabola y where m is a See also:

• POSITIVE (or PORTABLE) ORGAN

positive integer, the See also:

• AREA

area of the curves when m is negative or fractional . He attempted the quadrature of the circle by See also:

• INTERPOLATION (from Lat. interpolare, to alter, or insert something fresh, connected with pollee, a polish)

interpolation, and arrived at the remarkable expression known as Wallis's Theorem (see CIRCLE, SQUARING OF) . In the same See also:

• WORK

work Wallis obtained an expression for the length of the See also:

• ELEMENT (Lat. elementum)

element of a See also:

• CURVE (Lat. curvus, bent)

curve, which reduced the problem of rectification to that of quadrature . The Mathesis universalis, a more elementary work, contains copious See also:

• DISSERTATIONS

dissertations on fundamental points of algebra, See also:

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

arithmetic and geometry, and See also:

• CRITICAL (in alphabetical order of authors)

critical remarks . The De algebra tractatus contains (chapters Ixvi.-lxix.) the See also:

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

idea of the See also:

• INTERPRETATION (from Lat. interpretari, to expound, explain, inter pres, an agent, go-between, interpreter; inter, between, and the root pret-, possibly connected with that seen either in Greek 4 p4'ew, to speak, or irpa-rrecv, to do)

interpretation of imaginary quantities in geometry . This is given somewhat -as follows: the distance represented by the square See also:

• ROOT (late O.E. rot, adopted from Scand., cf. Norw. and Swed. rot, Dan. rod; the true O.E. word was wyrt, plant, represented in Ger. Wurz or Wurzel; the ultimate root is the same in both words, and is seen in Lat. radix)
• ROOT, ELIHU (1845– )

root of a negative quantity cannot be measured in the See also:

• LINE

line backwards or forwards, but can be measured in the same See also:

• PLANE

plane above the line, or (as appears elsewhere) at right angles to the line either in the plane, or in the plane at right angles thereto . Considered as a See also:

• HISTORY

history of algebra, this work is strongly objected to by See also:

• JEAN

Jean See also:

• ETIENNE, CHARLES GUILLAUME (1778-1845)

Etienne l'vlontucla on the ground of its unfairness as against the See also:

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

early See also:

• ITALIAN

Italian algebraists and also Franciscus See also:

• VIETA (or VIETE), FRANCOIS, SEIGNEUR DE LA BIGOTIERE (1540-1603)

Vieta and Rene See also:

• DESCARTES, RENE (1596-1650)

Descartes and in favour of See also:

• HARRIOT, or HARRIOTT, THOMAS (156o–1621)

Harriot; but See also:

• AUGUSTUS (a name 1 derived from Lat. augeo, increase, i.e. venerable, majestic, Gr. Ee0avr6s)

Augustus De See also:

• MORGAN
• MORGAN, DANIEL (1736-1802)
• MORGAN, EDWIN DENNISON (1811-1883)
• MORGAN, JOHN HUNT (1825-1864)
• MORGAN, JOHN PIERPONT (1837–1913)
• MORGAN, LEWIS HENRY (1818-1881)
• MORGAN, SYDNEY, LADY (c. 1783-1859)
• MORGAN, THOMAS (d. 1743)

Morgan, while admitting this, attributes to it considerable merit .

The See also:

• SYMBOL (Gr. o-uµ(3oXov, a sign)

symbol for infinity, co, was invented by him . The two treatises on the See also:

• CYCLOID (from Gr. iciidws, circle, and ennos, form)

cycloid and on the See also:

• CISSOID (from the Gr. rcunr6s, ivy, and ethos, form)

cissoid, &c., and the Mechanica contain many results which were then new and valuable . The latter work contains elaborate investigations in regard to the centre of gravity, and it is remarkable also for the employment of the principle of virtual velocities . Among the letters in volume iii., we have one to the editor of the Acta Leipsica, giving the decipherment of two letters in See also:

• SECRET (Lat. secretum, hidden, concealed)

secret characters . The ciphers are different, but on the same principle: the characters in each are either single digits or combinations of two or three digits, See also:

• STANDING

standing some of them for letters, others for syllables or words,—the number of distinct characters which had to be deciphered being thus very considerable . For the prolonged conflict between See also:

• HOBBES, THOMAS (1588–1679)

Hobbes and Wallis, see HOBBES, See also:

• THOMAS
• THOMAS (c. 1654-1720)
• THOMAS (d. 110o)
• THOMAS, ARTHUR GORING (1850-1892)
• THOMAS, CHARLES LOUIS AMBROISE (1811-1896)
• THOMAS, GEORGE (c. 1756-1802)
• THOMAS, GEORGE HENRY (1816-187o)
• THOMAS, ISAIAH (1749-1831)
• THOMAS, PIERRE (1634-1698)
• THOMAS, SIDNEY GILCHRIST (1850-1885)
• THOMAS, ST
• THOMAS, THEODORE (1835-1905)
• THOMAS, WILLIAM (d. 1554)

THOMAS .