GASPARD See also:

• GASPARD MONGE (1746-1818)

MONGE (1746-1818)  , See also:

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

French mathematician, the inventor of descriptive See also:

• GEOMETRY

geometry, was See also:

• BORN, IGNAZ, EDLER VON (1742–1791)

born at See also:

• BEAUNE

Beaune on the loth of May 1746 . He was educated first at the See also:

• COLLEGE (Collegium)

college of the Oratorians at Beaune, and then in their college at See also:

• LYONS
• LYONS (Fr. Lyon)
• LYONS, COUNCILS OF
• LYONS, EDMUND LYONS, BARON (1790-1858)
• LYONS, RICHARD BICKERTON PEMELL LYONS, 1ST EARL (1817–1887)

Lyons—where, at sixteen, the See also:

• YEAR

year after he had been Iearning physics, he was made a teacher of it . Returning to Beaune for a vacation, he made, on a large See also:

• SCALE
• SCALE (1) A

scale, a See also:

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

plan of the See also:

• TOWN

town, inventing the methods of observation and constructing the necessary See also:

• INSTRUMENTS

instruments; the plan was presented to the town, and preserved in their library . An officer of See also:

• ENGINEERS, MILITARY

engineers seeing it wrote to recommend See also:

• MONGE, GASPARD (1746-1818)

Monge to the commandant of the military school at See also:

• MEZIERES, PHILIPPE DE (c. 1327—1405)

Mezieres, and he was received as a draftsman and See also:

• PUPIL (Lat. pupillus, orphan, minor, dim. of pupus, boy, allied to puer, from root pm- or peu-, to beget, cf. "pupa," Lat. for " doll," the name given to the stage intervening between the larval and imaginal stages in certain insects)

pupil in the See also:

• PRACTICAL

practical school attached to that institution; the school itself was of too aristocratic a See also:

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

character to allow of his See also:

• ADMISSION

admission to it . His See also:

• MANUAL

manual skill was duly appreciated: " I was a thousand times tempted," he said See also:

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

long afterwards, " to See also:

• TEAR

tear up my drawings in disgust at the esteem in which they were held, as if I had been See also:

• GOOD, JOHN MASON (1764-1827)

good for nothing better." An opportunity, however, presented itself: being required to See also:

• WORK

work out from data supplied to him the " defilement " of a proposed fortress (an operation then only performed by a long arithmetical See also:

• PROCESS

process), Monge, substituting for this a geometrical method, obtained the result so quickly that the commandant at first refused to receive it—the 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 necessary for the work had not been taken; but upon examination the value of the See also:

• DISCOVERY

discovery was recognized, and the method was adopted . And Monge, continuing his researches, arrived at that See also:

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

general method of the application of geometry to the arts of construction which is now called descriptive geometry (see GEOMETRY, DESCRIPTIVE) . But such was the See also:

• SYSTEM

system in See also:

• FRANCE
• FRANCE, ANATOLE (1844– )

France before the Revolution that the See also:

• OFFICERS

officers instructed in the method were strictly forbidden to communicate it even to those engaged in other branches of the public service; and it was not until many years afterwards that an See also:

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

account of it was published . In 1768 Monge became See also:

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

professor of See also:

• MATHEMATICS (Gr. /saBnµar1Kil, Sc. vOcvn or E7rlQTt'µn; from p iN.La, "learning" or "science ")

mathematics, and in 1771 professor of physics, at Mezieres; in 1778 he married Mme Horbon, a See also:

• YOUNG
• YOUNG, A
• YOUNG, ARTHUR (1741-1820)
• YOUNG, BRIGHAM (1801-1877)
• YOUNG, CHARLES MAYNE (1777–1856)
• YOUNG, EDWARD (1683–1765)
• YOUNG, JAMES (1811-1883)
• YOUNG, THOMAS (1773-1829)

young widow whom he had previously defended in a very spirited manner from an unfounded See also:

• CHARGE
• CHARGE (through the Fr. from the Late Lat. carricare, to load in a carrus or wagon; cf. " cargo ")

charge; in 178o he was appointed to a See also:

• CHAIR (in. Mid. Eng. chcere, through O. Fr. chaire or chaiere, from Lat. cathedra, later caledra, Gr. xaOi3pa, seat, cf. "cathedral"; the modern Fr. form chaise, a chair, has been adopted in English with a particular meaning as a form of carriage; chaire

chair of See also:

• HYDRAULICS (Gr. iS&,p, water, and ai,Xos, a pipe)

hydraulics at the See also:

• LYCEUM

Lyceum in 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 (held by him together with his appointments at Mezieres), and was received as a member of the See also:

• ACADEMIC

Academic; his intimate friend-See also:

• SHIP

ship with C . L . Berthollet began at this time . In 1783, quitting Mezieres, he was, on the See also:

• DEATH

death of E . Bezout, appointed examiner of See also:

• NAVAL

naval candidates .

Although pressed by the See also:

• MINISTER (Lat. minister, servant)

minister to prepare for them a See also:

• COMPLETE

complete course of mathematics, he declined to do so, on the ground that it would deprive Mme Bezout of her only income, from the See also:

• SALE
• SALE, GEORGE (c. 1697-1736)
• SALE, SIR ROBERT HENRY (1782—1845)

sale of the See also:

• WORKS

works of her See also:

• LATE

late' See also:

• HUSBAND

husband; he wrote, however (1786), his Traits elementaire de la statique . Monge contributed (1770-1790) to the See also:

• MEMOIRS

Memoirs of the See also:

• ACADEMY, GREEK
• ACADEMY, ROYAL

Academy of See also:

• TURIN

Turin, the Memoires See also:

• DES

des savantes strangers of the Academy of Paris, the Memoires of the same Academy, and the Annales de chimie, various mathematical and See also:

• PHYSICAL

physical papers . Among these may be noticed the memoir " Sur la theorie des deblais et des remblais " (Hem. de l'acad. de Paris, 1781), which, while giving a remarkably elegant investigation in regard to the problem of See also:

• EARTH
• EARTH (a word common to Teutonic languages, cf. Ger. Erde, Dutch aarde, Swed. and Dan. jord; outside Teutonic it appears only in the Gr. 'pq'e, on the ground; it has been connected by some etymologists with the Aryan root ar-, to plough, which is seen in
• EARTH, FIGURE OF
• EARTH, FIGURE OF THE

earth-work referred to in the See also:

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

title, establishes in connexion with it his See also:

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

capital discovery of the curves of curvature of a See also:

• SURFACE

surface . Leonhard See also:

• EULER, LEONHARD (1707-1783)

Euler, in his See also:

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

paper on curvature in the See also:

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

Berlin Memoirs for s76o, had considered, not the normals of the surface, but the normals of the See also:

• PLANE

plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him . Monge's memoir just referred to gives the See also:

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

ordinary See also:

• DIFFERENTIAL

differential See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular See also:

• CASE
• CASE, JOHN (d. 1600)

case of the See also:

• ELLIPSOID

ellipsoid was first made by him in a later paper in 1795 . A memoir in the See also:

• VOLUME

volume for 1783 relates to the See also:

• PRODUCTION (Lat. productionem, from producere, to pro-duce)

production of See also:

• WATER

water by the See also:

• COMBUSTION (from the Lat. comburere, to burn up)

combustion of See also:

• HYDROGEN [symbol H, atomic weight x-oo8 (0=16)]

hydrogen; but Monge's results had been anticipated 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:

• CAVENDISH
• CAVENDISH, GEORGE (1500-1562?)
• CAVENDISH, HENRY (1731-1810)
• CAVENDISH, SIR WILLIAM (c. 1505-1557)

Cavendish . In 1792, on the creation by the Legislative See also:

• ASSEMBLY, UNLAWFUL

Assembly of an executive See also:

• COUNCIL (Lat. concilium, from cum, together, and the root cal, to call)

council, Monge accepted the See also:

• OFFICE (from Lat. officium, " duty," " service," a shortened form of opifacium, from facere, " to do," and either the stem of opes, " wealth," " aid," or opus, " work ")

office of minister of the marine, but retained it only until See also:

• APRIL

April 1793 . When the See also:

• COMMITTEE (from commute, an Anglo-Fr. past participle of commettre, Lat. committere, to entrust; the modern Fr. equivalent comite is derived from the Eng.)

Committee of Public Safety made an See also:

• APPEAL

appeal to the savants to assist in producing the materiel required for the See also:

• DEFENCE
• DEFENCE (Lat. defendere, to defend)

defence of the See also:

• REPUBLIC (Lat. respublica, a commonweal or common-wealth)

republic, he applied himself wholly to these operations, and distinguished himself by his indefatigable activity therein; he wrote at this time his Description de fart de fabriquer See also:

• LES

les canons, and his Avis aux ouvriers en fer sur la fabrication de l'acier . He took a very active See also:

• PART

part in the See also:

• MEASURES

measures for 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 normal school (which existed only during the first four months of the year 1795), and of the school for public works, afterwards the See also:

• POLYTECHNIC (Gr. aroWus, many, and rEXvn, an art)

polytechnic school, and was at each of them professor for descriptive geometry; his methods in that See also:

• SCIENCE (Lat. scientia, from scire; to learn, know)

science were first published in the See also:

• FORM (Lat. forma)

form in which the shorthand writers took down his lessons given at the normal school in 1795, and again in 1798-1799 . In 1796 Monge was sent into See also:

• ITALY
• ITALY (Italia)

Italy with C . L . Berthollet and some artists to receive the pictures and statues levied from several See also:

• ITALIAN

Italian towns, and made there the acquaintance of General See also:

• BONAPARTE

Bonaparte .

Two years afterwards he was sent to See also:

• ROME
• ROME (Roma)

Rome on a See also:

• POLITICAL

political See also:

• MISSION

mission, which terminated in the establishment, under A . See also:

• MASSENA, ANDRE, or ANDREA

Massena, of the See also:

• SHORT, FRANCIS JOB (1857– )

short-lived See also:

• ROMAN

Roman republic; and he thence joined the expedition to See also:

• EGYPT

Egypt, taking part with his friend Berthollet as well in various operations of the See also:

• WAR
• WAR (O. Eng. werre, Fr. guerre, of Teutonic origin; cf. O.H.G. werran, to confound)

war as in the scientific labours of the See also:

• EGYPTIAN

Egyptian See also:

• INSTITUTE (from Lat. instituere, to establish or set up)

Institute of Sciences and Arts; they accompanied Bonaparte to See also:

• SYRIA

Syria, and returned with him in 1798 to France . Monge was appointed See also:

• PRESIDENT (Fr. president, from Lat. praesidens, post-Augustan Lat. for praeses, director, ruler, from praesidere, to sit in front of, preside)

president of the Egyptian See also:

• COMMISSION (from Lat. commissio, committere)

commission, and he resumed his connexion with the polytechnic school . His later mathematical papers are published (1794-x816) in the See also:

• JOURNAL
• JOURNAL (through Fr. from late Lat. diurnalis, daily)

Journal and the Correspondance of the polytechnic school . On the formation of the See also:

• SENATE (Lat. senatus, from root sen-, as in senex, old; the root is the Sanskrit sana, cf. Gr. 'vos; the same element appears in senor, seigneur, seneschal)

Senate he was appointed a member of that See also:

• BODY

body, with an ample See also:

• PROVISION (Lat. provisio)

provision and the title of See also:

• COUNT (Lat. comes, gen. comitis, Fr. comte, Ital. conte, Span. conde)

count of See also:

• PELUSIUM

Pelusium; but on the fall of See also:

• NAPOLEON

Napoleon he was deprived of all his honours, and even excluded from the 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 members of the reconstituted Institute . He died at Paris on the 28th of See also:

• JULY

July 1818 . For further See also:

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

information see B . See also:

• BRISSON, EUGENE HENRI (1835– )
• BRISSON, MATHURIN JACQUES (1723-1806)

Brisson, See also:

• NOTICE

Notice historique sur Gaspard Monge; See also:

• DUPIN, ANDRE MARIE JEAN JACQUES (1783-1865)

Dupin, Essai historique sur les services et les travaux scientifiques de Gaspard Monge (Paris, 1819), which contains (pp . 162—166) a list of Monge's memoirs and works; and the See also:

• BIOGRAPHY (from the Gr. (3ios, life, and yp&4 , writing)

biography by F . See also:

• ARAGO, DOMINIQUE FRANCOIS JEAN (1786-1853)

Arago (euvres, t . 1854) . Monge's various mathematical papers are to a considerable extent reproduced in the Application de l'anatyse a la geomeirie (4thed., last revised by the author, Paris, 1819) ; the pure See also:

• TEXT (Lat. textum, woven fabric, from texere, to weave)

text of this is reproduced in the 5th ed .

(revue, corrigee et annotee See also:

• PAR (Lat. par, equal)

par M . Liouville) (Paris, 1850), which contains also See also:

• GAUSS, KARL FRIEDRICH (1777-1855)

Gauss's Memoir, " Disquisitiones generales circa superficies curvas," and some valuable notes by the editor . The other See also:

• PRINCIPAL

principal See also:

• SEPARATE

separate works are Trailee elementaire de la statique, 8' edition, conformee a la precedente, par M . See also:

• HACHETTE, JEAN NICOLAS PIERRE (1769-1834)
• HACHETTE, JEANNE
• HACHETTE, LOUIS CHRISTOPHE FRANCOIS

Hachette, et suivie dune See also:

• NOTE
• NOTE (Lat. nota, mark, sign, from noscere, to know)

note &'c., par M . See also:

• CAUCHY, AUGUSTIN LOUIS, BARON (1789-1857)

Cauchy (Paris, 1846) ; and the Geometric descriptive (originating, as mentioned above, in the lessons given at the normal school) . The 4th edition, published shortly after the author's death, seems to have been substantially the same as the 7th (Geometric descriptive par G . Monge, suivie d'une theorie des ombres et- de la See also:

• PERSPECTIVE (Lat. peespicere, to see through)

perspective, extraite des apiers de l'auteur, par M . Brisson (Paris, 1847) . (A .