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one of file greatest, critics of his time, especially in ecclesiastical mat-ters, was bom at Paris , in 1657. When he published the first'volume of his Bibliotheque Umverselle des Auteurs Ecclesias-tiques, in 1686, the liberty, with which he treated some ecclesi-astical writers, gave such offence, that M. de Harlay, archbishopof Paris , obliged Dupin to retract many propositions, and sup-pressed the work. He was nevertheless suffered to continue it,by altering the title from Bibliotheque Universelle, to BibliothequeNouvelle. This great undertaking, continued in several succes-sive volumes, though sufficient to occupy the life of an ordinaryman, did not hinder M. Dupin from obliging the world withseveral other works. He was a man of prodigious reading ; andhad ail easv happy way of writing, with an uncommon talent atanalysing the works of an author; which makes his EcclesiasticalBibliotheque so valuable. He was professor of philosophy in theroyal college; blit was banished some time from the chair toChatclleraut, on account of the famous Cas de Conscience; butwas restored, and died in 1719.
DUPJ-E RATIO, among mathematicians, denotes the ratio of2 to 1. Thus tiie ratio of 8 to 4 is duple. Sub-duple ratio, isjust the reverse, or as 1 to 2. Such is 4 to 8, or 6 to 12.
DUPLICATE PROPORTION, or RATIO, is a ratio com-pounded of two ratios: thus, the duplicate ratio of a to b, isthe ratio of aa to bb, or of the square of a to the square of b. Hencethe duplicate ratio ought to be well distinguished from double. Ina series of geometrical proportionals, the first term to the third issaid to he in a duplicate ratio of the first to the second: thus in 2,4, 8, 16, &c. the ratio of 2 to 8 is duplicate of that of 2 to 4, or asthe square of 2 to the square of 4. Duplicate ratio is therefore theproportion of squares, as triplicate is of cubes, &c. and the ratio of 2to 8 is said to be compounded of that of 2 to 4, and of 4 to 8.
Duplicate, among lawyers, denotes a copy of any deed,writing, or account. It is also used for the second letters patent,granted by the lord chancellor, in a case wherein he had beforedone the same.
DUPLICATION, in general, signifies the doubling of anything, or multiplying of it by 2: also the folding of any thing backagain on itself. The duplication of a cube is a problem famousin antiquity : it was proposed by the oracle at Delphos, as a meansto stop the plague, to double Apollos’s altar, which was cubical.The difficulty of the problem consists in this, to find the side of acube that shall be double in solidity to a given cube; which is onlyto be solved by finding two mean proportionals between the sideof the given cube and double that side. Thus, if the given sidebe represented by a, its double by b, and the side sought by y ;
we shall have a a: yy:: y: b; and making z = EE, it will be a ; z ::y.b. So that «
)/, the side of the cube sought, is the second of two mean propor-tionals between a and b.
DUPLiCATURE, among anatomists, a term used to denotethe folds of any membrane, or vessel: thus we say, the duplica-tures of the intestines, peritonseum, See.
DUPOND1US, in antiquity, a weight of two pounds, oramoney of the value of two asses. See As. As the as at firstw eighed a ilist pondo or libra, the dupondius then weighed two ;and hence the name.
DUQUELI.A, a fertile province of Morocco in Africa ; 75miles long, and 60 broad.
DURA MATER, one of the membranes which surround thebrain. See Anatomy.
DURAMPOUR. a town of Ilindostan, in the country ofGuzerat, 45 miles S. S. E. of Surat .
DURANGO, a town of N. America , in the province of NewBiscay. Lon. 105. 0. W. Lat. 24, 50. N.
DCRANTA, in botany, a genus of the angiospermia order,and didynamia class of plants; natural order, Personate. Calyxquinquefid, superior; berry tetraspermous; seeds bilocular. Ithas three species, shrubs, with quadrangular branches.
DURATION. Sc- Metaphysics.
Duration, as marked by certain periods and measures, is whatwe most properly call time." See Time.
Duration of Action, according to Aristotle , is confined to anatural day in tragedy; but the- epopea, according to the samecritic, has no fixed time.
anciently named Epidamnus and Dyrrachium. It is 88 milesS. S. E. of Ragusa. Eon. 19. 19. E. Lat. 41. 54. N.
DURBUY, a town of France , in the department ofOurte, andlate duchy of Luxemburg , 20 miles S. of Liege. Lat. 50. 18. N.
Dukbuy, a late county of Luxemburg , now annexed toFrance .
DURCKHEIM, town of Germany, in the circle of the Up-per Rhine, now included in the department of Mont Tonnerre ;12 miles N. E. of Newstadt.
DURESS, in law, is where a man is kept in prison, or restrainedof his liberty, contrary to the order of law ; or threatened to bekilled, maimed, or beaten ; and if such person so in prison, or infear of such threats, make any specialty or obligation by reasonthereof, such deed is void in law ; and in any action brought uponsuch speciality, the party may plead that it was made by duress,and so he may avoid the action. Cowel.
DURHAM, a county of England, commonly called the Bisho-pric of Durham. It is bounded on the N. by Northumberland ,from which it is separated by the Tyne , on the N. E.; on the E. bythe German ocean; on the S. and S. \V. by Yorksiiire and theTees ; and on the W. by Cumberland and Westmoreland. Be-fore the arrival of the Romans it was included in the British prin-cipality, of the Brigantcs, and after their arrival made part ot theprovince of Maxima Caesariensis. During the Heptarchy, it madepart of the kingdom of Northumberland . It is now included in thenorthern circuit, in the province of York ; and is a diocese andprincipality under the government of its own bishop, being acounty palatine, the second in rank, and the richest in England.It extends 47 miles in length from E. to W. and 37 from N. to S.It is 107 miles in circumference, and contains 410,000 squareacres, or 758 square miles.
Durham, the capital of the above county, remarkable for thesalubrity of its air, and the abundance and cheapness of its pro-visions. It was built about 70 years before the Norman conquest ,on occasion of bringing hither the body of St. Cuthbert. It lies 14miles S. of Newcastle. T.on. 1. 27. W. Lat. 54. 50..N.
Durham, a river of the United States , which falls into thePiscalaqua.
Durham, a town and township of Connecticut in New-IIavcncounty. It is 22 miles S. W. of Hartford .
Durham, a town of New Hampshire, in Stafford county . Onthe top of a hill in this town is a rock, computed to weigh 60 or70 tons, so exactly poised on another rock, as to be easily movedby one’s finger. Its situation appears to be natural. Lon. 70. 54.\f . Eat. -43. 5. N.
DURIO, a genus of the class and order polyadelphia polyandria.The calyx is live-cleft; corolla tivc-pelaled ; style one; staminain five bodies ; pome five-celled. There is one species, a tree ofthe East Indies.
DURNESS, a town of Scotland 46 miles N. N. W. of Dor-noch.
DUROCORNOVIUM, an ancient town of Britain ; nowcalled Cirencester. Ptolemy called it Corinium.
DUROCORTpRA, or DUROCORTORUM, an ancienttown of the Rhemi, in Belgica ; now called Rheims .
DUROIA, a genus of the monogynia order, and hexandria classof plants. Calyx above is cylindrical and loped; border sjx-parted; no filaments; pome hispid. It has one species, a tree ofSurinam .
DUROTRIGES, an ancient British nation, seated in Dorset-shire. Their name is derived from the two British words Dtirwater, and Trigo to dwell; and they got it from the situation oftheir country, which lies along the sea coast, It is not certainwhether the Durolriges formed an independent stale under aprince of their own, or were united with their neighbours theDanmonii; as they were reduced by Vespasian under the domi-nion of the Romans, at the same time, and with the same ease, anclnever revolted.
DURSEY, an island about 2 miles long, and half a mile broad,situated near the S. \V. coast of Ireland .
DURSLEY, a town of Gloucestershire , celebrated for itsmanufacture of broad cloth. It is 15 miles S. of Gloucester. l.on.2. 23. ML Lat. 51. 4n. N.
DURSTOLORG, the son of llungus, and the 73d king of thePiets, according to Dr. Anderson. (Royal Gcncul.) lie wasmurdered by his brother Logan, who thus paved the way for the
union