A L G 



A L G 



tlif quantities between whieh it occiii-s are equal. Thus 

 2 + ; = 5, flitfws that 2 more 3 is equal to 5 ; and .v = (/ 

 — h ilunvs tliat X is equal to the difference of a and b. 

 The mark : : ligniHes that the quantities between which 



fined by an algebraical equation. Thefe arealfo called g«). 

 metrical lines, or carves, in contradilUndlion.to mechanical 

 or tranfecndental ones. See Curvf.. 



ALGE15RAIST, a perfon ikilled in algebra. 

 h [hmara;; pmportional. A^ aCb: : c : d denotes that a ALGEDO,ia5«,j.r^,from.Y,, afupprelTed gonorrhoea, 

 i. in the fame proportion to b, as c is to d; or that if « be attended wth pa.n n. the gen.tal and urmary organ, T us 

 •^ ' ...,,-• naniefeld.>ini)ccurs,except Hioldauthors. tjccUoNORRHOhA. 



ALGEDYM Zand, tn Geo^rjphy, is the name of aeon- 

 fiderable chain of mountains in Independent Tartaiy, which 

 ftretches from the river Yaik or Ural, towards the Altaian 



twice, three or four times, &c. as great as b, c will be twice, 

 thrite, or four times, &c. as great as <L 



Whenanyquaiitity i5tobeta!:enm<irethan once, the number 

 which fliews how niany times it is to be taken muft be pre- 

 ll\ed ; thus 5 a denotes that the quantity is to be taken ; 

 times, and 3 if reprefents three times he, and 7 ^<j' + b' 

 denotes that ^' a' + b' is to be taken 7 times, &c. The 

 ■numbers thus prciked are called eo-efficicnts ; and if a 

 •Quantity have no co-eflicient, unit is underllood, and it is to 

 be taken only once. 



Similar orl'ike quantities are thofe that are cxprcfTcd bythc 

 fame letters under the fame powers, or which dilTer oidy in 

 their co-efficients ; thus, 3*1:, 5 3 c, and %bc, are Tile 

 Quantities, and fo are the radicals 2^/ 3 + c a nd 7^/ 3 + c. 



a a 



T3nt unViJce qnantitios are tliofe whieh are exprelTed by dif- 

 ferent letters, or by the fame letters with different powers, 

 as 2 a i, 5 rt b^y and 3 a' b. 



When a quantity is expreffed by a fingle letter, or by fe- 

 -veral fmgle letters multiplied together, without any intcr- 

 ■vening fign, as a, or 2 a I, it is called ^.fimple quantity. 

 But the quantity which conliftsof two or more fuch fimple 

 quantities, connedted by the figns + or — , is called a com- 

 foimJ quantity ; thus, a—ltib + S"^'^ is a compound 

 quantity ; and the iimple quantities a, zah, ^ a b c, are 

 called its terms or members. If a compound quantity confifl 

 of two terms, it is called a binomial ; of 3 terms a trinomial, 

 of 4 tenns, a quadrinomial. Sec. of many terms, a miil/i/10- 

 viial. If one of the terms of a binomial be negative, the 

 quantity is called a refidual quantity. The reciprocal oi any 

 quantity is that quantity inverted, or unity divided by it ; 



thus — is the reciprocal of _, and — is the reciprocal of 



b a a 



^. The letters by whieh any finiple quantity is expreffed 

 may be ranged at pleafure, and yet retain the lame fignifi- 

 cation ; thus ti b and b a are the fame quantity, the produft of 

 a and b being the fame with that of b by a. I'he feveral 

 terms of which any compound quantity confifts may be dll- 

 pofed in any order at pleafure, provided they retain their 

 proper figns. Thus, a — zab + ^a'b may be written 

 a -^^ ^ a' b — Z a b, or — z a b ■{■ a + ^ a- b, for all thefe 

 reprcfent the fame thing-or the quantity which remains, when 

 from the fum of a and 5 a" b the quantity z ab\s dedufted. 



For the method of performing the feve-ral operations in 

 algebra, fee Addition, Subtraction, Multiplica- 

 tion, Division, Fraction, Involution, Evolution, 

 Equation, Series and Surd. See alfo Application 

 of yllgebra to Geometry, Binomial Theorem, Construc- 

 tion of Equations, and Reduction of Equations. 



Algebra has been alfo applied to the confideration and 

 calculus of infinites ; and from this application of it a new 

 and extenfive branch of fcience has arifen, called the 

 doctrine of Fluxions, or Analysis of Injinites, or the 

 Calculws Dijf.rentittlis. For an account of the rife and 

 progrefs of Algebra, as well as other branches of mathe- 

 ■niatics, fee the laft. and moll improved euition of Montucla's 

 Hift. des Mathem. 2 vols. 410., Paris, 1794. 



ALGEBRAICAL, fomcthing that relates to algebra. 



Thus we fay, algebraical chai-adlers, or fymbols, curves, 

 folutions, &c. An algebraical curve, is a curve, wherein 

 the relation of the ablciffes to the femioi dinates may be de- 



range. 



ALGEMISI, or ALGEM.r/EN, a fmall town of 

 Valencia, in Spain, not far from the river Xucar, near 

 which grow quantities of Pita, as it is called, or Ame- 

 rican aloes, agav^, of which the people make cordage, 

 and the Catalans fpin it of a fuiTicient tinenefs for making- 

 lace ; it is fix leagues fouth of Valencia, and five north- 

 north-weft of Gandia. 



ALGENEB, or Algenib, in Jfironwiy, a fixed ftar 

 of the fecond magnitude, on the right fide of Perseus. - 



ALGEO, or Carbon, in Geogri^)hy, a river of European 

 Turkey, which runs into the fea, eight miles w^elt-fouth-well: 

 of Olimpia, a town in the Morea. 



ALGERANCA i/land, one of the Canaries, in the 

 North Atlantic Octan. N. lat. 29=' 23'. W. long. 15^ 58'. 



ALGERI, or Aloher, a fniall peopled city of Sar- 

 dinia, fitiiatcd near a bay on the Weilem coaft. It is a 

 bifhop's fee, and has a coral-fifiiery. It is 79 miles north- 

 well of Cagliari. The bay of Algeri is fpacious and affords 

 good anchorage ; it is formed by the fouth point of Cape 

 della Caccia on the north, and by a point of land on the 

 fouth. N. lat. 40° 31'. E. lung. S-- 30'. 



ALGEZIRA, orALGERizA, a fea-port town of Spain, 

 in the proviace of Andaluiia, on the Straits of Gibraltar, and 5 

 miles weft from it. The Moors entered Spain by this town 

 in 713, and were difpoffefTed of it in 1344. It is faid to have 

 been the firll tovi'n in wliich cannon were ufed. The word 

 Algezira in Arabic fignifies an ifland, and as the harbour is 

 formed by two illands, it has been called in the plural number 

 Algeziras. It was alfo called Old Gibraltar, 'i'he har- 

 bour is now decayed, and the town lies in ruins N. lat. 36° 

 5'. W. long. 5° 20'. 



Algezira, or Alzora, is alfo a town of Spain, in the 

 province of Valencia, fituate on a fmall illand on the river 

 Xucar, 20 miles fouth of Valencia. Tliough the town is 

 fmall, its iiiken trade has been extenfive. 



ALGEZLTR, a fmall town of Portugal, in the province 

 of Algarve, at the n;outh of a fmall river near the Atlantic 

 Ocean, 17 miles north-weft of Lagos. It contains about 

 800 inhabitants. 



ALGHEMI, acounti-y of Africa, on the Slave coaft. 

 ALGHISI, Thomas, in Biography. The father of 

 this writer, who was a furgeon of eminence, at Florence, 

 took care to imbue his mind early with the principles of his 

 art. His inftrudor in anatomy was the celebrated I^aurentius 

 Bellinus. At a proper age he was made furgeon to the 

 hofpital at Florence, where applying himlelf particularly to 

 the operation of lithotomy, which he performed with An- 

 gular facility and fuccefs, he acquired confiderable reputation. 

 In 1703, he was made doftor in medicine at Padua. In 

 1707, he publidied a treatife on lithotomy, in 4to., written 

 in ItaUan, which contains, Haller fays. Bib. Chir. vol. i. 

 p. 5S0., feveral original obfervations, the fruits of his owa 

 experience. Exftat etiam, he adds, hujus Authoris, De 

 Mumia jEgyptia involuta perpulchra epillola ad Valif- 

 neiium. He died September 17 13, being only 44 years of 

 age, in confequeuce of the amputation of his left hand, 

 which had been wounded by the burfting of a tufil. 



ALGIABARII 



