A L G 



A L G 



Unity of God." But he was fufpecSed of hcrefy, and one 

 of liis ]iieces, entitled, " the Rtfurreftion of tlic Law of 

 Science," was condemned after liis dectafe, bctaiife it ccn- 

 fured iome of the indiil.';cnces of the Iflamitic law ; and if 

 any copy of it was foiuid within the Saiaceii empire, it was 

 ordered to be burned. He alfo wrote a treatife " On the 

 Opinions of Plsilofophers ;" and another, entitled, " The 

 l^cflruction of Philoiophers." After living in great fplen- 

 donr as a public preceptor at Bagdat, he diibibuted his 

 riches among the poor, allumed ll\e habit of a hermit, and 

 retired to Mecca. From Mecca he travelled into Syria 

 and Egypt, and (laying fome time at Cairo, and after- 

 wards at Alexandria, he returned to Bagdat, where he 

 died. Pococke Spec. Hid. ;\rab. p. 371. Ilerbelot, 

 p. ^6z. Leo Afr, c. 12. Brnekcr's Hift. Phil, by En- 

 field, V. ii. p. 243. 



Ai-GAZici., in Zoology. See Antilope. 



ALGEBRA, a general method of refolving mathemati- 

 cal problems, by means of equations : or, it is a method of 

 computation by fyrabols, which have been invented for ex- 

 preffing the quantities that are the objects of tliis fcicnce, and 

 alio their mutual rcUitiou and dependence. Thefe quantities 

 might probably, in the infancy of the fcience, be denoted by 

 their names at full length ; thele, bcl^g found inconvenient, 

 were fucceeded by abbreviations, or by their meie initials. 

 And, at length, certain letters of the alphabet were adopted 

 as general reprefentatlons of all quantities ; other fymbols or 

 figns were introduced to prevent circumlocution, and to fa- 

 cihtate the comparifon of various quantities with one an- 

 other ; and, in confequcnce of the ufe of letters or fpeeies, 

 and other general fymbols, or indeterminate quantities, al- 

 gebra obtained the appellation of fpcc'wus, liicral, and un'i- 



I'Hrfal ARITHMETIC. 



The ter]T>, algebra., is of Arabic original ; but its etymo- 

 logy has been varioudy affigned by different writers. Among 

 the Arabians, from whom it was immediately tranfmitted to 

 us, this fcience was denominated al-giabr almocatuhih ; and 

 as giabara fignifies to rcjlore, and kabala to compare or to op- 

 fofe, the nouns formed from thefe words, with the prefix al, 

 denote the fcience of rejlttution and comparifon, or nfolution 

 and equation ; and thus underftood, they exprefs its nature 

 with fufficient prectfion. Accordingly, Lucas de Burgo, 

 tlie fird European author on algebra, calls it the ru/e of rc- 

 Jloration and cppo/lllo-n. Others, however, have derived it 

 from Gebtr, either the name of a celebrated mathematician, 

 to whom they aferlbe the invention ot the fcience ; or from 

 the v/ord gcbcr, which forms, with the particle al, tlie appel- 

 lation algc'lra, fignifving, according to Golius, in his Arabic 

 lexicon, a reduction of broken numbers or fractions to inte- 

 gers. Herbelot fays, that gcher or gibr is never ufed by the 

 Arabs for algebra, without adding the word mokahelah ; but 

 Dr. RuITjU ("Hilf. Aleppo, v.ii. 107. )obferves, that, at Alep- 

 po, and alfo in books, rt/G/Z^r is ufed fometimes alone, as well 

 as in conjunftiuu with mohabelah. This fcience has been dif- 

 tinguiflied by other names, b;fides algebra. Lucas de Burgo 

 calls it V arte magiore, or the greater art, by way of contra- 

 diftindlion to common arithmetic, which is denominated I'arte 

 minorc, or tlie lefer art. The Italians called it resrcla de la 



coja, or ret; cofa with them fignifying 



or thing, and 



being ufed in the fame fenfe with radix, or root ; whence 

 proceeded the terms rule of cofs, and coffic numbers, denot- 

 ing the root, fquare, cube and other powers. Other Italian 

 and Latin vvnters have called algebra regula rei et cenftis, or 

 the rule of the root and iquare; ce:</'.is being ufed feir im- 

 provement, or the fquare. By a corruption of ceiifus were 

 formed zenzus, for the fquare, and the term zenzic applied 



to the fquare root. Hence alfo the charaAers "C,, 3, l^, 

 deduced from the letters r, z, c, became the lyjiboi.* uf 

 res, ZWCI/J-, ar.d cuius; or, in our mode of cxprdfion, I'le 

 root, fquare and cube; jufl as R and >^' , formed from /?, 

 /•, arc with us the figns of radicality, Waiiis's Algebra, 

 c. i. p. 3. 



Some authors have defined algebra, as the art of refolving 

 nuithcmatlcal problems; but this is rather the idea of An.\- 

 LYSis, or the analytic art in general, than of algebra, which 

 is only a particular branch of it. Algebra, duly confidered, 

 confilts of two parts, vi%. the method of calculating magni- 

 tudes or quantities, reprefeiited by letters or other charac- 

 ters, and the mode of applying thefe calculations to the fo-« 

 lutie.n of problems. \\'hen algebra is applied to the folution 

 ot problems, all the quantities that are involved in the prob- 

 lem are exprefTed by letters, and all the conditions that fervc 

 to denote their mutual relation, and by which they are com- 

 pared with one another, are fignlfied by their aiiproprlatc 

 characters, and they are thus thrown into one or more equa- 

 tions, as the cafe requires : this is called fy.ithcfis, or comi)0- 

 fition. When tills has been dune, the unknown quantity is 

 difengaged by a variety of analytical operations from thofe 

 that are known, and brought to ftand alone on one fide of 

 the equation, whilll the known quantities are on the other 

 fide; and thus its value is inveHlgated and obtained. This 

 procefs is called analyfis or refoliitlon : and hence algebra is 

 a fpeeies of the analytic art, and is called the modern analyfis, 

 in contradillindion to the ancient analyfis, which chiefly re- 

 garded geometry and its application. 



The origin of algebra, like that cf other faiences of ancient 

 date and gradual progrefs, is not eafily afcertained. The 

 molt ancient treatiie on that part of analytics, which is pro- 

 perly called algebra, now extant, is that of Diophantus, a 

 Greek author of Alexandria, who flouriihed about the year 

 of our Lord 350, and who wrote 13 books, though only fix 

 " Arithmeticorum," of them are prefervcd, which were 

 printed together with a fingle imperfetl book on multangu- 

 lar numbers, in a Latin trandation by Xylander, in 15 7 J, 

 and afterwards in Greek and Latin, with a Comment, in 

 1 62 1 and 1670, by Gafpar Bachet, and M. Fermat. Tolofje, 

 fol. Thele books do not contain a treatife on the elementary 

 parts of algebra, but merely colleftions of fome dltfiiult quef- 

 tions relating to fquare and cube luunbers, and other curious 

 properties of numbers, with their folutlons. In his prefatory 

 remarks, addrefltd to oneDionyUus, forwhofe ufcDlophautua 

 probably wrote, he recites trie names and generation of the 

 powers, the fquare, cube, 4th, 5th, 6th, &c. \vhich he calls 

 dyuamls, cubus, dynamodinamis, dynamocubns, cubocubus, 

 according to the fum of the indices of the powers, and he 

 marks thofe powers with the Greek initials ; and he ex- 

 preffes the unknown quantity by ajiS/^c,-, or the number, 

 fimply marking it in the folutions by the final or, and denot- 

 ing the monades, or indefinite unit, by ^''. In his refcarchcs 

 on the multljilication and divlfion of fimple fpeeies, he (hews 

 what powers they produce, and obferves that minus (/.<i4-if) 

 multiplied by minus, produces plus (i«rap|.v), and that minus 

 multiplied by plus produces minus : the mark which he ufes 

 for minus is \ or the 4- inverted and curtailed ; but he has 

 no mark for plus, exprelFmg it by a word or conjunftlve co- 

 pulative. Suppofing his reader acqnainte<! with the common 

 operations, viz. addition, fubtraftion, multlphcaliou and di- 

 vifion of compound fpeeies, he proceeds to remark on the 

 preparation of the equations that arc deduced from the 

 quellions, which we call reduilion of equations, by collect- 

 ing like quantities together, adding quantities that are minus, 

 and fubtrafting thofe that are plus, called by the moderns 



tranfpoiition. 



