algebra

[In Sw., Dan., Dut., Ger., Sp., Port., and Ital. algebra, Fr. algèbre. Evidently all from Arabic. Many etymologies from this language have been given. It has been taken from the Arabic phrase, al jebr e al mokabalah restoration and reduction ( Penny Cyclo.). This view is e entially adopted by Wedgwood, who spells the phrase el jabr wa el mogabala, and renders it = the putting together of parts, and equation.] What Sir Isaac Newton termed universal arithmetic. The department of mathematics which enables one, by the aid of certain symbols, to generalise, and therefore to abbreviate, the methods of solving questions relating to numbers. was not till a late period that the Greeks be It came acquainted with algebra, the celebrated treatise of Diophantus not having appeared till the fourth century, A.D. The science came into Western Europe through the Arabs, who probably derived it from the Hindoos. It conducts its operations by means of alphabetical letters standing for symbols of numbers, and connecting signs (+-, .) representative of arithmetical proce es. Of the letters, those near the commencement of the alphabet a, b , c, d, . generally stand for known quantities; and those towards its endx, y, and z-for unknown ones. One of the most important operations in algebra is the solution of what are called equations a beautiful and interesting proce which, without tentative gue es of any kind, fairly reasons out the number or numbers for which one or more unknown quantities stand. "The Greek Algebra was as nothing in comparison with the Greek Geometry; the Hindu Geometry was as little worthy of comparison with the Hindu Algebra."- l'alcutta Review , ii. (1846), p. 540. Double Algebra : A term introduced by Prof. De Morgan for a kind of algebra, which he thus defines: " Signification of Symbols in Double Algebra, -This particular mode of giving significance to symbolic algebra is named from its meanings requiring us to consider space of two dimensions (or area), whereas all that ordinary algebra requires can be represented in space of one dimension (or length). If the name be adopted, ordinary algebra must be called single." De Morgan: Trigonom. and Double Algebra (1849), c. v., p. 117.