ALGA:, in botany, an order or division of the Cryptogamia class of plants. It is one of the, seven families or natural tribcs into which the vegetable kingdom is dis tributed, in the Philosophia Botanica of Linnzeus; the 57th order of his fragments of a natural method.
The plants belonging to this order are &scribed as having their root, leaf, and stem, entire, or all one. The whole of' the sea-weeds, and various other aquatic plants, are comprehended under this di vision. From their admitting of little dis tinction of root, leaf, or stem, and the parts of their flowers being equally inca pable of description ; the genera are dis tinguished by the situation of what is sup posed to be flowers or seeds, or by the resemblance which the wfiole plant bears to' some other substance. The parts of fructification are either found in saucers and tubercles, as in lichens ; hol low bladders, as in the Ind ; or dispersed through the whole substance of the plants, as in the ulvx. The substance of the plants has much variety ; it is flesh-like or lea ther-like,membranaceonsor fibrous,jelly like or hormlike, or it has the resem blance of a calcareous earthy matter.
Lamarck distributes the algx into three sections : the first comprehends all those plants, whose fructification is not Nips., rent, or seemsdoubtful. common ly live in water, orupon moist bodies, and are membranous, gelatinous, or filamen tous. To this section Ile refers the byssi, confen it, ulva, tremella, and varee. 'The plants of the second section are distin guished by their apparent fructification, though it be little known, and they' are forniLd of' parts which have no particu lar and sensible opening or explosion, at any determined period ; their substance is ordinarily crustaceous or coriaceous. l'hey include the tassella, ceratosperma, and lichen. The third section compre hends plants which have their fructifica ton very apparent, and distinguished by constituent parts, which open at a certain pcnod of maturity, for the escape of the fecundating dust or seeds. These plants are more herbaceous, as to both their sttbstance and their colour, than those of the 0111er two sections, and are more near ly related tothe mosses, from which they do not e•ssentially differ. Their flowers are oftencontained in articulated and ve ry elastic filaments. To this section are referred the riccia, Iblasia, anthoceros, targioA hepatica, and junger-manna. In the Linnxan system the algw are divided into two classes, viz. the terrestres and aquaticze. The former include the an thoceros, blacia, riccia, lichen, and bys sus ; and the latter are the ulvarneus, and eonferva. The fructification of the algx, and particularly of' those called aquaticx, is denominated, by a judicious botanist, the opprobrium botanicorum. ALGAROTH. See.ANximox Ir. ALGEBRA, a general method of re solving mathematical problems by means of equations ; or, it is a method of computation by symbols, whichhavo hem invented for expressing the quantities that are the objects of this science, and also their mutual relation and depen dence. These quantities might, proba
bly, in the infancy- of the science, be de noted by their names at full length ; these, hieing found inconvenient, were succeeded by abbreviations, or by their mere initials; and, at length, certain let ters of the alphabet were adopted as ge neral representations of all quantities ; other symbols or signs were introduced, to prevent circumlocution, and to facili tate the comparison of various quantities with one another; and, in consequence of the use of letters or species, and other general symbols, or indeterminate quan tities, algebra obtained the appellation of specious, literal, and universal arithmetic. The origin of Algebra, like that of other sciences of ancient date and gradual pro gress, is not easily ascertained. The most ancient treatise on that part of ana blies, which is properly called algebra, now extant, is that of Diophantus, Creek author of Alexandria, who flou rished about the year of our Lord 350, and who wrote 13 books, though only six of them are preserved, which were printed, together with a single imperfect book on multangular numbers, in a Latin translation by Xylander, in 1575, and afterwards in Creek and Latin, with a comment, in 162.1 and 1670, by Caspar !Sachet, and 241. Fermat, Tolosx, fol. These books do not contain a treatise on the elementary parts of algebra, but merely collections of some difficult ques tions relating to square and cube num bers, and other curious properties of numbers, with their solutions. Algebra, however, seems not to have been wholly unknown to the ancient mathematicians, long before the age of Diophantus. - We observe the traces and effects of it in many places, though it seems as if they had intentionally concealed it. Something of it appears in Euclid, or at least in Thcon upon Euclid, who observes that Plato had begun to teach it. And there are other instances of it in Pappus, and more in Archimedes and Appollonius. But it should be observed, that the ana lysis used by these authors is rather ge ometrical than algebraical ; this appears from the examples that occur in their works ; and, therefore, Diophantus is the first and only author among the Greeks who has treated professedly of algebra. Our knowledge of the science was deri ved, not from Diophantus, but from the Moors or Arabians* but whether the Creeks or Arabians were the inventors of it has been a subject of dispute. It is probable, however, that it is much more ancient than Diophantus,becauae his trea tise seems to refer to works similar and prior to his own.
Algebra is a peculiar kind of arithme tic, which takes the quantity sought, whether it be a number, or a line, or any other quantity, as if it were granted ; and by means of one or more quantities given, proceeds by a train of deductions, till the quantity at first only supposed to be known, or at least some power of it, is found to be equal to some quantity or quantities which arc known, and conse quently itself is known.
Algebra is of two kinds, numeral and literal.