ALGEBRA. 
are more herbaceous, as to both their sub- 
stance and their colour, than those of the 
othe'r two sections, and are more nearly 
related to the mosses, from which they do 
not essentially differ. Their flowers are 
often contained in articulated and very elas- 
tic filaments. To this section are referred 
the riccia, blasia, anthoeeros, targiona, hep- 
atica, and junger-manna. In the Linnaaan 
system the algae are divided into two classes, 
viz. the terrestres and aquatic®. The for- 
mer inc ! nde the anthoeeros, blasia, riccia, 
lichen, and byssus: and the latter are the 
u!va, fucus, and conferva. The fructifica- 
tion of the algae, and particularly of those 
called aquaticae, is denominated by a judici- 
ous botanist, the opprobrium botanicorum. 
ALGAROTH. See Antimony. 
ALGEBRA, a general method of resolv- 
ing mathematical problems, by means of 
equations ; or, it is a method of computation 
by symbols, which have been invented for 
expressing the quantities that are the ob- 
jects of this science, and also their mutual 
relation and dependence. These quantities 
might, probably, in the infancy of the 
science, be denoted by their names at full 
length; these, being found inconvenient, 
were succeeded by abbreviations, or by their 
mere initials ; and, at length, certain letters 
of the alphabet were adopted as general re- 
presentations of all quantities ; other symbols 
or signs were introduced to prevent circum- 
locution, and to facilitate the comparison of 
various quantities with one another ; and, in 
consequence of the use of letters or species, 
and other general symbols, or indeterminate 
quantities, 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 analytics, 
which is properly called algebra, now ex- 
tant, is that of Diophantus, a Greek author 
of Alexandria, who flourished about the 
year of our Lord 3 >0, and who wrote 13 
books, though only six of them are preserved, 
which were printed together with a singie 
imperfect book on multangular numbers, in 
a Latin translation by Xylander, in 1675, 
and afterwards in Greek and Latin, with a 
Comment, in 1621 and 1670, by Gaspar 
Bachet, and M. Fermat, Tolosae, fol. These 
books do not contain a treatise on the 
elementary parts of algebra, but merely 
Collections of some difficult questions relat- 
ing to square and cube numbers, and other 
curious properties of numbers, with their 
solutions. Algebra, however, seems not t* 
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 Theon 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 analysis 
used by these authors is rather geometrical 
than algebraical ; this appears from the ex- 
amples that occur in their works ; and, there- 
fore, Diophantus is the first and only author 
among the Greeks who has treated profes- 
sedly of algebra. Our knowledge of the 
science was derived, not from Diophantus, 
but from the Moors or Arabians ; but whether 
the Greeks or Arabians were the inventors 
of it has been a subject of dispute. It is pro- 
bable, however, that it is much more an- 
cient than Diophantus, because his treatise 
seems to refer to works similar and prior to 
his own. 
Algebra is a peculiar kind of arithmetic, 
which takes the quantity sought, whether it 
be a number, or a line, or any other quan- 
tity, 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 are known, 
and consequently itself is known. 
Algebra is of two kinds, numeral and literal. 
Alg ebr a, numeral or vulgar, is that which 
is chiefly concerned in the resolution of 
arithmetical questions. In this, the quan- 
tity sought is represented by some letter or 
character ; but all the given quantities are 
expressed by numbers. Such is the algebra 
of the more ancient authors, as Diophantus, 
Paciolus, Stifelius, &c. This is thought by 
some to have been an introduction to the 
art of keeping merchants’ accounts, by dou- 
ble entry. 
Algebra, specious or literal, or the new 
algebra, is that in which all the quantities, 
known and unknown, are expressed or re- 
presented by their species, or letters of the 
alphabet. There are instances of this me- 
thod from Cardan, and others about his 
time ; but it was more generally introduced 
and used by Vieta. Dr. Wallis apprehends 
that the name of specious arithmetic, ap- 
plied to algebra, is given to it with a refer- 
ence to the sense in which the Civilians use 
