43 
ALO 
ALG 
AH 
rous, There are eight species, among which 
are, 1. Aietris capensis, a native of the Cape 
of Good Hope. It is with us a stove-plant. 
The liower is pink. 2, Aietris farinosa, a na- 
tive of North America. This, though the 
most hardy plant of the genus, requires to be 
sheltered under a frame. The flowers ap- 
pear in June or July, of a whitish green co- 
lour. 3. Aietris fragrans, a native of Africa, 
and, when placed in a stove, produces fine 
spikes of white flowers in March or April. 
4. Aietris hyacinthoides, or Guinea aloe, pro- 
duces likewise white flowers when kept in 
proper warmth by a stove, in the month of 
July. 5. Aietris hyacinthoides, the Ceylon 
aloe, is -with us also a stove-plant. 
ALEXANDRIAN manuscript, a famous 
copy of the New Testament. This MS. is 
now preserved in the British Museum, It 
was sent as a present to king Charles I. from 
Cyrillus Lucaris, patriarch of Constantinople, 
by sir Thomas Rowe, ambassador from Eng- 
land to the Grand Signior, about the year 
J62S. Cyrillus brought it with him from 
Alexandria, where probably it was written. 
In a schedule annexed to it, he gives this ac- 
count: That it was written, as tradition in- 
formed him, by Theda, a noble Egyptian 
lady, about 1300 years ago, not long after the 
council of, Nice. But this high antiquity, and 
the authority of the tradition to which the 
patriarch refers, have been disputed ; nor are 
the most accurate biblical writers agreed 
•about its age. Grabe thinks that it might 
have been written before the end of the fourth 
century ; others are of opinion that it was not 
written till near the end of the fifth century, 
or somewhat later. A fac-simile was pub- 
lished by the late Dr. AYartle. 
ALEXANDRINE, a kind of verse bor- 
rowed from the French, first used in a poem 
called Alexander. They consist, among the 
French, of twelve and thirteen syllables, in 
alternate couplets; and, among us, of twelve. 
They are well characterized by Pope: 
Then, at the last, an only couplet fraught 
With some unmeaning thing they call a 
thought, 
A needless Alexandrine ends the song, 
That, Ike a wounded snake, drags its slow 
length along. Essay on Criticism. 
ALENIPHARMICS, in antient medicine, 
were properly remedies for expelling or pre- 
venting the 'ill effects of poison; but some 
having imagined that the. animal spirits, in 
acute distempers, were affected by a malig- 
nant poison, the term has been understood to 
mean medicines adapted to expel this poison, 
by the cutaneous pores, in the form of sweat. 
In this sense alexipharmics are the same as 
-eudoiilcs. 
ALFECCA, in astronomy, the star other- 
wise called Alfeta and Lucida coronas. 
ALGAE, Flags, one of the seven families, 
or natural tribes, into which the whole vege- 
table kingdom is divided by Linmvus, in 'his 
Philosophia Botanica. They are defined to be 
plants, whose root, leaf, and stem, are all one. 
Under this description are comprehended all 
•the sea-weeds, and some other aquatic plants. 
In the sexual system they constitute the third 
order of the twenty-fourth cryptogam#, 
and the fifty-seventh order in Limmis’s Frag* 
menT of a Natural Method. 
ALGAROT, or Algarel, in chemistry, 
an Arabic term for an emetic powder, pre- 
pared from regains of antimony, dissolved in 
acids, and separated by repeated lotions in 
warm water. 
ALGEBRA, a general method of resolv- 
ing mathematical problems by means of equa- 
tions: or, it is a method of performing the 
calculations of all sorts of quantities bv means 
of general signs or characters. At first, 
numbers and things were expressed by their 
names at full length; but afterwards these 
were abridged, and the initials of the words 
used instead of them ; and, as the art ad- 
vanced farther, the letters of the alphabet 
came to be employed as general representa- 
tions of all kinds of quantities; and other 
marks were gradually introduced to express 
the operations and combinations, so as to en- 
title it to different appellations. 
It has been called specious arithmetic by 
Y'ieta, on account of the species or letters of 
the alphabet, which he brought into general 
use ; and by Sir Isaac N ewton it was deno- 
minated universal arithmetic, from the man- 
ner in which it performs all arithmetical ope- 
rations by general symbols, or indeterminate 
quantities. 
Some authors define algebra to be the art 
of resolving mathematical problems: but this 
is the idea of analysis, or the analytic art in 
general, rather than of algebra, which is only 
one particular species of it. 
Indeed algebra properly consists of two 
parts: first, the method of calculating mag- 
nitudes or quantities, as represented by let- 
ters or other characters; and secondly, the 
manner of applying these calculations in the 
solution of problems. 
In algebra, as applied to the resolution of 
problems, the first business is to translate the 
problem out of the common into the alge- 
braic language, by expressing all the condi- ’ 
tions and quantities, both known and un- 
known, by their proper characters, arranged 
in an equation, or several equations if neces- 
sary, and treating the unknown quantity, 
whether it be number or line, or any other 
thing, in the same way as if it were a known 
one: this forms the composition. Then the 
resolution, or analytic part, is the disentang- 
ling the unknown quantity from the several 
others with which it is connected, so as to 
retain it alone on one side of the eduation, 
while all the known quantities are collected 
on the other side, and so giving the value 
of the unknown one. And as this disentang- 
ling of the quantity sought is performed by 
the converse of the operations by which it 'is 
connected with the others, taking them al- 
ways backwards in the contrary order, it 
hence becomes a species of the analytic art, 
and is called the modern analysis, in contra- 
distinction to the antient analysis, which 
chiefly respected geometry and its applica- 
tions. 
There have arisen great controversies and 
sharp disputes among authors concerning the 
history of the progress and improvements of 
algebra, arising partly from the partiality and 
prejudices which are natural to all nations, 
and partly from the want of a closer exami- 
nation of the works of the older authors on 
this subject. From these causes it has 
happened that the improvements made by 
the writers of one nation have been ascribed 
to those of another; and the discoveries of 
an earlier author to some one of much later 
date. Add to this also, that the peculiar 
methods of many authors have been de- 
scribed so little in detail, that our informa- 
tion derived from such histories is but very 
imperfect, and amounting only to some ge- 
neral and vague ideas of the true state of the 
arts. 
It is highly probable that the Indians or 
Arabians first invented the noble art ; for it 
may be reasonably supposed that the antient 
Greeks were ignorant of it, since Pappus, in 
his mathematical collections, in which he 
enumerates their analysis, makes mention of 
nothing like it: and he besides speaks of a 
local problem, begun by Euclid, and conti- 
nued by Apollonius, which none of them 
could fully resolve, a circumstance that could 
not have occurred had they been acquainted 
with algebra. 
Diophantus was the first Greek writer on 
algebra, who published thirteen books about 
the year 800, though only six of them were 
translated into Latin in the year 1575. This 
algebra of Diophantus only extends to the 
solution of arithmetical indeterminate prob- 
lems. Before this translation of Diophantus 
came out, Lucas de Burg©, a friar, published 
at Venice, in the year 1494, an Italian Trea- 
tise on Algebra. 1 his author refers to others 
who had preceded him, and from whom lie 
had learned the art ; but their writings have 
not come down to us. lie also assumes, that 
algebra came originally from the Arabs, and 
never mentions Diophantus, which makes it 
highly probable that his work was not even 
then known in Europe. Purge's Treatise 
goes no farther than quadratic equations. 
He was succeeded by Stifelius, who was a 
good author, but did not advance the science. 
After him came Scipio Ferreus, v Cardan, 
Tartagilla, and some others, who proceeded 
to the solution of cubic equations. • 
In 1590, Yieta introduced his specious 
arithmetic, to which we have already al- 
luded, which consists in denoting the quan- 
tities, both known and unknown, by symbols 
dr letters. To Yieta we are indebted for 
the method of extracting the roots of equa- 
tions by approximation, which has been since 
greatly improved by Raphson, Ilallev, Mac- 
iaurin, Simpson, and others. 
Yieta was followed by Oughtred and Har- 
riot: the former invented several compen- 
dious characters to show the sums, dill’er- 
ences, rectangles, squares, cubes, &c. of 
any given numbers; the latter left behind 
him his Analysis, which is highly esteemed 
•at this day. Jn 1657, Des Cartes published 
his geometry, in which lie made use of the 
literal calculus, and the algebraic rules of 
Harriot: he applied his method to the higher 
geometry, explaining the nature of curves by 
equations, and adding the constructions of 
cubic, biquadratic, and other higher equa- 
tions. 
'1 he elements of the art were compiled and 
published by„ Kersey, in 1671, in which spe- 
cious arithmetic, and the nature of equations, 
are largely explained and illustrated by a 
variety of examples. Sir Isaac Newton’s 
Arithmetira Universalis was published in 
1707, which abounds with useful and impor- 
tant instruction ; and since his time we have 
had a great number of excellent treatises on 
the subject, from almost any of which the 
science may with very little difficulty be 
learned. 
