53 
A L I 
A L G 
A L t 
equation of « dimensions being i, the second 
term may be taken away, by supposing x — y 
± —A 
tl 
Car. 2. The second term may be taken away 
by the solution of a simple equation, the third 
by the solution of a quadratic, and so on. 
Prop. III. An equation may be transformed 
into another, of which the roots shall be equal 
to the roots of the given equation, multiplied or 
divided by a given quantity. 
.Let y — xe, or y — — . 
e 
Then substitute for a- and its powers, or 
e 
ye and its powers, and the new equation will 
have the property required. 
Cor. 1. An equation, in which the co-efficient 
©f the first term is any known quantity, as a, 
may thus be transformed into another, in which 
the co-efficient of the first term shall be unit. 
Thus, let the equation be ax 3 — p.x 2 qx — r 
Suppose y — ax, or x — — , and for x and 
a 
. . V 
its powers insert — and its powers, and the 
' a 
equation becomes — < 4- — r — 0, 
a 2 a" a 
Or y 3 — py 2 -[- qay — a 2 r — 0. 
Cor. 2. If there are fractions in an equation, 
they may be taken away, by multiplying the 
equation by the denominators, and by this pro- 
position the equation may then be transformed 
into another, without fractions, in which the 
co-efficient of the first term is 1. In like man- 
ner may a surd co-efficient be taken away in 
certain cases. 
Cor. 3. Hence also, if the co-efficient of the 
second term of a cubic equation is not divisible 
by 3, the fractions thence arising in the trans- 
formed equation wanting the second term, may 
be taken away by the preceding corollary. But 
the second term also may be taken away, so that 
there shall be no such fractions in the trans- 
formed equation, by supposing x — 
« +P 
3 5 
-j~ p being the co-efficient of the second term 
of the given equation. And if the equation 
ax 3 — px l -}- qx — r — 0 be given, in which p 
is not divisible by 3, by supposing x ~ — 
the transformed equation reduced is z 3 — 
-j- 9 aq X x — 2 p 3 -J- 9apq — 7 a 2 r z=z 0 ; 
wanting the second term, having 1 for the co- 
efficient of the first term, and the co-efficients 
of the other terms being all integers, the co-effi- 
cients of the given equation being also supposed 
integers. 
General Corollary to Prop. I, II, III. 
If the roots of any of these transformed equa- 
tions be found by any method, the roots of the 
original equation, from which they were de- 
rived, will easily be found from the simple equa- 
tions expressing their relation. Thus, if 8 is 
found to be a root of the transformed equation 
z "4” c 2i 
z 3 -j- 23z — 696 ~ 0. Since x — — ' — , the 
5 
corresponding root of the given equation 
8 | c 2 
Sx 3 — 6x 2 -\-7x — 30 rz: 0, must be — y— zzz2. 
i! is to be observed also, that the reasoning in 
Prop. II. and III, and the Corollaries, may be 
extended to any order of equations, though in 
them it is applied chielly to cubics. 
From the preceding principles and operations, 
rules may be derived for resolving equations of 
all orders, 
ALG ENEB, a fixed star of the second 
magnitude, On the right shoulder of the con- 
stellation Perseus. 
ALGOL, the namh of a fixed star of the 
second magnitude in the constellation Per- 
seus, otherwise called Medusa’s head. 
This star has been subject to singular va- 
riations, appearing at different times of diffe- 
rent magnitudes, from the fourth to the se- 
cond, which is its usual appearance. It has 
been conjectured that the cause of this varia- 
tion is owing either to the interposition of a 
large body revolving round Algid, or to some 
motion of its own, in consequence of which 
part of its body, covered w itii spots, is peri- 
odically turned towards the earth. The pe- 
riod of variation is said to be 2d. 20h. 49' 2". 
ALGOME1ZA, a name given to the star 
Procvon. 
ALGOR, among medical writers, a term 
used to denote an unusual coldness or chil- 
ness in any part of the body. 
ALGORAB, a fixed star of the third mag- 
nitude, in the right wing of Corvus. 
ALGUAZIL, in the Spanish policy, an 
officer whose business it is to see the decrees 
of a judge executed. 
ALllABOR, among the Arabians, is the 
star which we call Sirius. 
ALHIRTO, a fixed star of the third mag- 
nitude, in the constellation Capricorn. It 
is sometimes called rostrum gallincE. Near 
this star, in the year 1600, appeared a new 
star, which lasted 21 years, and then disap- 
peared again. 
ALIAS, in law, a second or farther writ 
issued from the courts of Westminster after 
a capias , Sec. has been sued out without 
effect. 
Alias Dictus, the legal description of a 
person known by two or more names. 
ALIBI, denotes the absence of the accused 
from the place where he is charged to have 
committed the crime. 
ALIDES, among the Mahomedans, a de- 
signation given to the descendants of Ali ; 
between whom and the Ommiades there was 
a warm dispute about the kaliphate. 
ALIEN, in law, a person born in a strange 
country, not within the king’s allegiance, in 
contradistinction from a denizen, or a natural 
subject. See Denizen. 
An alien is incapable of inheriting lands in 
England, till naturalized by an act of parlia- 
ment. No alien is entitled to vote in the 
choice of members of parliament, nor can 
enjoy an office, or be returned on any jury, 
unless where an alien is party in a cause ; atul 
then the inquest of jurors shall be one half 
natives and the other aliens. 
The issue of an English woman, bv an alien, 
born ’abroad, is an alien in law. But if an Eng- 
lishman, living beyond sea, marry a wife there, 
and have children born abroad, they are de- 
nizens, and shall be heirs to their father. 
Aliens can have no heirs, strictly so called, 
because they have not in them any heritable 
blood; yet natural-born subjects may inherit 
as heirs to their ancestors, even though their 
ancestors were aliens. 
If an alien is made a denizen by letters 
patent, and then purchases lands, his son be- 
fore his denization shall not inherit ; but a 
son born afterwards may inherit, even though 
the elder brother be living. Blacks. 
Every foreign seaman serving on board an 
English ship two years in time of war is natu- 
ralized. 
Masters of ships arriving from foreign parts 
are to give notice at every port of the num- 
ber and names of all foreigners on board, 
under a penalty of JO/, for each alien whose 
name is omitted; 33 Geo. Hi. c. 4. And 
by the 42d Geo. 111. c. 22, commonly called 
the alien bill, iiis majesty may issue a procla- 
mation ordering' aliens out of the kingdom, 
and in case ot disobedience, the alien tor the 
first offence shall suffer imprisonment for one 
month, and for twelve months for a second 
offence, being liable to transportation for life 
for the third. Secretaries of state may grant 
warrants for conducting such aliens "out of 
the kingdom as they apprehend will not pay 
due obedience to the proclamation. 
Alien-duty, an impost laid on all goods 
imported by aliens, over and above the cus- 
toms paid tor such goods imported by British 
and on British bottoms. 
Alien-priories, a kind of inferior mo- 
nasteries, formerly very numerous in Eng- 
land, and so called from their belonging to 
foreign abides. 
ALIENABLE, denotes something that 
may be alienated. 
All estates are alienable, except those in 
tail and for life : a bond too, with condition 
not to alien, is said to be good. 
ALIENATION, in law, denotes the act 
of making over a man’s property in lands, 
tenements, &c. to another person. 
To alien or alienate in fee, is to sell or 
convey the fee simple of lands, &c. 
Alienation, in mortmain, is making over 
lands, tenements, &c. to a body politic, or to 
a religious house, for which the king’s licence 
must first be obtained, otherwise the lands, 
&c. alienated, will be forfeited. See Mort- 
main. 
Alienation of crown lands is always sup- 
posed to be made under a faculty of perpe- i 
tual redemption. 
A perpetual copy-hold is also a kind of j 
alienation. 
Alienation, in Roman antiquity, was 
used for a father’s discarding a son in his 
own life-time. 
Air e n at i o N-q^// cc, is that to which are 
carried all w rits of covenants iind entry upon 
which fines are levied, in order to have lines 
for alienation set upon them. 
ALIMENT, among physicians, denotes 
whatever is capable of nourishing the human 
body. Aliment is either animal or vegetable’ 
of an attenuating or incrassating nature ; and 
with respect to tire taste, is sweet, fat, acid, 
astringent, salsuginous, bitter, and acrid. 
AL I M EN TA il\ duct, a name by which 
some call the intestines, on account of the 
food passing through them. See Anatomy. 
Alimentary duct is sometimes also used tor 
the thoracic duct. 
Alimentary children, in Roman anti- 
quity, an appellation given to those educated 
in houses not unlike our "hospitals, erected for 
that purpose. There were likewise alimen- 
tary girls, who owed their maintenance to 
the bounty of several empresses, as the boys 
did theirs to that of the emperors. 
Alimentary law, among the same 
people, that whereby children were obliged 
lo maintain their aged parents. 
ALIMONY, in law, denotes the main- 
tenance sued for by a wife, in case of separa- 
tion from her husband, wherein she is neither 
chargeable with elopement nor adultery. 
Anciently this was recoverable only in the 
spiritual courts, but at present may be obtain- 
ed in chancery. 
ALIPILARIUS, or Alipilus, in Roman 
