SUR 
surds are commensurable in power, and by 
being multiplied into themselves, give at 
lengtli rational quantities ; yet compound 
surds multiplied into themselves, commonly 
give still irrational products. But when 
any compound surd is proposed, there is 
another compound surd, which, multiplied 
into it, gives a rational product. Thus, if 
^ a ^ 6 were proposed, multiplying it 
by v' u — s/ f**® product will be a — b. 
The investigation of that surd, which, 
multiplied into the proposed surd, gives a 
rational product, is made easy by three the- 
orems, delivered by Mr. Maclaurin, in his 
Algebra. 
This operation is of use in reducing surd 
expressions to more simple forms. Thus, 
suppose a binomial surd divided by ano- 
ther, as SO ^ 12, by \/ 5 — \/ 3> 
the quotient might be expressed by 
^ 20 4- V . jjut this might be ex- 
V 5 — v/ 3 
pressed in a more simple form, by multi- 
plying both numerator and denominator, 
by that surd, which, multiplied into the de- 
nominator, gives a rational product : tlius, 
V20-f-v/12_V^<Hryi!:? ^ «/3+‘/3 _ 
V 5 — \/~3 ^5 — ^3 ^ 
v'ToO-f 2v'60-f 6_16 + 2 v/ 60_ j, , 
5—3 “2 , ‘ 
2 s/ 15. 
When the square root of a surd is re- 
quired, it may be fmmd, nearly, by extract- 
ing the root of a rational quantity that ap- 
proximates to its value. Thus, to find the 
square root of 3 -f- 2 v 2, first calculate 
,/ S— 1,41421. Hence S -\-S </ 2 = 
6,82842, the root of wliich is found to be 
nearly 2,41421. 
In like manner we may proceed with 
any other proposed root. And if the in- 
-dex of the. root, proposed to be extracted, 
be great, a table of logarithms may be 
used. Thus, \/ IT may be most 
conveniently found by logarithms. 
Take the logarithms of 17, divide it by 
13 ; find the number corresponding to the 
tjuotient ; add this number to 5 : find the 
logarithm of the sum, and divide it by 7, and 
the number corresponding to this quotient 
will be nearly equal -to \/^ 5-1-^ 17. 
But it is sometimes requisite to express 
the roots of surds exactly by other surds. 
Thus, in the first example, the square 
rootof34-2v/ 2isl-f-v/2: fGrT4v2 X 
a-f-V2=:l4-2^/2-l-2 = 3-l-2v'2. 
SUR 
For the method of performing this, the 
curious may consult Mr. Maclaurin’s Al- 
gebra. 
SURETY of the peace. A justice of the 
peace may, according to his discretion, bind 
all those to keep the peace who, in his pre- 
sence, shall make any affray, or shall threat- 
en to kill or beat any person, or shall con- 
tend together in hot words ; and qll those 
who shall go about with unlawful weapons, 
or attendance to the terror of the people ; 
and all such persons as shall be known by 
him to be common barrators ; and all who 
shall be brought before him by a consta- 
ble, for a breach of the peace in the pre- 
sence of such constable ; and all such 
persons yvho having been before bound 
to keep the peace, shall be convicted of 
having forfeited their recognizance. When 
surety of the peace is granted by the Court 
of King’s Bench, if a supersedeas come 
from the Court of Chancery to the justices 
of that court, their power is at an end, and 
the party as to them discharged. 
If surety of the peace be desired against 
a peer, the safest way is to apply to the 
Court of Chancery or King’s Bench. If the 
person against \vliom security of the peacer 
be demanded be present, the justice of the 
peace may commit him immediately, unless 
he offer sureties ; and dfoi'tiori he may be 
commanded to find sureties, and be com- 
mitted for not doing it. 
SURGERY is that division of the healing 
art, which is chiefly conversant with the 
treatment of the external and local disorders 
of the body, of the effects of accidental 
injury, and of such diseases in general as 
are curable by manual operation. Yet its 
field is not entirely confined to the depart- 
ment just alluded to ; since local disorders, 
and particularly accidents, often affect the 
whole frame, so as to induce a general de- 
rangement of the constitution ; and again, 
diseases of parts arise out of constitutional 
affections, or, although originally inde- 
pendent, may be greatly aggravated by 
them. Hence it is obviously necessary that 
tlie surgeon should be acquainted with the 
nature and treatment of such general dis- 
orders ; and consequently, in marking out 
the limits, which divide the departments of 
the surgeon and physician, it is hardly possi- 
ble to attain sucli a pitch of accuracy as to 
prevent all supposed encroachment of ei- 
ther side on the province of the other. 
The care of the external and local affec- 
tions of the human body was, in the infancy 
of science, a branch of the art of medicine. 
