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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
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To Fxtract the Square Loot, accordine 10 the Methoa
Suppose a a = c = 2.
For a cate anx Binomial, 25 suppole r - ]- 5
is best Eo maker == 1, (1. 0.) toche trst ROOF, Or
Side, ot rhe siven Square, becaule chen d will con-
verse rhe (OOneT.)
Then wilt rr 1 2r5 155 = a a =
Reject the Porver oF S, as beins ot lmall value
Then will rr. F 275 = 0, Or2r5 = c = r7
Divide all b7 2r; ard etien S =
eohich is che standins Theorem.
Suppose hereforer = L; then = c = 3
Make 2 n che Divitor ) 1,0 l, 5 = 5
To obviare wtich, eis much bercer ro. use etze
tollowins as, whichis Mr. Ward S.
Wtence atises chis Thectem,
dividins all Br r. F 25.
 9 
Pet chen (a5 betore) che SquATE ROBEOLZ = C
a an be required.
First, Takier = 1: Then talve che Resolvend
= 1: And som it rake L r r =. 5, there
remains. 5 =D. Make
Tochehcr = 3, adet ,3 = 5, For a secondr, in  = 2, che Divis.) . 50 (4 = 5. subseri. = S5 - B under
order For a new Operation.
Then L,5 ische newr, che Square oF Wetich, is
2, 25 ==rr; Trom which Subtract 2 = c because
2 i5 lels char 2, 25, and vis Aand chus.
48 = r5 ] = 5S Eche Cypher
Di. = r L 5= 1, 4) 20 (20 (1, =5
145 = r 5 ] =55
Let S beFOr == 2, 2nd r -]- 5 = a.
Are AI by 2; chen ris : r5. = 55
C
of Convergins series.
Y = 23 23
da
Themrr I 215(55=
iie lcten, al 10 2d
27 = D, ic Dividend.
11. - 8 1 5 = l, 4 11 5500 (3 = 5
4234,3 = rd 2dd
2r = 3)0, 25
Which mustbe dividedbr 2r = 3, and che Ouo-
tiene will bc--. 083 =S; erhich havins a dese-
etive sien, must be subcracted trom the last
et ae  14l3) 12633010
113072 =r5 F :55
r = 5 = 1, 4138) 1347800 (9 = 5
e
127246, 5 =75 7255
2,41389) 7533500 (5 =5
9069462,5 = r5 )= =55
38:
2341
  25 5693. 40403133 d
ies Square beins 2,007669 =r r, (as beloe8led
cex Mhan 2 = c.) Lalie 2=c tolu llllo.
Lhis ROOE a == 1, 413895 ditters ton ne 1O-
met RoOr Found, bur by 0,000022 (a lictle more
TalI 2050 3) FOr no exaet Roor can befound by ei-
Which will Be a neirr, For a chird Operation; anc
2,007883
cher waz.
Flere also, is more exactnels had been required,
ehe Remainder enelcaleuo) Csptiers, migtie have
been inade a ne Diridend, and 1, 4r3895 a new
Divitor; and (o rou may proceed on a5 Far 25 YOU
Lcablo. 607689 = 5.
Wrhich beins divided by ervice chelater, = 2,654
sives in che DuOtIeHE =. 002783 = 5; and chis
S subrracted trom che last
Former, any one ill soon sind chac rill eer borh.
19 4l7
30278:
chir HC.
The vast Adrantase of ehis Method aborertic
2,414217 = a
An Lxamole ofsus, in a true square uet
Wrhich sires the ROOE +0 7 placeS AE FhrCC O pera.
FIONS.
Buc if more exactnels be necellarr, call ic a
nerr, tor a tourch Operacion, une procced julta5
betore.
N. B. This Method, which iS MT. Raphson S,
is very precer, buc ic labours under cvo Inconre-
niencies, viz. The creaness of the Divisors, andihe
bigh Involutions; especiallr in extractins ROOrS OuE
OE hieher POWerS, aS che Cube, Bequad st
Foret, a.
ThCSquare ROCC O 133LL3, noLeScntCla,
66612,2 = = C.
43 5 =
=r == 3) 216 (6
198 = r5 ] E5S
0) 1812,5
1812,5 =75 ] -55
0000,0
Therctore, a = 365.
SQCIARHIC