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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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Z
quor just boil, and chen prets it hor chro a Cloch;; in ererr Memiber bB, 2b AC, 3c A Bd 4
altex ehis, craporare che siltered Liquor to iis due ehe Sum of che FxponeHE OE he Capital Letters
Consistence.
15 4. (Phere ic mar becaken norice, ot, Thac b
THus are the Fxtracts oE Rhubarb, Centian, the Exponent OF a Letter, is meane the Number
WorinWvood, (9c. made.
erhich expresses irhat place ic has in the Alpracl
LXTRA Fudiciat, in Lam, is irhen Judo- Thus a is che Lxponent ot che Lecrer V.) Elend
ment is giren in a C ause or Casc nor dependins inis derired chis Rule For tindins che Capical Lerrers
thac Coure where such fndsmenris siren, or Where. OF all che Members char belons ro any Porer.
in che Fudge has nor furildiction.
EXTRACTION, is a separarins oF Etie subrle
Parr oF a mixed Body, Trom che more srols: FOF
Fxample, When che Scrensch ot any Medicine is
Fixcracted by Spirir of Wine, thac wrhich is lete af-
rer the craporation oE he Menstruum is called che
Fxtract.
EXTRACTIONof Roots, in MachemarickS, is
the method ot tindins our cherrue ROOEOF any
Number orOuanciey siren. See Square Root, Cube
ROOt, _CC.
In Philos. FranC. DF 240. The Ingenious Mr. ABF.
de Moirre sives thefollomins method os Pxeractine
ehe R00t os an Insinite E quation.
PHFOR P M.
1E aZ F b3 Y c2-F d5 + ez
_c. = 5y  By2 -  i 92 ) k yt.  1gr +
_c.
Then Wvill ZbC = 5. y 1
i - 2b AB =c _,, ,. L =bB =2b 4
=30 A B = aA, , 1 = 2bBC = 2bAD
= 3C AB. = 3cd. C = +d N B cA
m= 2bBD = b CC = 2 b AF cB:
ScABC - 3CA D = 6 d A B = 4 d A
C=3e A B =5N y ec.
Combine che Capical Lesters as osten as gou ean
matee the Sum of the Fxponents equal 50 the In-
dox of ibe Porer co mhich chey belonz.
S. That ite Exponents ol ihe lame L etcers whicti
are irricren betore ihe Capitals, exprels hion mans
Capicals chere are in each Member.
6. Thac che Numeral Figures ox Vncia charoceur
in Thele Members, exprels che number oF Permu-
cacions Wrhich the Capiral Letrers oF each Member
are capable ot.
For rtie Demonstration or ihis,
Sippose Z = A y L By  C y  3, a
Substiturechis Series in che room oF Z, and che POW
ers oEchis Series in che room of the LoWetsel L
there rill arise a new Series, CHEH CdKC The LO.
+ 2), Xc. and the C O. etACtenEs A, B, C, D, (30
Will be tound much asis derermined in the Theo-
rem.
This Theorem mixhr hare Bech made muetimore
general, by suppolins
a2 =b2 402 2+ 2, ec. = 8  h +
L 1g2 ec. Then all the POerS OF chC Se-
sies Ay + By = Cy, ec. designed by etie urii
versal Indices must hare been caken successirelr.
This Theorem may be applied contiat is called
the Reversion of Series; Tuch as tndine etie Numbet
For the understandins ot ehis Series, and in or- trem its Losarichm siven, elic sinc trom ils arse
derro conrinue II a5 tar as ve pleale, ir is ro be che Ordinate ot an Flliplis From an Area sirentobe
oblerred,
cur trom any Poine in che AXIS.
I7 Thacererr Capital Lerter is equal to che Burromatre a parricular Application oF ic, we II
Cocficient oF cach precedins Term: Thus the suppole chis Problem as to Besolved; viz. The
Leter B is equal eo the Coefficient h= b A=
2. That che Denominator ol each Coetsicienti
alvaySa.
3.Thar che tirst HembeF oF cach Numerator.
is alwars a Coeficient ot the Series z y ) - B y
L iy, ec. viz. The Arst Numerator begins ieti
the Coesicienc e, the second Numeraror with che
second Coefficiene h, and (0 on. nioi
Chord oF an Ark beins siVe Wo nd he Lhora
oF anocher Ark, thar Mall De rorhe trlt aSn FOL.
Lec y bethe Chord eiven, Z The Chord requis d;
non ihe Ret belongins 1o che Chora, i5 y. L ∞ d 
39
10 t = 2 4s au che Ask beloneine 20 che
Chord 2, 15 Z = 64 = 404F 1124 
the FrE OF these Arts, is co the 2d as iton; theres
q. Thac in every Nember alter che srst, the Pore mulriptrins itie Fxireams and Means cogertier,
Sum oE che Exponens oF che Capiral L erters is al
ways equal ro the Index ot the Porver eo which
ehis Member belongs: Thus considering the Co
iciene L= bB = 2b A C - 3CA B = d A
retiet belonso 10 chc Poee y, ve hail sec ac
ve Mal have chis Equarion, Z = 68.  40de
+
+
n aer de = n7 + a
5n 3, 8
112.
1
10 
efFICIEHES WIIICH DCIOMS CO The Sereral POrVerS OF
correspondins Co. Culens e inc Settes 8) L B7
in ehis neir Series, and make them equal ro thé
Com: