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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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Note, AIL3 LhatenC Sut et an
FixpOnentS AV. This beins well understood, chere is chio
ot ervo Pumbers or Ouantiries, in any Creotie
trick Progression, makes the Exponent et 
Produet os hose tuvo TermS.
Tmis  JV S or at is che var ol exesline
che Product oC x inco v, and +
X   is the Product OL X 3 into x .
AICO X F 1 3 Or X : is che Product 0
xinto ic selt, or che Square oF x
And ihe DiserencC Berween the ExpOnent Ot
any vo Terms, ische Exponene ot che Ouorier
arilins by Divilion ofche grearer by rhe lel5.
TImS, x= SOF X  Is the ExPOnenE OF ch
Ouorient ol v b7 vt, 930.
LeE p RCPre(CnE TC ExPOnent OF N any Numbe
ac pleature; and lex P = 1.
Then Will N = N : N P F  = N, ana
= N3 NPF 3 = N2 30.
Or it p = 3.
Then will N = N3 and XB = 3 = N6.
Bc
And Negativety,
N =V = N = and N = V + =N 3c.
Also, 25 0 is an Arichmerical Mean Beroeen a
Postire and a Negatire Ouancity equally distant
Erom ic, (1. C.) - 6. 0. 6 are Arichmerically
Proportional: 50 is r. a Geomerrical Nean bC
civeen an Aftirmatire and Nesatire Porver, at c
qual distances from ic.
Thac is, N P. 1. NP -:
Trneretore, + = N = P X NP. And dividine
al by N P = = N
Sochac  27 is all one wich N
t
X ~ F = = + X ∞ 5 = v
And = dirided by = vill sand in chis Ne
Cion. cus. ): . (= - -.)  5 (-.
= (∞ =7 = 1 Xx
General Rule For rhe sindins the Fluxion ot any
Pover, Whecher Perfect or Impertect, viz. Mulei
) the Pover (first brouehr one Dezree lover) by ibe
Index of that first Porver; and then, That Productby
the Fluxion of ihC LBI.
2 X X, ecc. and che Liluxion ol x will bc 3XXX
ThaE OF x Wwill bC 8 x X, _C. Or it m expressche
Index oF any Pover, as suppose xn. Then irS Flu
rion Will Bem ~ = L X OE M X r = =- . FOF X H
brouche onc degree lorver (m beins a general In.
dex) must be x = 2: then thac x by m che Index
mates mxm = , and ehis last by che Fluxion ot
che ROOT PrOduces m n = 2 X.
IFche Pouex be produced Fromr a Binomial, C3C-
25 suppose xx  2 x y  y Y, ies Fluxion will be
2 X X F 2∞ y -F 2 Xy L 2yy, By workins ac
cordins co chis Tourrh and the second Rules.
Eche Fxponent be Nexatire, as suppose 
Or =, ies Fluxion will Be = m X X = m : Oe
il rou moula doit by way os Fraction =m
(For rhe Square oF xn iS as Wel x 2 m 25 ∞e n2) OF gC.
cordine rO ME. Nemton SWay, Which is vet MOr-
mX
ret, mot 1. Sec Casc 4. P. 252. 0s bis erim-
cixia.
And co add some Lxamples os Musciplicarion
and Division in chis Way,
ui
che Pover be Impersect, i. c. is ils Fxponene
be a Fraction, as luppose V: X: Ox in che orter
Noration x . Let us suxpose X n = Z. Then
it vou raise up cach Member ro che Pover ot n’il
vill Randthus, xm = 2. The Fluxion ot which
will be, by ehis general Rule, m xm = = x = n
ma.
2u  i. Wheretore L willbe = n Za = - (by
diridins boch Parrs by n X - 1: aud mrno-
n7 2
m  X Or  Y: x n -  by purine in
Aead oE n n = = its Vatue n Xm-=. S0 chac 10
sind che Fluxion of any kind oF POver, you muse
procced chuS.
Mulriply the Pover eiven byits index or Exponent,
and then that Product by the Fluxion of the Root es
the Pomer siven, and afcer this Subduet One or Dnity
fromthe Index of the Pomer.
AS For the Fluxions oF Surd Onantiries, WIr.
Frayes pires che followins Examples in his Frearise
OF Fluxions non in the Prels, Which will mahe the
chins plain co anx omechac will render himsellready
aectie Practice oF this AI.
Or
Thus he Fluxion OF x x Will bC Z X N, SOP X L
= X X X, buc The LIUXION OL H R X = X X  X X
LROL