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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0343
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F
ca  Lions oF the Numerator and DC:
R VL F. V
Eo sind che Elunions os Surd Duanriries.
Let it be requird co And che Fluxion ot
V 2Y X = X X, OF 2 r X = x x (E. Suppole
ErX = ∞ ∞ (2 = Z. chen 15 2 r X - X X = Z 23
and consequentty, r x = x x = 2 Z, and by Diri
vision,  x =  = = Z = (by Substitution)
ri = +  = c0 che Fluxion OE Y 2 Y X = X X
X y - 23)
24 X y - y y
X1 a X  X x
X X  9
ToFnd che Fluxions oF Ouanriries compoundec
oF Rational and Surd Ouancicies: Let ic bc re-
quir d ro sind he Fluxion oF b X2 - Ca X - F ea
Tet it be requird co sind ihe Fluxion OF X V X X =F aa = 2. PutB ~ F CA X  ea
VZYX = X X
a y = X x (3; FOF A y = X s (3 DuE Z and chen
ay = X X = 23, and a y = 2 X X = 5 Z 3Z:
= P, and V X X F a a = 9. Then chc givem
Ouancies is P g = 2 and che Fluxion chere.
Aml muliplrins b7 3, 3a y = 6X 1 = 2 Z; OE is P 4 F q p = . Z But Z i5 =
and consequeny, 34 23 y - 623 X x = 2 =
ser. F aa
(Substimtine a y - X x  = 23) 3 ad g y = 6 and p 15 = 2 b X N F c a . Theretore in Mhe
a X y y = 3 a Xt y - 6a y X X + 12 a7 X3, Equation P q  g P = Z; il in place oF P, 4,
x 6X5 x = +0 the FlUXiOn OF a y = X X (. P, 9, We restore the Ouantiries chey represent, Wc
The Fluxions of imperfect Porvers may be also
Investieaced by (Arr. 20.) che general Rule, and Mall have   = 5 a ∞3 F e a X X X + 2b X X
exprelsd ocherivile, and more brieAy chus:
The FIuXION OF 2 r X - ∞ x)= i5 = = X
2r ∞ = ∞ X) = = X 2 r _ = 2 X i=
x= X 
NZTX = ∞ ~
V X X  e a
V X X  a a X X -  CA X Y X X L a a X X = Z
Erhich beins Redue d eo one Denomination, sires
3b ∞d F 2 a0 v f ear x F 2b a x F Ca X X
V X X  a e
Tho Purion OE ay = X a . 16 = 3 X ay =  ~  = 2 = r0 che Eluxion oc che eiven Cuamity.
X a y = 2 X x, which beine reduced, will BC
tound equal eo che Fluxion chereot formerty
Found.
The Fluxion OC V X y -- 77 10 = E X
X y F y yl = E X y x  X y   2yy (ArE. 13. )
3 i = x y F 273. TheFluxion oC sal t a xy
2 V X y- y y
16 = = X at F a Xyy ( = X a y i = 2 a X y
a y X =  2 a X y y
2 V ar - a X y.
Thepreceedins Fxample;
E X a X Y ∞ x  V at + a x y y
a y 2 X - 2 a X y y
a  = 2 X x Y 2 V a  F a X y y
ax- L 2 ∞ X
RVLF VI
2o find che Fluxions oF Povers, nhere thE Expo
The Fluxion os V ax. F x X F S at F a Xyy
is == by che Art. 20. Rule,
nenes of chole Porers are themselves Fluent
Quamriries. By Mr. LI. Dirton.
TetZ, v, X and v, Be Rovine Ouanricies; che
Variecies chac may happen here, are reducible 10
these follovins C’ales.
TEis Cictier Z  ZV  ZDZ ZE 2V in volicti
last Case, X is che Fxponent oF y, 25y ic SetF is
al(o OF Z.
C ASF L.
Let Z De proposed, and Suxpose Z = v, ThCH
E +: p es = v. L v, buc 2. ]  = - +
Fy 2 = y - 2  Crejectins all che contequene
Terms oF the Series, in Which anY POIerS OF PFO.
ducts oE Fluxions wonid Be Found) ergor- Lv =
17  9Z7 + 9 =1 Z and Z = ) -- y = 3 +-
2 V a X = X X - V a ] a X y y -] Z = 2 = v, bIE D = Z; FrOM WHenCC Z V + y
a y2 x -  2 a X y
 y 2 3 + y = 2 q -  = 0, is tor chat realon
2Vantat Sa FALBKEVatan (ine Value ot Me Punion requirect
Tue Prasion ol V a n. H x 2 1s (4r. 14 203)
y)
X X
X V +9 +93
nralatt)
3V a X - il Xl