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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 806933011:0344
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ns
2. Tet 2  = v, Men Z ( = 1
= v.  v, buc Z 7  +) ta t2- 29 tig + t
F9Zγ + y + ~ + x = 2 Zp x Z YY + x + X1
erso 2) + y +.  t  , = X X  + )-
 Z
CASE HI.
3. Tet X = v, Meno F o = =1  ).  jia 
EZ) X + 9v + ~ 9 -  xy X ZD~ + yu + ~) = 1 Z
Crom erhence ailes q)  -+ y  -.  )  2
X ZV~ + 9 r + ∞y - 1 q - 23 = = v.
ASE IV.
4. Tet 2= = 0, chen v + v = 21 2)
2 F 2
un
9 + ry - 9 9X + vy - y
yX + xy - y = - +
x2 u
1x + 
2, itience Z
y onatry - gi - 1.
x Z
Z = v.
CASE
Latis, Tet Z = v, ihe Fluxion oF y =
    ∞ 9 v ut 1 = 1 y - g; ergo ve have v-
y = 2: V
4 ny ~ L 0 - 1
.i magaii -15
ti-
Fy =  qgi t 2 = 9- Z; ane chence is
plain, ehac v = - y i    +  - 13
i ay  t - - 1 - q
Next Forthe Dule Inversetr, c0 snd che Flowine
Ouantier belongine ro rhe Fluxion ot any POrer
Whether Perfect or Imperfect; procced thus.
J. Pate He Fluxionary Letter or Letters ont or
the Equation.
II. Augment rhie Index oF the Fluxion by F. OF
Uniey.
TII. Divide che Fluxion by che Index oF irs
Porver lo increased by Onitr.
Lxamples.
Onity, ic Will be 3 x x x. Then diridins ic by 3,
ins non lausmedred) index, che Quorier will l
 xa, che Plorins Ouamis reguised.
tatins avar che Fluxionary x, ic will be
=1: By ausmemins che hudex bs Dnies
m
(i. e. tatine avay - 1.) ic will be x: Anc
lasr, BY diridin8 che remainine paecolche Fluri
on by Pretixed 20, or Mulciplied inco v, ihe
Ouorient will be x n: Whict is che Flomine
Ouancier Couehr.
Tou will sind Framples enoush oE ihis lnverse
Method: The Caloulus Integralis, Ox Summatory
arichmeriele, in M. HaysS B00L OE Fluxions,
Soct. 4.
Some Instances of rbe Proporrions os Fluxions in
Various Curves, by Mr. EL. Diuon.
Texx and v express Abseisses, y and Z che Cor-
respondemr Ordinares univertally. Ttien in ihe
Ciecle we have ;: 2: . =  = x  rv = v
ane supposine che Abscisse ro don unitormiy, aud
consequemly x = 0, we tave y: Z: : rZ = x Z.
ry = 0y : : r = x:  3 That is, che
Fluxions C e, Ei, are toone anotter aS BO, 10
O; che Points beins ever determined by che
Perpendicular h 8. let Fall trom h che Incersection
Of che Radius OC, Wwich che Line Dh.
Tis cerrain chat 5O = , 7 = 2, trom che Si-
milax Friansles C F O, h8O; sor b8 = D B
=9, and Z: r - v: : g: 1 v
AC = +
AB = x
CF = 2  HI i =
DB = y
AF = v Cc = y OB = 
Again:.
da
Suppose x x a Fluxion propoled: B;
ec
ClBC MC A S F. II.
EF 3 X X X evere propoled; by catins avay x
In che Parabolick Curres, purcins P ee Pata.
metet = 1, cheny = 2, and Z = v, chen y:
a
c
Z: : n x
nonid.. 
it Will be 3 x x; and by encrealing its Index by
Theletore