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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 806933011:0214
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ertrich since accordine ro che Equation it is to b
aerila by r s, make 25 r = s: PB = l ex + 99
8. IF chis Equarion
First sind a Fourch Proxorriona l eo m, by ala L
lxtrich lec ic be p, cheretore pm-hk and conte.
quanelys che Equarion will Mand chus, 
cheretore m: P:: k: X, 10aCHI.
on
=2 vecc monotes.
Construction OF aM thC THrCE FOrMS OF Duadra-
Mechod ot Solurion.
Dran ruo Concentrick Circles, a5 in the Fi-
eure, and ler the Diamerer oF che grearet de cal
led S, and he Diamerer oF the leser beD.
Which Lerters Sand D do represene chie Summ
ricke Equarions, accordins co Mr. Oughereds
and Disterence of the Rods Wouna; a5 I and d do
che halt Summ and halt Differencc.
PB: 10 a LMd Proporrional,
3. In chis Fquation a
n
=
n: p, 2 Fourth Proxorrie
nal; chen vist  anc nes(
Since theretore his Theorem lS. Tha
4R: Let V: R be imade d Langent r0 che lester
the Hyportienuse LI, ane Cast etie Base oF che Tri
anele d
Then Will HFF d d= R, (ThaF I5; = SS- bD
=R. ) Wheretore NH--R + d d; and cheretore
E= V. R + d a3 chus FY, iF required, is toun
iC ex had been siven, and d lequired; non since
HF B dd, cheretore VHH R = d
And havins chusiound IT arta d, chen H FC
) the grearer ABOc a; and H-
 che lesser Roor e. Which will Be
Adrmarive or Nexaci accordins cophe form
OF che Equation.
cher Mechod, in imirarion ot Des Cartes.
In the FirstFOrm, WIILI 1S, a a f d a = R.
DD
Circle, and a Riphr Sinc in che greater, and deaw
: Ot
DC X TOuBHE.
First, MakC, 25 a:
in Case 3.) c + d : b- 3. 4: 1.
Or vou mient, (a5 in Case 2.) have le
and
mean Proxorrional berween a and b, a5 al50 Bc.
eween in and n, which beins called (as there
and q. che Equarion voula hare A00d Thus,
DP -94
Fa
: Then harins raker AB = B, and (DF OC BL=. d, 1. e. halt che C0. eficient.
on ic a5 a Diamerer deamn a Semi cirele, and ap.
elgins in BC =g, the Square ot AC will be =p
qq Wotich since ix is co be divided by c L i
matie, ad c+ d: AC:: AC. y, che Quanciry
Couxtr.
4. Dec etis Equarion a abe = 2, be propotect:
First sind our (p) a chira Provorrional 10
and a chen fp==aa; the Equarion will Aand
tus, C = 2 chatis, DC =
Seconcly, Find a Pourch Proportional (9) 10 f.
and b, laving, a5f: p:: b: q ihen will fg
pb; and consequentu the Equarion will Aand
chus, F2= = Z. chac is, 2E = 23 and cherctore (as
Reule 1.) 8: 4: : d: Z. Couxte.
COHSTRDETIOH Os Ouadratieks attex ano-
LeF FC= a, the lesser OF rhe EWVO ROOIS, and
dta; and conleguenitus
EL L6, 6y 36.
D. Euelid.
Then i
intu