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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 186v, page id 00068196:0368
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Geueralissime:
quod eodem redit..  si scriberemus:
fy dae + g, X dys +
ere
Sit data aequatio (1) inter X et y.
Scribamus arbitrariam Z ap. Sdx + g Xdus + h+ lx + dx + P  td
C cuau
m+ pX + 4
ete
Ex aequ. 1. datur aequatio (3.) inter de.   X. y. dy
ex
+syret +
Exae. Assumetur aequatio  inter . y. Z.  vel quod eodem redit inter X et Z
Inde fiet aequatio (5) qua habebitur   dZ quibus substitutis
x
in aequ. 2. sublata erunts  dque dx. dus, et fiet aequ.  (6)
ubi huabetur V pure et rationaliter per X. y. g. Denique ex aequ. 6
tollantur literae X. V. ope aequationum 1 et 4. Habebitur
aequ(7) in qua quae erit quaesita si v non ascendat ultra
Quadrat Simplicem valorem.
Quoniani autem hoc semper haud dubie procedet, ob duplices
arbitrarias, videndum saltem, quomodo id prestetur compendiose
Est et alia via sine Transformatione per additiones
rationalitr
ordinatarum: Datur quadratura figurae cujus aequatio est X Abxtequ
itemque fid X + b X + Cxy+ dy + C aequ. 0.
OnQuia enim omnes figurae Rationales quadrati possunt vel
absolutae vel ex data circuli et Hyperbolae quadratura. Hinc
+ KX
datur quadratura figurae, cujus aequatio est axx bxytexeus + f aqu. o
cujus aequatio
Datur et quadratura figurae
27+ h77 +1Z + my t n aequ. 0.
Sit jauss. 93y + hyZ +- Cx + i Z + n aequ. 0.
Fiat jam py + QB aequ.  Z
per aequ. 1. est
y aequ axx + Cx + F
(b X - e
In aequ. 2 substituatur valor ipsius Z ex aequ. 3.
frei +gyy + hqyo + l’y + mgv +n aequ. 0.
aX
py
mpus
+hgry
liqu exaequr. fier:
+per
29 ac X + 2g af X + 2gcf X +
Ehp..
2hp
+g c+.
+lip
2 hp
+hp
 12 Pabx +a exxHC
Inip
+higr
bc
+lt.
2beX+C
bx+ x +
adequ n
sbtticex
+qm V +B
+mt
+ qub vx + qmibexvt qme v +rbXk tu ibex n
 
f
a XX+C
bx+ e
taexx+tex et
+ab Hb5 X +b5.
in4V + n
bx + e
Im B+n
+gA XXB
abX + a e XX + CL X + e)
+ bc. fb5
53
+
toia
ubi ut tollamus X: X.
taciemus +g +hp aequ. 0
e a ab aequa et siet.