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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 22r, page id 00068229:0043
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t. vel p
si ordinata et abscissa simul sunt rationales producta semper est rationalis
N
+ - x
Ergo p p Xt yx = y
y+p
Ergo +y- p+p, 1y. y   =P 1 3
+ - X
C
Ergo pt B yX. Ergo tpagt ty - XY
Ergo +p Xy. e1
Hinc patet rectangulum sub du abus
productis aequari verdangulo sub ordmata e
abscissa.
2aX - X H y. Unde sta. Xxtr N, sive tB 3
LX
Data qua figura, invenire lssum ordinatam
continetur tota ars numero numeris rationalibus
effidendi problemata quibus insunt potestates.
item fax - fX H FXP, sive p, ax -x
sam p t ⊓ yX. Ergo t p VX
Ergo y
a x H WX sie
Ergo L
P5XI
ax - X 2
ex Y V 1a X. X ax. X  vY
a -X
Ergo V Y 2a - X  a ∞X
2a = 2AX = aX + Z
v
1aX - X af- et yt
a = X
∞X B Pt. Ergo 3 H X
ut d
FH F (F:
Mimmam item, et si figura est in se recurrens maximam; an maximam infra datam
X - LyX + X= Y - y + a o
X F
V’- a
Ne y1xy) axy +Xb
+ lx + am r
X + n Bo
+nX + nlX num
y3- a
 bX-g
+-y
vaxvaxy
x XYt Xy + Xy- a3f X
-∞+Xy+X
a
+Xe Al. ebm..
t yk - Xy -X
tyr- Xy-X + X y+ X - a
aap
N +M X ant X + nom B 0. conferatur haec aequatio cum data X + Y X~H X. y
+ l +am
c. 1een + n  70.
fiet V e n + l. sie rep
et n 4 3 ul + 12 Cl + bm
+a
Ergo m B - n  - 3 p l - 1  - a, - n 3 - 3n Y - l 
D. sive a  n3 + 3p l + 1n
conferaturcum X + PXFm Pone 0. et tantim opus erit oubstucere
sive X + PX 1mpjo. ludica.
+ m..
Pone erx. et Ap+ ap 3ten et nc  emp. Ex priore eut Cr) rml et
ex posteriore Ca
1
3n
sive l ne, vel c, imp lp+ m Ergo  mP + Emp p
n
nx
12
smo
3X sive imp  et m
sine 7p H P M pne a ⊓ + P+ V, Ret Y suot si P. L  pou en Sn, fet hmpom 1d +
1
rationalem ad abscissam. Hoc problemate