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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folio 33r, page id 00068073:0065
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22
5.
∞. J. 3
t
 5 E F.  e  
f. E 1.
5) EV
eaequ. +Y +2gh- gti
faqu +s + 2gh- k h
ex  as la
Caegu. p +geh +2. 2et- 2fh
sts
o
n5
5. F
 X s.
=  F et D
 e
2
 et
5
a X
e 
+
e s
2ydo e
e 
e
F5. = ∞ 5 .
f 5.3 s
∞25
12 
la S. sice
s K 2C
C. 8 F  d = X
2Ft
sin.
(F. 115
P
a  5
 C 
e
d is
bago n terh +∞ tt rX3h+3.3 fh -3. 29L
E
 F. bEF
e 23
e 1.
5 LX 2 F
E
25 X n 1 
EF c
que i togo
  
B  e
e s 1 F
en te 
daqu.
Ex propessione autem valorum ipsius b. ubi paulatim tolluntur orbine literae c. d. C. f.geu. habetur tandem series
 - = 1t ~ 5.
a 
10 +).
infinita pro ipsa b vel pro ipsa= et habetur aequatio infinita pro ipsa h. cum vero valor ipsius E. quaeratur
et tunc habebitur ipsorum n. p. 9. ecc. progiessio in infinitum. Et si tollendi altiores termini, faciamus primum
naego 1. . quequ. 0. raego . saequ. 0. v aqu et et ita haberetur Z aego 1 - in F - ntc seu aequ. 3
im aequ  seu h aego:L et N x cetum qun + P  aequ. 0.
e
I+M
4l ae
unde pariae quidem pro arbitrio sumere licet
agarnus Z(si explices literas ascriptas) semper includere ipsam cu circuls senseriem infinicum pro arcu
circuli licet mutilatam. Unde patet cmvam analyticam quae circulum tangat non posse inveniri, nisi
ansiem curvam arcuum vel similem tangat nem posse inveniri nisi data jam longitudine arcus
ubi sit contactus. Atque ita demontratum est, istam methodum ad exitum perducere non posse
Videndum an generaliter hinc demonstrari possit impossibilitas quadraturae sperialis:
arc aego +_ - L + +3 - t erc aequ. b + cF + d f erc. itqu ut () sit valor quantitatis aalica algebraicae
adhibeatur valor algebraicus generalis,
quo facto si nulo casu effici potest, ut destruantur termini altiores in infinitum per suppositam algebraicam
finitrem, demonstratum est impossibilem esse quadraturam
+ E
2
2 F p 1 5 2
= X
 e = 
videndum est sequales nam esse debeant n. p. 9. J. ut tollantur termini altores ipsius h. vel si cerminis ill
et fieret e
=2t
dem dnas ex his tribus 1. m. n. verum patet tamen quicquid
4s
5. + + 3
=11S, F i
8. X f. 0 Y FC: 
8, 67.E
F C.  
4
pF 
. 5
d. 3
Xe
5
F1-
Caegu. p +queh + ryse As. 23ti3 +33 Ch - 3X (h5. bagu. ans ar   n23 H3 erc mi. t F mi f
15ic.
g aequ +o +2th - iti se fiet boqu. n + P 2h 193h + Y 4 h3 + 55h + vbh er
ex. baequitm aequ 
F 
2
a
E
eo fut 1 + 5
D
X. F F. 8 ∞ F 
2. 3 p 1= dd ∞ E+
2: 3
X 9 e
C a. 5
+ 5 5   p
. 4 3. x 5.
F
+ a  sit P
2.
P. 2A  F
t. s FF X ∞
s 3.5.
N P. 8
F EuS
daqu. quiaht 2. affli. 29h
e aq.
si
ce 3
63 ∞ X 5 +
5 + lus
NC
Cagut P +2dn- et. baequ. n + P 2ht hi- 2eti
Daeqo. 29 +2eh- fh
2
t r.
2E 5
E. FesB
E 
b aequ. M + 2ch - ds1
=
e
A5
n
A
F
A FF
s
s 3.
es
e
1
e
x  us
 
C5
F.
e
 +
+X 2
5 2 3
sd  Z
1  vi-
+ 
F
E R
Ae A
1- P
 5. f ∞F 3
E i
 
E+
5
ar
o X
5. 0 i
5 
v1
A
=
NC
15
e