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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 17
# Folio 2v, page id 00068035:0004
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XN yy a1
Sidendum an res sic probari possit. d  x
ax + 2XaC + coa  y + 3y A + 3yM N.
Exa
2 aa + 357
auferantur hinc ax, illinc yt, aequalia  ex natum curvae, item hinc 2xaco, hinc
ByA, ex constructione, erunt oa GA t N
onfido at eadem Es  in dupli 9y. ergo
et 3y)
904
de
+ n 4Xad i
Jann  ce p 39 + 1.
3y + s Ergo 91
exae a
P L. seu 393 p 4 Xa ut 31 p 3X a. Ergo 3N a p4 X a,
quod est absurdum.
V Sumamus aliud exemplum sit natura curvae: aX p y  fiet:
a X 3a XC) + 3aXC+ cSF (y) 4575) + 10y A + 10y N +7 A+ A
du
et (x)y - 2XyB 3x(Y)e anferendo hina 3ao, illine a X, illinc  ex nalica carvae, atem hinc 3ax c0, illinc
seu 2()y+ x9, 3Ny) AGA ex constructione restabit 10A quia
Ergo X A(7)
1D R2X43
B 10V
seu 595
DH 53t Bet Co
a v3ax
9a+   3aXF a Co 9ar  3aXrao. C 
et = 3aex p seu 3a 3X + coA, 6a73
3aX 5y+ p
1) Erg. 3X+ Cd seu  + co p.  + 1xa
4) Eui 
Sed nondno
est
et
f  o r
3aer taeco
p 1 + 1 x5 y5
 
 y pa
) Ergo co A Y B V quod est abferdum Ergo coly B A 
hoc satisfacit.
Generale hoc Lemma. demonstrandum est:
innumerae aliae imposibi Si duae potentiae ut diversi utcunque gradus, a duobus binomiis utcunque
citates poterunt ex tamentibus diversis , du babeat habeant a duos  altissimos
duci et forte omnes propositiones terminos mus pominis unius potentiae, aequales duobus altissimis terminis
impossibiles ex tangentibus 
habent orrginem suam itaque auus nominis alterius potentiae
si general Terista ad tangentes) proximo:
sapplicemus, generales sane mirus
aequationum imposibilium
formas dababin t
346, 2cd
a +bp C+d
ast 
es
Ergo 
a+2ab +b
inquam, id est
cimis
altissimum altissamo, proximum
ipsas potentias aequatet esse impossibile est.
a +4 ab16ab , aab b
si a⊓ C ent a cpa
C+ 2cd + d
C+ gcdred + d3t
+ 4d 16Cd 1 4c8 + b+
4 ero apa
atb p AC3d. cueu 
ego a p a  embgem sit
 si a thaeb+habtb erudisus 84
a a (2, b (2
eut c+ d ea +b +A cuo et  et jam a
Ergo ap 3bC nmiB ate c+d7 a+ b +f.
axtis: 3 ergo A+C+d A+ B+ a de b+fC
entm
4C ergurum . C. pp  C Bl
co tmodura B C.. 4ab rcd s = a bp ac d) en de sta   am 12 cid
a +b c+d.
voa + 4a bpC Ctdumm
ae  ccond,
Ergofiet: ad a
a x H
a n
a Es
eon.t id st oduissis S aequalibus
estb
Ergor C++ b pi a Xa
coadAZbC  Satis video thcoremats de istrationm analytice
Ruisu coiza
quaerundam, idque procedendo didine, x
1a Ergo Ergo Analytica idemonstratio per calculum, ad
sive 27 ad
v 1 BC
EB seu 27 b.
Est autem
EpV. Ergo Cp a
et c+d p arb.
a  C. Ergu v t d H C +. b. Ergo dp b
Videndum ergo, quomodo ad hanc
a3 + ab x ia b, 1 +C + d C+ ad a adribB a. cad b, e
Cporb M, C N 381 13
decuoastrationem
novum denique nos ducet theorema, et ita non dubitem ad simplicissimam demonstrandi
rationem, nos denique perventuros.
redibit aequatio pinst.
Ergo +d+ 1b
Eogo d . seu cd p ab. at ad pbc
neua Eergo cd + ad H ab tubc.
ciar a.
c
tictandem
puliterime
jam yye ax
seu (Dyr X).
no nuter
seu fiet a ) P. E. d.
co
a tt
Hy - 2X3p a(r) B  xy ram ay. 6) X51 aB
Ergofiet 3XYI
imutatione hulus
inventa
3yp A
v (X) - X 4y
Ergo (X) - X - 5 2
 ergo
va atidem
b7) a ccon