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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folio 15r, page id 00068033:0029
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na. si 1681
Tunenbndum observaoex
utem imoiferentiaus Differentialia Transcendentium et nova de
Tunstendeatum.
Cquadraturis per aequationes transcendentes
Et si faile sit transcendentium differentralia invenire licebit
adu
tamen  quibusdam aatis invenire alia
a. V
l
E
a inea
posito unitatem esse a erit
mogntrm 
d
a
item dat quia x
e
si sit aequato.
C
b aequ. y sic exprimi debet exacte
2
X
a
 aequ. ) a, ut servetur lex
 b equ. y. dat a b aqu dys
aequ ,v
si sit equatio
(e
V
hinc d b aequ. b d prv
+b db
b aequ y reducatur ad havc Pa aequ y.
X aequ V faciamus X aequ C oritur absurdum, si
C constans. fac amus ergo
d
X aequ 
ey
fi et C aequ y. seu
fiet C aqu Ha ergo his duabus aequationibus resolvi potest quaesitum et fiet
cago.  aqy
et habebimus
X. b aequys, fiat y aequaX
Y aequ
aqueo. Ergo si tantur tangentes rujus
datur autem d
dy
de
du
Xe
ax
1
1.
des
2
et habetur
x W + X aed
3 4
yoeX 1 4 27 256 ∞25
X
27
3, 232212861
20. 16
beu y fiet:
ax
du aequ ed x+Xco
scribatur 2xaequ vofiet: yaequ
et uno dato habetur nlterum.
aequiy et
X aequ
x
aes
codx
Ergo aequ.
.
V
X
deo xb aequ y. quia quaentur
dabantur et prioris curvae
alis
scribatur e aequ
baego y fiat:
X agu V. fiet b aqu. y.
t.  aequ y.
X
bX a
6a 3
 256
superest ergo ut
3l25
vel differentias
tantum tangentes talium: X vel X etc. aliorumque similium
inveniamqs,
item b Ex his datis caetera facilius habentur
ex datis
a X datur et dX  vel contra; quia si XL aequ. y erit
Xaequ 
yv yposititita
256