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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 57r, page id 00068199:0113
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ly gar
db +B sAXCX). Qua
seriei L +  + L +:  etc. summatio pendet
ab hac quad comaeetue abhuc a curva con-
structione cujus aequatio entialis est
tangentialis sit dy: dx as(dx: X) : 1b+ x
fiet dydx = (240) dx dx a sClx : X):, b + x =(3ti0) dcodeo
constanti ede(4to) dydx. Et differen
fiando aequ. 4 fiet dy dax + dxddy = (5to) 0
et adx: ddus = (6to) - dx: dy. jam ex canone
generali est ddy: dus = (7 mo) d (dx: dy): (ddx: ddly) aY
et siet 2 log dy = D log (dy: dx). seu 2 log
seu dydu: do doo = dy: dx  seu dydx = modeo
ut ante. unde nihil hiuc obtinemus novi
quod mirum non est cum calculum institue
rimus communem omnibus curvis, seu quisi
aliquid dedisset novi, solvisset omnestan
gentiales aequationet qualiscunque fuisset aequ.
s
(b +X) dy = a dx sdx : x 
a dx sdX: X = deo fieto dd X fdx: X +dx p
- dx: Xsax: X
sed facile intalligitur hinc asi aequationem
ec
ubi valor ded
praecodentem redire posse seu vatorem
dy., aa x aa dus =) xxdx + yydos
sit xptgaqe et ix ax + rydus = ad
tollere y et du. Nam ex
1
XX = aa  e (v+ Z) aa:
possumus
yy=aasAZ.
fiet dam ax a dB.x) a ( i_) fiat dx = a d (v: Z
et dy = a(dz: Z): 2 4543: 2
21ua (d7.
dz
an
av: Z)- 
rag
 Q + 1 +
in
1
et fret
sed A- dZ-
s
L
AiZ
10-
AZ