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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 83r, page id 00068197:0165
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Febr. 160
de differentiodifferentialibus
Adax quaenitur an regula generali
haberi possat: fiet si sit X progressonis
arithmeticae erit: ddx aequ.o
(ddx ee aequ. dx. sed quid (dk ddx
s
t
aax adx aequ: dx. Et ita ponro
ed quid (X dax 2 si Xaequ. y erit Axaqu
eritdd axaego 2ydy. et dax aego 2Hady + 2dy
et faciendo dus progres aequi constansi seu e
unitali, erit adus aequi0 et d aeglus Bet fiet:
s
Xddx aequ 2yydy aequ  aeqo= d
2
sin Xaequ y erit dxaego hyglus. et dd
dax aequ. 3ygddys +6y dus aego 6ydus
et (X ddx aeqo 6syt dus aequ 6y aequ. X
3.5
Unde respectu solitu X non potest haberi valor constans
Videamus an possit constanter exnimi per X et dx.
sit scilicet: Sx dax aequ X d
v
Si X aequ y e generaliter si X aequ y erit:
dx aequ. Cd. y et ddx aequ d. c0- 1. y02. et
a
X dix aeqo, co. c0- 1. y
 aquaEx
te X. dX
ea
h
210-2
et Sx ddx aego co. co-1. 20-1
h.
h
et1
2cd-s
p
pat r+1
ax +_thX ax +rmx. de
+nm. Z
fiat sed nihil hinc duei potest nec tolli dx eot nec idem
fieri  aego ex. posseinus tamen facere e+1 ugo -1
ea hunc
sed tunc quaere retu summa ∞: deo
eut
videndum an detur lummu X ex
ac datur
Veram nec