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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 104v, page id 00068200:0210
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 dax p d X seu ddx  d X
seu ax est media proportionalis
inter x ddx et ordinariam quantitatem
Generalibenta Habebit calculus.
dx (1) O
3
fiet dx D e iu C et ddx D + dx d D,, ddy c, dydo
est esto autem dD    dx +,dus et de ndx + pdue
ergo fiet: ddx D C d,, d
dyX p y+ ly. X+, dx D ddx -Bddy _ p - l d. X  m axdy + n dy dx + p d’y
est autem d du p dZf ds D e C d, Dar d0. + do. 0
est autem Od Ddx Y  Dddx + d D dx O, Ddx + Ld xt cu x
ld X+mdxdys
Ergo fier: ddus i) ta de ApDaxdus. 70D ddx fl d x Im Oax dy
at supra H per 6. fiet. ad y si D ddx + 1d + maxdus = ndydx - pdy
: Ergo hos duos valores aequando habebimus:
= n D aex f pD dxdy = 0Dddx + 10 dx + mo dedque
aluo
d
HOD ddx + lO d X + mO dxdys = nO du dus - p 0 dr y
seu. An D L pro du substituatur valor D dx. et pro  vater d 4 X
+10
fe
- 10
et sublatae erunt omnes differentiales ipsis y.
nempe fiei.
fn D d X f pD ~ x  +10 d x =   fm D dx 
+
-
I + OD ddx
Unde patet aequationem esse identicam, s si  fiat-
nam et in equ. 3. et 10 latent amphiboliae. Ituque non
potest to possunt tolli omnes difserentiales
a
satius ergo fi in aequ. b. tollamus solum diy ope dldys.
fier enim: 5 d dx - C ddy p, + l d X - m d. X dy (+ p D dX
eu landum an oste
pdx +n dx dy 0.
dy. ddg. dddus etc. 
simplicium nec ad potestates assurgentium tolli possint, omnes
potentiae ab y. dus. ddgs. ex. Hoc enim Cfedd denique
haberetur aequatio in qua qualibuscunque existentibus terminis
ipsius f, fiat: dy ... + daus . . . + dddys .... erc.  x
ita enim posita y progressionis seometricae haberetur, y per quanti
finitam
 per aquationem rationalem  ex solis X. dx. ddx. daux et c. et
norum potentiis. vel potius  haberetur sacillime ex serie infihus
ipsius Y. surgendo ly. dags. Cc. poncudoque dxsa. undle dax 0. absolu
sed dubito an res sucedere possit. Res eo redit quomodo terminus
seriei haberi possit ex numero terminorum antecedentium, et diferentis
ne differentus differentiarum dc. si seriei ipsius.
da D
4) 3