# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0361
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0361?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 183r, page id 00068196:0361
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=361
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000361.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Sublatio quarundam differentialium
 (2) 
sit exempli causa ax +dus = X: 1 dy seu deidue=
s
X: y = 1
reperi licot bis quaereretur difforentio. differentialis non tamen tolli posse tam ddx
epe duarum differentialium, Xt pulo quia alioqui nor posset servar ex dimensionalitatum
ee ex ag. 1. fit
dilx + ddyue = X: y ddy + dxody: y  X dy: yy. sed ex ae qu. 2. fit
ddx: dy - drdus: dy2 (+)
A
axa dx: y - a x dus c.9y
 Ex aeq. 3 est ddx = cyx y ddus +ydraus - xdus ryy ady,: yyius 
ex aeq. 4 est ddx = ydu dx = xdue + yy dx ddus.: jydus
unde deuique fit desructis destinendis  exeae et dividendo per yaaque, fiet
xhy a y dy + oax ut ab initro aeq. 1 itaque frusta tollitur dax
Sed videamus an tolli possint ax et X. et quidem ex aeg. 3. sollendo p per
aquo 1.
fiet: ddxddus= Ax: ctus dilus Fadu)  dx dy: y - dus. y dx. dy-dj7
et 20q4 tollend X Et, ex 6y. Ct sollendo X per aeg. 1. fiet
ddx: dus = deddus : dus..
Cux: - dx : y- dy:y.
ed coincidunt
aequatio 8 et 0g. 7. itaque non pocedit sublatio am ipsia X quam ipsius dx
simul
aeterum non video quid strohibeat certam rlatione
pro arbitivo, assumi inter dax. adque et x ul y fiagamus
sergutatem sumi progressionemi
fificium ergo tate succurrit illud saltem X et ax
lolbre quo est extra dayue. ita enim deinde ponene
day Lo restabit solummo do ddus  ddx sint X et dx
si et cum in hoc casu praesente id sponte eveniatr, et faciento adue =o
i fiat ddx = = du: y. ideo dum ds sit constans assumta
2
fiet (a dx = dy - dpsitg: y et X . X + b = y (dy sady: y
pero nos ope rujus artificii de omni utcunque perplexo problemate
taudem trium faturos