# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0647
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0647?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 326r, page id 00068196:0647
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 325v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=647
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000647.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 88 lines, status machine
# Lines: 88 recognised, mean confidence 0.84
# 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.

si initius absit y, utamurque solum du. et X. fiet
10du  11=0 data quaesita non potest ascendere supra gr sit fiet ergo 20y+ 21  (0
Ex 2 differen tiando fiet:  20 du + y d 20 + d21 = 0 et tollende y fiet,
20dy (+ 20 y d20 + d21
209 420) = 120. 21
=0.. Ergo 10- 10d21 - 10. 21 d20 20. 11 = 0
d in legibus homogeneatum idem praestat, ac si a gradu aufertir
 edus + 10 L0 (nam dus est homogenea cum dimensiont cujus ex ponens 0d
209+21 =0 20dy + yd20+ d21 =0und  Tollantur y et dy, nempe
tollendo y ex 2 et 3 fit 2020 dus+ 20yd 20 + 20 d21 ()o super est ut tollatur dy, fiet
e dio =0 seu 20e d2] = 212 d20 + 20. 20. 11 si jam ponatur d.=
+2020. e dy + 20 ed21 (et
= 20. 20 e dy = 20. 20. 11
=20yd20) = 21 420, 61
ao fiet 20  ed21: 11 et 0 ne dd21 + n de d21 = e dui di1
si jum d2o = 0 et dd21 = 0 fit 1t de  edu.
Helque
de suzo- espro du
alte
si dddri = 0 fit et de sd 2) L e dr. dd2, + e de dd
dd21: 20 = du d 1: e = 11 de: ee Et disfe t   d 11 - du de  e ial seeditce
je e
seu fit eeddu - e du de = est dde = e du de 4 2. 11e= 0 seu Sud  - d iedt
(180
seu + ee dd11 +211 de
si sit dedd 21 =0 ft, dibet 14 differentio differentiari, et fiet dd du - dd ide 
(20)
= e. 11. dde. - 2e. d11 de
si sit d 21 =0 fiet  d’du. - d’ude = 0
Generaliter ergo si sit d2o = 0 et sit d
Generaliter ergo si sit 20 constans, fit dut =
et sit  constans d21 fiet 0 = du - 1de, et d21 =
ee
dd 31
d du -d ude
d- dd ude
d au - d ude
ee
si sit
Generaliter si 20 sit constans fit d2t = 20. 11: C seu d 21: 20 = 11: C
Ergo si  constans sit d’21, da 21, d’a1, d’21 respertive fit e A = ude, vel edtor de di - 1d de fa 
vel edrande  vel edu ide eceditu d lie, dd n: e, d’a: e, d 1: C, 20
1
11I
seu i edi = 11 de =0
H eefdd  cededm ef udde = ve ded 1 = 2et ded1 + 2p1 de = o
III e si 20 sit constans fit 20 = e d21: 11 et fiet 11. e dd 21 + 11 ded21 = e d1 d21 =0
et fit dd21 = e du d21 - 11 da d21, : 11 C
sed si Ad20 sit constans redeundum est ad aeq. 6. nempe fit  ex ag. 6 est d20 = 20 edu - 201, : 21C
sidro conpun Eb.  no hat = daie sidiltro stans fit o = dd 20 421 - dil 20: 11
21e
Uade s drole. 
I Geaerulius si tit gstant L 120
dd20
11
sido constans fit 0 = d 20d2 - d 20 1
20d11 - 284) si 20 sit constans, fit 20c e det : 11
 sit o- - deodn - decti
d20d
derodes - ddt i
dprodu-atc
sisit caustam 20, et 21. fit 0=- 20211: 21e, absurdum
sigstampe, t det fit o- 20 d5Y
Si onstanssit 21 fib 07 21ed 20 + 20. co. H et fit 21 = - 20)11: Cd2o
 d21 = 21 420: 20 +20. 11: e 
21d20 + 2011
Hinc si sit constansqu tat fit 0 = (u 0 2aj v
id21
d321
ic
dd G u aro + da ( 10. 11
esurio +  (ri
Quod si ergo res possibitis,
ufique aliqua ex differentus
iliu 20, et aliqua ex
differentiis ipsius 21 debet
simul esse coustans.
Ergo aliqua ex differentus ipsius
ipsius 20 d21 = 202. 11
2IC
et aliqua ex differentiis 321
ipsius  +. 20. 11
aebet simul esse constans.
Sed sciendum est; quae quantitas indeterminata non est integra ejus nullam differentiam 
Ergo necesse est, u20 et 21 esse integras formilas sic assumibole
28: 1
oporte
dividi per 20 P. Eorgo necesse est de