# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068199:0377
# Permalink to this reading: https://leibnizlegible.com/page/00068199:0377?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 189r, page id 00068199:0377
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=377
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000377.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 74 lines, status machine
# Lines: 74 recognised, mean confidence 0.86
# 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.

fit (divisa per n
o=  al + My +ndy unde differentiando  adl + dmy + mdy  ddys 0
set
Cui coincidentietur data:
+ du.
+imus Alocadus
P +g y +F dy + ddy =0
differantur aequatio considentialis Termini puri ad finem, quia ea sola continef l; pono
aam 
ex duabus aequationibus reliquis, sit: h agg- aadm: mner = anre aadn :in
et fiet agnn- aandm amss- aamm = aamdu. Ubi  si fiat
m = n = fm: a, fiet dn = (f: a) dm + (df: a) m A
seu fiet
aqtmm: aa) mm-atmam=fumr frmm- aanm -af mdm-adf mm
seu  q(f: ad m= a fam) = fr m - aam ( afam) - adf m, et evarse
et evanescit M, nec quicquam est effectum, et revera per
hinc discirrus in aeq. 6 non nisi unam esse incognitam f seu n: m.
P utrum adsit an absit in aequ. data nihil interest
Aliter
a dl + dm y + in dy + ddy
n
+ dn dy
Ih + hm y + h dy
sen
ans
a
s
D
P +9y +  dys t ddy
sed ait inde
possimus et negligere multiplicata per h, quasi h esset - 0, et ficto
Am = gn: a n -= AD rn: a = an. Ergo dm = ran:a + Endr: a an
=nq: a ubi si esset dr = 9 haberetur quaesitum nam fieret
ran: a = dan. Resumamus
al + my +ndy =0 unde differentiando et dividendo per n fic
dl + dm y + m dy + ddy =0, haec coincidentietur
datae
P + 4 y + 7 dys + ddy-
C
fiet Et per dy fiet m = rn:a - dn ergo dm = rdn: a + drn: a = dan
dn dy
sid per y est em = qu: a. Ergo fiet 4Z dr- an + dn - ddn =0
quodsi jam ponatur 4 = dr fiet ddn: n = r: a et superest
superest t ob coincidentiationem
termunctum absolutorum adl: n = p, seu dl = np: a atque
per y Et habebitur n
Tantum ergo tantandum est an liceat aequationem datam transmulando
ita habebitur quaesitum
ad eam formam revocare, ut fiat q = dr. sed video si id liceret
non fore his subsidiis opus Nam ex p+  dr y +rdu + ddy =0 fieret
a
Sp + Xy + dy = 0 quae fite quam resolvi constat. Tentemus
tamen sit aequalio data a +Cy + ae + S + gdu + a ddp -
C
ponatur  v = hy: a, et fiet du = hdy  dhy: a et ddv = h day pdhdy +ydah, ia
et fiet ae + fhy: a +ghdy: a
+odty:a
-0 quae comparetur hp + hdry + d illus
+ly dahr +2dhdys +hddy s
d
cum ipsa
(9 + 2a dh: h) = du + 2a d (dh: h)
aan - o ten du constans tirtet dr:n = dr: r - q:r seu log ren = (q.r
debet esse  fh +gdh + addhZ: h =
sed haec comparatiae effectu est difficilis
Nec video quid prohibeat, hoc loco
resticula lege homogenes  (odr- gdx) n. a + Xdn - a
Bs. ru seu n = Y: b scqlair)
si e in aess. C fo esse
seu r:n =
X
dem in patet atia cast cit deleminatus  tonu i pi
deria it st atita leases erit deteminatus contun trp hul lup im prde
verum en