# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0217
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0217?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 108r, page id 00068200:0217
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 107v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=217
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000217.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
# Lines: 98 recognised, mean confidence 0.79
# 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.

sit jam ex natura p problematis:
(y (aequ.  y aequ + za 2X a
65)
fiet: Xaequ. 2Z +2.3 yy
(20)
du
(17) V
aequa
dx
4 a
1 et fier:
Ergo in aequ. 1. substituendo
(19)
a. et y  ex aequ. 2. fer y aequ +v + 4.5 Xa
(21
pl 7yaequ. 4vy +4. 5x a
quas duos valores equando, fiet. jam 2. 4 aequ. 3. 5. per 15. Ergo 2. 3 aeiu 4.5
per equu
Ergo 3 aequ.  E at insig in quantitatibus signa significantibus
non differunt 2. 3 a 2, nec 4.5 a E Ergo per aequ. 15. habett.
2
2. 3 aequ. 4. 5. Ergo aequando valores 28 et 2) fit: + 4vy aeu 37 a.
247
seu y aequ. f3. 4. Za. Unde in aequ. 18. erit Xaequ 2Z + 2. 327a
(25)
0v
pro X et y
fiet: ZV aequ 2 vZ 4 2. 3ZZa + 32Za Unde posito 2 aequ+
aequatio est identica
(26
idus praevideri polerat, revera enim
non nisi tres aequationes habentur 1. et 2 et 17
Ex cegu 18 est dx aequ. 2 dZ + 2.3. (2) y dys aiqu 2dque f 2. 4 yd3
et quia y aequ + 3. 4. Za
et fiet: 2Z
+
laet
+a
aego 2dZ +2. 4. Wayd Z
nfiri: 2dqe + 2. 3(3 aa Z
3( 7y
AB
3. 4.  dv oguaque
C
aequ. + (
0o
vv
Z
dy
ous
AB sit B, et ATsit +. Q aequ ~ Daego y + y2. lagoX+a
Dago y + 3 + a seu B aequ. 3+ seu y rego a8 a gt -a
dx aeqo dt, dyrego a d . dxergo at aequ= rgo
at
Ergo
ago tL
a d
e
du
8 seu 
Nunc aliter logarichnicum considerem
ad
trego s. + d
a
y
ac
v
noperito E tsus aplolos logiidimicue, EA aequ R F aequa BCy
aequ a-y
ext Anstu
22)
a AP siu Zaqo (X + 3 dy cum autea essee
(4),  aequ. (9 + X dx aqu) y + Xa -xy
du
xaro Reg
(5)
alanay
egu a -y. Ergo 7 aeqo 1-  seu y a y 24 aZ - av
a
(0)
a- y
Ergo per 5 out: ab -lxZ aequaaz aav (= ax Z + axV. et fier:
X aequ. A vZ+ av - aZ aequ. Z+ a - aZ  i d
Ergo per gerit dx aequ. dque - d d et per 5 erit du aequ. ad . Ergo pert
(13
Et sumando
Z- a Z aequ. 8 va
quae est aequatio ad prarabolam, quod et verum est cum 3p est a
X= a aequ. aa - ray + y.7
V et
Nala
paribolam esse Nam relatione inter
BPaeqr. y dy s ADvrl Blaqu. y. per 3Y av aequag. + Xa -xy. y aequ. pr seu y aequ av - xa aequ. aZ- av per 5
dx (12
dy aequ.
2
dz- a d Z
A Z