# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0223
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0223?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 112r, page id 00068198:0223
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=223
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000223.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
# Lines: 98 recognised, mean confidence 0.80
# 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.

A aydx = dx a + abXX + ac)
fiet ydx = dx s(e  + 2e5z + 2dae932
f = 11 a
2.10
sit XX = Z2+ afZ + aa,:, Z2 + 2toz + hh
+ aass 3d + 2a f9Z+ a 99): 22t2h2 +h
lBz + ab (3 + aab922
c
, t eh + 2 fh Z2 = abghZ
l
rebhtizZ tabshhz + abgtt
ac Z 19 0ih Z + 6 achsi Z +4achZ + acht
q d 9 = 13aa - 13da
V
C
2.10f
ergo fiet 14 (a4 = 13. 13(aa
10
11. 11
fit 12 = 2. 10. 13 + 1D. 11. 11
4. 10
seu 4. 10. 11. 12 = 8. 10.10. 134 11
2. 10. 11a: 2.10
si data formula confe–
renda cum conto,
102 + 11 Z3 + 1aaZZ + 132Z+ 144
multiplicetuur dividatur per 10,
conferaturdem de cum
qu a
24 +257 + 2a947
+ff27 + 24597 + aag9
2. 13aa + 11. 11 aa = 12 ac fit
4. 10.10
10
et 114 = . 13. B 
10
11. 1
et  11. I1. 14 = 10. 13. 13.
l
9-
de
s14 13 aa 1aa
o
Erge
10 210 f 110 11a
14
9- 1
e
12 290
ie
 4. 10. 12 - 11. 11 13- (14
N 8. 10.10 = 1
videamus an brevius considerando X tab XX taec habere duas radices secundum XX, quae sunto
aβ et aV. fiet considerando ergo velut aequationem fiet XXtaB = 0 et XX+ aY =d
seu  ez2+ afZ + aag + β = 0 seu + ezZ + afZ + aag = 0. seu 77 + aStrhBy
F 2hz+ hhr
 10Z7+ 11 aZ + 1a0 20 fret 22+ 1 a7 + 12 aa
77 + 11 aZ + 11. 11. a4 = H. 1aa -9.10. 12 aa
V ∞ 2 4. 10. 10
seu Z=
4. 10. 10
= 11 a + 1 (11. 11 a a - 4. 10. 120a)
2. 10
BZZ+ 2h(32 + hh β3
et β
10
aa9thhp
et B
Unde E - af + 2hβ. + s (aap + ahitBB - 4 aa eg - 4 2a9β 4tl. eC)
=4 etiti B
+ 4afhB
2, C+ β
sed eadem Z aequale eidem valori secundum V loco B
Et haec una aequatio praestat duas hinc
enim sequitur tamaf +2h β + s... . .)
= =a f + 2h7 (4)1(.3. 7 pro B)
e
quomodocunque interpreteris + et  sic tamen, ut  non nisi bis duae hinc
sriantur aequationes et si oriri possent quatuor eodem carculo
qui si aa g + hhB (. afe) = afq A 2h ()) + (et 7) 1(.. .. per B
CafC) = afβ(+ 2h β)) + (e+ () (.. . . per Y
=
aaff qu (β- 7) +2 af (3.))).. .. per (B)  qu (et)), C... . per β) = qu (et () (.. per )
(11)
et 2af (β-7) (et Y) +(. . per B) = +9 (et (3) ((... per V) - aaf qu (B. Y) 
quam aq. quadrando habebitur aequatio ravalis
1899 + abgtih rach. ( sen
ee+ bet ac
_ = 17
10
9 (C1)
... per ()
243F9 + 2abgh. + 4 ach (+4(a 9 9ta bghilitach t) (2aa e 9 t aafs ta byst rabs h reblit actih
a) 2a C5 + ab f+2beh + queh Z. qu (2aef + ab f + 2beh + 4 aCh)
abFkk
8 qu (ee +be + ac)
habebimus opus attollere ad quadratum
 aponatuer 9 = hih: q’e tunc dissiurulando q et e non