# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0143
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0143?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 72r, page id 00068196:0143
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=143
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000143.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 123 lines, status machine
# Lines: 123 recognised, mean confidence 0.76
# 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.

dic + dio  + 1odu
II + 10y
+
d21 + d20y+ 20 dy
21 + 20y
Si in data absit Y du fiet n = -m.
10, 11, 20, 21, M, n pendent ex X
dividatur au
t
2 per
s sed pongmus nunc quidem potius in aeq. data esse 11I =0 = 110.
fiet m, ae - 420 =
20
120. a seu log. (0(Z a (120
00
20 00 M
entis ipsius dus (divisus prius per 102 10. 20) est
d11. 21 + d10. 21 Y
+ dl. 20 Y + d10. 20Gy
11d21 + 11 d20 y
+ 10d21 y + 10 d20 yy
+10. 21 dy
+ 11. 20 dy
+10. 20y dy
S
+ 10. 20ydy S
n
e)
Data
=06 100 +by + 1209y150) dy +Ilydy, oua
ubi 100, 11V, 120, 101, I1, dantur ex X
quaeritur y ex X
10.20, it aq 2 par III vel ponater At =1 d ac coincidet oefficientus ipsius idu coefficiantes
a et firt n =-m. dividatur aeque 2 per
1 10.20, et 4 coefficiens ipsius yy,
posita igitur m cognita, suo arbitrio assumta Habetur 20)
20
10 a
a
Porro loefficiens ipso coeffi
M, 218 - 11. = 101a Et fiet 21 = IIY + 101. 20a vel 21(18) 11Z 4 1 0110c Y
20
10
00
00M
6
a
et multiplicatio per m: 00 flam
Ob coefficientem
ipsius es divisum per 1B2o sit in 44. 2, Cg in aeg. 2, aequalem nihilo I10 = 0,  evon superflua est divisio per 1d. 20, C explicemus autem in eo  20 = 10l:a
L
20 et 2l jam inventos
fint (d10. HIY + (d10. 10 (101. Y
ut divisis omnibus per 10, fiet
erminus ulismus
a
I1 = a
10
od
k
(=11 Y d 1o) - 11, 10 dt ) 
00 m.
I (+ dI1. IOY L
a
200d
a
a
sate
c
 -11. 10dr - 10. 11 dr (-10X d11) 910r7
a
a
a
de01Y). quod si faciamus M= 10) nam inarbitrio est, erit ratio I1  10 constans
mq postedivisionem per 10. 20
at qui utrinque comparatus
repertos fit 00 du.  H. X M 4 00 dH. t
otn
d
2
i
d10) 10 d(
00m
01. Y
12
00m.
est autem 20 = 10Y
merest
14)
et 10 = II. 200ar:, a d (iolr: M) compendr 10= - 11 t:a
a
u
Ergo 10.20 = 10. 1Orea =, 11. I1 EF: aa. Et tandem d1. 21 - 1 421, V 00 m = 100. 11. 1Et: aa et vel  21 d - 1d2x a
l 11 d21 = 21 d11 - : 11. 11 = = 100H: aa, id est 21H7
evanescet aequandu duoqvalores ipsius 21
∞
m dI. 21m = 00 11 d21 m = 100, 10. 20a et substituendi valore
00H
a
21: 11
fiet ex aequ. 14
e e et-
e1 = H,
a
e
et
  (100tF.
00. aa
andem prodit oome= m 110ott= quarm - 101der, eet porro ex  eg7 est  
Sed ita postremo quaesita
(ex 11g. 10, 14) 11Y
voaa (100.
C
120
1D. 1= bcn
a
101. pL
a
-
Er: m = 2. vordr: aoirim) m. sed ila apparet ut quaeratur M, prodire aequationem ipsa data dificiliorem.
ooma
Eryd
assumta