# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068010:0079
# Permalink to this reading: https://leibnizlegible.com/page/00068010:0079?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 13
# Folio 40r, page id 00068010:0079
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068010&page=79
# Source image: https://digitale-sammlungen.gwlb.de/content/00068010/jpgs/default/00000079.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 72 lines, status machine
# Lines: 72 recognised, mean confidence 0.82
# 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. ac. aC. ac.ac ac. a
a. ac. ac.
1. aPL.. C. C
a ae a
X
propositis aequationibus
pluribus plurium incogni
taram ex iis fabriae
tur totidem notli quod
sunt incognitae in quibus
incognitae sint eodem
modo compositae, aliis
incognitis, ut hoc obti
neatur assumtis;
v+b
A
quo facto
C cestabit
4 calculus ille
tugens, qui
alias necessam
ad tollendas
ordine incugnitas
et solvi poterit
facilius problema
poterunt solvi problemata, etiam
non ad unam incognitam redu.
cantur dum scilicet ducendo in altiores
arbitrarias formulus simire aequationes
obtenebuntur sinila etitia altior
quarum nota resolutio est, facta scilicet
ex formulis continuis in se ductis
4
a a
2pr
23
A p3
ec. ac ac c79
denaetae àc ac. 
Data prima er aggregato, ex secunda et sexta in serie  sex
mediarum proportionatium continuarurue neperite aggregatum
primae et quintae: hoc aggregatum quaesitum sit a. erit
quisita, a -b. sit secunda e erit sexta. d- e. Est autem sextus
in primam, nempe bd - be, aequalis secundae, in quintam  ae- be. ergo
fiet ex, bd Ergo erit: prima b. secunda od tertia tertia (C) quart se) bd3
a3
boe
quinta  bd  a - b. Ergo fiet: a - ba (, bd4
Sed si aliter inquiramus: sit prima b. secunda e, tertia: C. quarta e quinta C
t
sexta: e
a5- ba
+b1C
be
a
et sit e+ C p d patet has duas a e5 + bte p db
a
b
4
b
ds
ae -bac5 + b ea - b ac
aaequ. b. C + aC aequ. d. nonc ap (X + in 3Y
et e aequ. PX + qy + Y inde substituendo et
aequationes componendo fiant duae aequationes in
equibus X et y. se eodem habeant modo:
N. ompia pablemata reducta ad duas incognitas eobo
bd - ba + Sda - bda
Sirmaliter se hate 10 sylui quetune por rectionem anguli ant inreationem
a
udia
modiorum u propritionatium