# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/486/text
# Catalogue record: 486 — [Aufz. zur Algebra]
# Incipit: Possibilitates et impossibilitates seu limites aequationum per
# Date: 1683-03
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=486&katnr=58063
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 64 (from the shelfmark LH 35, 8, 30 Bl. 64): 2 pages, canvases 127–128, page ids 00068124:0127 to 00068124:0128
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=127
# Lines: 110 recognised on 2 of 2 pages, mean confidence 0.87
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 64r — 00068124:0127
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000127.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 79 lines, status machine
dua oquationes, ad e habeant divisorem
en radicem communim, quoad eandem literam
lope earum tolei pote
litera illa nisi omnes
divisores in una divida sint in eltera quaque
seu una alteram d vida
Mraevidere asumentiam aequationum ex numero
ladicure. Si sint duae aequatione  x
et un
ultra
+dx + C = 0.
y
Arig
ut
asclato.
posst
eu
ma
omnibus
2
il +y∞ +C=0
subato X non ascendet y
sed quod si utraque litera X et y sit
X2+ ∞x + C=0 et X7
7
12+ L = 0
ascendet, X ad gradum mum
possibilitex les et impossibilitates
liuntes aequationum per cirvarum
maxumas
aequationis
adices mulat in falsas; et consua
A
faulitas mauo
veras
Non salissperunt
limites iiti constet non posse assiguari alitores.
Avribends plunestinea diversae puhanorem. ecta
regua cutaus homogeneumoparationis secare dabet in tot
punctis, quoc sunt radices ae quationis, et un tot locis ei appropu
un
quare et ab darecedere
urvas
quol sunt radices imagin
ecta quater ad retam e
et quateor ab ea recedat; si quatuordim ensionum sit aaequatio
Neure cum app accedit ad eam nec eo pervenit fugo in metro
quam cursu sistt. Et iterum cecedit. semper mo in casu istius appro
piaquationis untie semper duae numerandas imaginaris, quas
uti duae esent sectiones adeoque duae appropiaqvationes des
ragessionest. Punra reversionum quot sint in curva inveniri
potenit ex numeo mapi
vel umaum rdicum aequa
ponis ad luaxua vel minima determinatae.
sed notanta
p Fq.   pX + 9X+ r = y, quia di =0, omula evane cunt
puc nulla est reversio curvae deo a despensu ad ascensur
eu) cnon reperitur, quod nobis per qmmodum aecidet ad
designatidum ordinam punctorium, quod foret difficle
mostare ex curga si ea sursum trevertere
ex punctis
reversionum ab ino lalusad aliud habetar exadte
e
e
an
quasio serviens ad investrganduum aequalivnis propo
sitae diorsore possibilitur exprassum quadraticum tothabt
daiget quol aequatio ipsa lo verum quol radices
habet aequatio sunt siniones, hoc inellige posito semper
V du cis quasibe
dadices habes rectantatum Is
ut sit possibiliter exprrimibilis debet aequatio pro inveniendo
illadis secundo agertrotermino civisoris
+ax + b, ubi
pro indegiondo a, si aequalio dibidenue sit  sex gradem
assendentur ad gr. 15 ut et pro b. itaque aequatio ita sempe
habet divisorem quadratieum possi
biliter exprimibilem
u

## Folio 64v — 00068124:0128
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000128.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 31 lines, status machine
 aequatio proposita omnino vel aliquo casu
si AX sunt aesra ant
tunc A() sunt negativae radices
ossibilis
vidend AX affirmativa radix
affirmativa
A(X) negativa, A(XY imposi bilis radix
XY vel (X) (Y) sunt homogeneum compara
tionis quaentur joram
liceat aliu ducere homonentum pparationis
parollelam ipsi AX aequo distputem ob ea quam Y (Y
((X) sC
ut
uner et utrum ex quoque linem ubi secatura persectione, quoque
curvae ab ipsa factae a sinistro cateres exhibeant radices
infinitis modis perfficitur nistra
Melhodo doctrnn. demaxnois et minims noh non sit opu
nec tollere irratio.
quod non suto.
plures aequationes reducere ad unam
limites de pluribgae quationibrs
seut ad tre, ve plures utee
nales et tamen habeantur
espiciendum maxime quid fiat,
tamen forte.
ad eius imitarem
uciu ncognita
cm sed maxune apo in prictatu, si ae qualio sit
es curva non pe extriber
involuta irrationalibus. ubi admirandur usque Melhodi mea. Ex
odine maxim um et miimarum habebitur odo radiaum