# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/16902/text
# Catalogue record: 16902 — [Math. Aufz.]
# Incipit: Cum qvaeritur ut duo puncta ejusdem curvae
# Date: 1697
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=16902&katnr=45250
# Work: https://leibnizlegible.com/work/DE-611-HS-958803
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folios: Bl. 159 (from the shelfmark LBr 57, 1 Bl. 159): 2 pages, canvases 319–320, page ids DE-611-HS-958803:0319 to DE-611-HS-958803:0320
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=319
# Lines: 82 recognised on 2 of 2 pages, mean confidence 0.79
# 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 159r — DE-611-HS-958803:0319
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000319.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
cum quaeritur ut duo juncta ejusdem
curvae facinnt eundem seffectum conside
rari et ee aliquam rectam ope puncti de
terminatam esse radicem aequationis, et
in qua plurium radicum effectus idem per
coeffictentes determinatu en. gr. termiaque
alimus est rectangulur indiali. quaritur ergo
curva, quo a recta ex dato puncto edncta si
 recturguum sub duabus emissit
puncto frvo ad duo punctu n quibus recta
secetur si
curvamfrct, iquale ipsi aa. ergo
rro emitis sumi potest
ad YC
proeterea
e
si
e
es
e
taa-
ubi
missa X abscissa ex hic aequatio ribus varie
inter se copositis fint nova ad curvelu satis.
falientem. Quon. Y aeJ. V per
ee
d
abes et ca
a
e et
a
2. fes
undo si be sit conpans ca fut yy + CXtaa 20
inr cum notarem
otim ex Epistolis Cartesii, Ferma
tium scripsisse, polse a se curvas
1
H
exriberi in quibus plura puncta
suuat eundem praestent affectum
ude
pseripsi ad margia
effici licet
per radiet
quationuo
saequationum.
isque druper velegens non intellexi
intio, voner taudem vidi per
cognitus iaqua nonum citera
ave effici.
non
aeculiare foret
onones radices effect
praestarent sed verb. (gratia
huane ima R minima simu
cultis cn problemate
sicinbulesdni ciredt
aiua
2
bomodo enm eligipotest proqui
ou

## Folio 159v — DE-611-HS-958803:0320
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000320.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 21 lines, status machine
ptimaratio erit assumen aequationem ex. gr.
in qua constat ex ullimo, esse
dectangula radicum
0.
iuom
aequ. ac. verb. gr. XX + x + aa. iade
Huic jungatur aequad rectam, ubi ax ny, ex na
furae rectae quae curvum quae tam secare debel. surpo
nitur autem b dari ex n ut cunque e quod s
jam ope aegu. C et 2 tollatur n, habetur Ereg. 3
sin qua X et y abesq n, quae est ad carvam cxcest
tam, joront ergi b, alitratus aliter assumitur ex a et
a. rationaliter tamen, mutabitur curva. videndum
e
aa non priu liceat tellere exaltare aequationes  et
L. seri mulliplicando et componere inde 2tiam
n. Jane si aeq. 1. mulliplices
ex
et tollas deinde 1 per 2. fint ag. 3 divisitulas in duas
ut tum cemum tillerti
seu non procerit multiplicatio