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# Piece: https://leibnizlegible.com/api/records/27887/text
# Catalogue record: 27887 — Aequationes plures plurium incognitarum ad unam unius revocare
# Incipit: Praescribi potest quousque
# Date: 1679-10
# Other printings: Knobloch: Beginn der Determinantentheorie, 1980, S. 137
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=27887&katnr=56665
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 257 (from the shelfmark LH 35, 14, 1 Bl. 257): 2 pages, canvases 513–514, page ids 00068201:0513 to 00068201:0514
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=513
# Lines: 68 recognised on 2 of 2 pages, mean confidence 0.93
# 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.
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# 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 257r — 00068201:0513
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000513.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
a
octot. 679
L
+bX + cxy + eed x + eV + fp0
my +nx + PXy + qX +ry +s r, d
Quot sunt puncta in quibus se curvae duae
hujusmodi intersecare possunt tot sunt
aequationis radices. Caeterum cum duae curvae
rie sint sonicae nec possint sese convae secare
Qvaluls
nisi in duobus puntis manifestum est non esse
nisi quatuor radices
ditas
ponamus ruas curvas an intion  sactatu
seu duas esse eadices aequales; item ponam
eas adam alibi se fangere seu tras esse trudues
duas radices esse bis equales Vel etium
ponamus tres esse cadices aequales, apparebit
quousque deprimatur propositio. Quae ratur enim
tangens prioris curva iiemque poste fioris satim
apnarebit depressio. Id si frat ad huc semel
alerum apparebit nova depressio, et animadve
tendo quousque fiant depressione, cognoscere
hinc poterimu scutcherrima latione quonsu
quot sint radices aequationis; etiansi involutae
essent imrognitae irrationalitatibus. Hoc
aptificium procedet etsi plures sint incognitae
pluresque aequationes nec dubito generalia
linc Meoremata condi posse nud C praenosce
tar, quousque semper ulculus sit ascensum
ad summumu modo tamen inter calculandur
postea inutiles in se ductus evitemus. ita enim
nonnunquam efficimus alioqui, ut calculus altius ascendat
quam opus est

## Folio 257v — 00068201:0514
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000514.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
requationes plures plurium
incognitarum ad unam unius
revocare: et quousque ea ascendat prae
videre ope numeri radicum, item methodo,
tangentium,
Praesciri potest quo usque assarrectura sit aec
novissima aequatio. Qe Exempli causa
sist duae aequationes, una unius incognitae X
utcunque assurgens, altera alterius utriusque X et y
in qua X est gradus inferioris quam pauto
in priore; at  solum simplex nec ad ullam
potestatem assurgens. Ajo sublata X in posteri
re aequatione ope prigris, aliam aequationem
inveniri posse in qua sola remanent oes
V non assernectura ad aequationem altiore m
quam quae erat prior.
X + pX + 9X + YX + Sx +t 10.
XY + bX + CX + dX + C + y70
Habebitus _ V.. Y .. Y. . y. y. 
e
Nam X habet 5 radices, cumque V inventa
et pure habeatur et  simpliciter patet
tot fore non plares ipsius y valores quam
sunt ipsius  X.
vel er + 1
decimum
ad gradum sextmus. si
si in aequ. 2. fuisset
aequatio assurr exisset
fuisset: dx)+ ey+ 
ascendiss et ad gradum tetium, et ita pornum
 decimum quintum
si
duae incognitae sint duaeu, literae viocitur