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# Piece: https://leibnizlegible.com/api/records/603/text
# Catalogue record: 603 — Variatio aequationis ad curvam mutata directrice
# Incipit: y³ + by²x + cyx² + dx³ + ey² + fyx + gx² + hy + gx + l ⊓ 0
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=603&katnr=58180
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 71 (from the shelfmark LH 35, 14, 1 Bl. 71): 2 pages, canvases 141–142, page ids 00068201:0141 to 00068201:0142
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=141
# Lines: 63 recognised on 2 of 2 pages, mean confidence 0.82
# 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 71r — 00068201:0141
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000141.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
y3 + b y X + CyX + d X + e y + fYX+ gX + hy + gX + l +0 C
ABHX. BC, _ y. EAp in VABn. m, m + X. et DB,, , MAX
et DC y +  mAx
DCH DF + FC2
q
EA, AV, VE
CF, FD DC
 DE EFAZ. FCB cd
et. DFp e, m X . + Z
et
m
DB
DF. DEA
EB n+X
EV a xm tEmxr + 2EYZ, mAX, +Z F) DF2
 con
(  W F
V. Ergo DEpu EY, in+x
m
FI y +2n mytxy, + n mt Emxtx
EF A B H 
FDF EL AmExAq
seu cont EV im + EVX + mZ et X F, Con = m Z = EVm
vel
osito
vel  in + X X fiet: con 4 EVE + mZ
te
et Z p con- mZ. ex E Co n-2conmzue + neg
1h
et scon- 2Hum C0Z+
ut 2 ele+ 1 2CdZ- 22 + 2+C0p y + in roe  1
mEt
EY 2
(+ et
F2m CoZ (  Er Z ( inmEv Coz niWu Z) + nli Co nit, 
= y2a.. - n .. - n2
F2n mEVyCo
= 2Nem EV y
Sive tuErprnito e, fiet: te n’ ( - non co Z - n’nqz Y X mé Vtrneme yeoq v mer
+C m
- n4..
sed ren facilius confici posse puto; per sola Triangula similia.
Eovor forte in colculo semper enim alioquii abet  inveniri pure
in aegu. 0
Invento jam valore ipsius X pariter e: ipsius y eumque substituendo, habebitur nova aequatio
ad eundem locum cum priore, quae si cum nova indeterminata comparetur positis
b. c. d. e. etc datis, et assumtis n. m. pro arbitriis (fomelsi adtm nova arbitrori
mi possit sumendo pro EF, potius GF; atque ita explicatis, ut y est p
quanam debeat, et proresioinis comparationibus explendis aliquius ex ipsis b. c. d. sumtis pro
arbitraris; potebit seu incognitis, patebit, quaenam si esse debeat reliquatum relatio ut
una aequatio aa ad aliam alteius formae revocari queatejam statim veniri poterit ad
aequationum formas: et enumerntionem omissis tamen semper ny +gx quia sempe tolli possunt. Inde reliquae
frmulae omnes enumerabuntur per conbinationes. sed quia nimi combinationum numerus satius radice
neu xaminari per
compantiones, quando e eadem curoae et quoties diversis surdis expum potest. Totres
enim una  expessio ad aliam redibit
aequationis ad
curvam mutata
directrile
curvam ad alium
retene axem.

## Folio 71v — 00068201:0142
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000142.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
ILHELM LEIBNIZB
RSACHSISCHE LADDESBIBLO.