# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0449
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0449?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 227r, page id 00068196:0449
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=449
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000449.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.83
# 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.

X67. 1676. Figmra quadramt comparatur cum alta alterius disse
In opistola cuea ad Cloenbumum
aexb
furhatidano
scupta 1676. est formila generalis differentiarum
Erit
gradus cubici, ubi si tolli possent tres puae
lite primi termini erga
4Z. X2Z haberetur
quadratura Hyperbolae modo restet XZ.
videamus, fit, 3bc + 4ab (0. seu 3c + 4 ab 50
tursus 6b ce + 4b d po. seu 3cC + 2b d. 10. et nabcipo
seu 12 ab + e 10 fiet: e- 4ab, - Bab
quod est impossibile ergo tollo non possunt su tex mini
fieri potet
i proposita nira invenire equadrabititatem anatysticam
absolutam, idem est aequatisongro sita curvae aequatione invenire
aequationem exprimentem differentiarum inter ejus ordinatiis
et hanc data compara; sed quia id sae pepolixilum alia
crcumspicienda ars.
3
sit aequatio a a + bX + cy + dXy +Cx + y + gxythxG + b
itis
fiet alia et b bdx + duxdus t2exdx +2gXyCX +2t Xy S) e
cay cdy ayex 12fydy te
2
+ 3lX2dX
3My dy
agridu
+
hydx
Alterutia jam ex his dx vel Sy pro constante altra
2.
aro i variante sumi potest et pro varia substitui
in
Ox esse constantem et cyp.
et data sit rtlto exprimurs relationem inter q
et X  posito Z esse ordinatum, X ubscissam
curva cuci quadratura quaritur, quaeritur aut ila data
asquation in duas inter Z et X, assumto pro arbitrio valore
ipsius y per Z et X expresso, duae aequationes datis similes
formari posint H ita procedat, fingatur aequatio relatiorem
 exprimens inter Z. x. y. et ea tollatur Z ope datae
quod generalissime fiet. Sublata comparetur cum generacissime
nata idi
ex solis xs composita. An rectius erit non universatem
assumere x X. y. Z. sed datam inter X. y. dividere induas
t XX+ Z  ita dividere, b X + fapX cu 0
CH X
d.
agas es