# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0515
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0515?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 258r, page id 00068201:0515
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 259v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=515
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000515.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 83 lines, status machine
# Lines: 83 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.

Esto aequatio ad Circulum,
by - y (X +dX. + ea.
et salia aequatio ad circulum, fy - y ) X + gX + ha proy posterioris ponendo
ejus valorem ex priore fa: nembe X + dX + ea - b9. fier:
srecta X + ha, ideoque yp +d X - ea
fy - by + X + dX + ea 
nd quae aequario est ad Triangu
duobus cinculis solui potest id etiam uno cinculo et linea
recta solvi posse.
+9 + haseu XyYC + C
sed aliter veniamus ad radices attollendae aequationis causa.
faciamusque bus ga ea + d ( N  X + d vel 7 + (M+ d. Imo
et pro y substituamus V+D fet 5 bV + bst - v - 2V1 AV ea + d et
brevius by - y + ca 1) X + d. et alia aequalio eya Y + fa p X
fiet Abg- y t ca  Sey- y + fa + d, ei quadrando utrobiqu
onsyttetur vel
bys - y + ca 1 ey -Y + fa + d + 2d... Multiplicetur atraque aequationis
pars per y + Ergo antequam huc procedatur multipli
aequations pars per Y + g. 0, fiet,
fier. NbV +269V + qby - y- 29V3
per y+g.
u
fiet
Multglicetur utraque
seu radices per fy4agy+
et multiplicetur utraque aequationis pars
y + cay, + gby -91 +gea p ey 17 etc. male
non ita assurgemus ad cubum, ergo sic potius
una aequationum datarum
by - yt LX, + dx + ea  multiplicetur per y +G fiet:
by - y2 - yX + dXY + ea Y + bpy - ∞Y + X + ad X. + ea ) 0. pro X substi.
Auatur ejus valor ejus ex aequatione ad lineam rectam, nempe XM C + Cd
fiet: - . V
..
=2 nto 1
+ b .
+ da.
+cad
= c. ut
=co V
+dd...
+2ndc..
+ea..
+ bc
+eda..
Ergo, b p 2 (n C∞ - d = c m2
+ Cd
+ cdcd
fiet postrema equatio haec: - c to
Esto jam aequatio (ubica pura:
conferenda cujus factitia plana ad cubicam
quo valore ipsi in tertio termino cedente inserto
adeoque d e -  +  n ad C + ea + 2 - cV n
sed notandum est ipsam
_X  Y  + 2(C, +Cd
2 X X 
13. p0.
sublata: fiet c +cd  arx2
=a (+ eC - ema)
substituendo valorem ipsius d in
170
caelera erunt p0.
nondum haberi,
arx
uy
+ C
+cdp, Ho
eoque valore in ultimo termino
inserto, sit.
isus valor in termino ultimo
niserendo
e
mno possumus pergere ut ante
00 + do ejgslocum in aequatione ultima
 -C∞ + 4 MDC + ea C = c n+ c3p, +
+ M2 a2∞
Unde sequeetur ex tot incognitis super c. . M. e omnes demta una sumi posse
pro arbitrio. Quod videtur absurdum sane C non potest sumi pro arbitrio, alioqui
posset cabus ax habere radicem quam libet. Unde sequi An forte tunc sequitur
ipsam C esse radicem imaginariam, et sequeretur in omni aequatione subica simplice
unam esse radicem imaginastiam, sed nihil referret tamen, nam et ope radicum
incpparicnum postent deprsui aequatires ,si coqurisserentu
u