# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0466
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0466?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 232v, page id 00068200:0466
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 233r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=466
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000466.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 107 lines, status machine
# Lines: 107 recognised, mean confidence 0.75
# 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.

par b
Operae pretium est, ut videam aneffici possit, ut duoe termini de ex Aequatione data Terminus
secumus et tertius simul tollantur Habem qp in Aequaline quadrato quadratica
habemus: ap  C.  4 p FI 1.
ejus valorem, fie
e
itemque p - 3lp F -am. et pro p substituendo
iga
Bl -am sive l am
240
aequationis quad iato quadraticae
+4 Sam. Antequam
ego possimus utrumque terminum, secundum et dertium simul toller, efficiendum est in aequatione proposita
ut secundus termini cognita quantitas, sit quadrupla radix quadrata cognitae quantitatis termini
tertii. Quod an effici illa arte queat, videndum est. Si aequatio cubica esset foret
foret
23
+ 2p2
a
ba
+ 3P
=B3 Unde pei L. et 3p - 2lp  pam am. vel
-l .. - 2l p . = lx2
am +amp
+anp
Aequatio data calica esto, ut dixi
a 3
k
j
2d
= 2l 5 - am, vel l 7 dam alvel le
vel ldam. Quod ut in data aequatione
efficere tentemus:
yN
+an) + an
Ponons Z
Pouamus ZB SXg. Quare id sit terminus secundus aequalis radici p se terti duplicati
erit aequatu
a
v - 6pl + l 
alia ergo arte opus est, nimirum, ponendo
et yn
adi
sive omnibus per  divisis:
v
eritque 9ga-69al+
s
9a-6lag +am
op2 = 6pl + ham, quae aequatio identica, mutelusque
t x
 51. a + g.. EgoZ3 F
+ 39a X + 3agX + a
Unde rursus mutilis inquisitio, patet, hc
arte quidem ista, quod quaeriimus effici non posse.
itemque 3agr
er
req
ulag.  lag
+am..
+4 3
+an
+dofrx
Aey. 1.
C+34Xrq
+392
ex
+39a - 1ga
e
et fiet nova aequatio:
+lga ∞am p 0 quae sirdae ps  multiplicatae jugatur siet
Aeguda
dac
da
an
AL
ang + lgaaem ere sive g- an fg +D , +3a +D
sive gF 4 
am
2l
2l
assa
4C
ga..
HI
ss
cunque sit sge+ Ega fietque gF ex dicta aequatione 3tia, g am. ideoque at rursus
g1 L ergo = ( am sive l  ham,, ut supra neque quicquam effectum
est tanto conatu dignum. A Nisi quod rationem deteximus ex aequatione qualibet
X _-3m X - n ostensum est ab aliis secundum Regnlas Scipionis Ferrei
s
confera mu jam aquationes duas unemus
quoritur valor ipsis 
sed m  m fi  n 15): poratur eggo m FJ A 1 N(3) L  C, sive e  M- R s
A - 3m X - n 1 0 itam 72 X 2m Z 2n b(h bem N
as nn posse rai applicars nnsi sit  n6  m. ac proinde  s H p Y ( B note
poramus eam in
ut
tollendi terminum  tertium vel antepenultimum. Bopum est certitudinis
Si sit aequatio
erg
-1lfg .. 2 lg
2lag + am 10, et prore multipli aequatione multiplicata per d fiet:
Acg. 3.
e
2
in
+amf.. gang.