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# Title: LBr. 705 · Overbeck
# Folio 104r, page id DE-611-HS-861255:0207
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=207
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 116 lines, status machine
# Lines: 116 recognised, mean confidence 0.79
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Cardamus vrlta Cartescus docuere squationeum radices augere
minuere multiplicare dividere Mirum quod substituere subsbitere, ubi maxime
Asiit
pergendum eral, nec docuere aequationes radices quadrare, cubares surdesolidars quod
tamen longe majoris co solutiones moinenti est. Mraeterquam enim quod h scepearontio
radis per se intractabilis cujus tamen potentia fit tractabilis c utique  fit serendum maximum
inde ad) umentum afferri ad veras aequationum desolutiones. Analyficas
pro exeltandis aquationibus res semper procedit multiplicando per formulam
arbitiariam cujus deinde literae invenientur, per destructitias aequationes, sit
quaequnque aequabro gradus e, attollenda ad ge, n per formulam terminorum adeoque
gC- 9. patet cum termini tot solum in nova aequatione remanere debeant ter
mini, quod erant in aequatione primassendatas etiam tollendos esse terminos ge-g, adeoque
pro quadrato id compendeum es, ut pro aequatione datar ad quadratum abfollenda
litetarum
sufficit eam multiplicari per formulum qua non differat a data oquatione
et esse literas quol aequationes destructitias
n mulliplica per
v g.  X3 + pX + gX + YZ
idem sine multer catione
es
signis locorum parium 
Hlici potest, quadrando tantum, si, ab una parte colloces terminos prium, tertium quintum 
B et habebis X +. X +. X +. X
hb attera secundum quartum sextum ee, et quades utrinque at x+ qx = -px-  unde
inp, b
X - pXX + GX -
X + 29X + 94X =. pp X + 2pY X +YYS. seu x f 29 X + 99 XX = rY = 0
s
N +21X + 22X + 27 X + 24X + 23X + 26
X + H1X + 12X + 13
X +2IX +Z2X +23X +24X7 25X + 26X
+11 = +112
12.
= 16X
11. 72 1823
12. 21
M
+
+ Bm
+mx eu
n. 22
13. 2)
P
1123
12.23
13.22
e
1125 I26X
1224, 12.25
1323
M X
S
An 3. 11. 12 + _ 3. 13
m = 123 - 2. 11. 12. 13 +3. 13
Lbs
pp
32b
-1:
n3 = - 1
0
= 21Y.
21 = - 11 22 = +112 - 12
2
24 = 11. 13 - 21. 12 + 12 - 11. 23
25 =. = 11. 13 + 12. 13 - 12. 23
= 112 13 + 11312 - 11. 12 -11. 23
26 = - 13. 25: 12
= - 13. 24 - 12. 25:11
Ergo. 31. 13.25 = 412. 13. 24 4 12. 12. 29
11. 12. 13-11. 12.13+12. 13- 11.n1321
Ergo 25 = 11. 12. 13- 12. 122.13 = 1313-11. 12. 13.28,:, 11. 133
Ergo (,V. 13(4 11. 12. 137-11. 12. 13, 23f 11.13 11. 12. 13-11. 12.13-113. 13.2
-Vnx ( 11. 12. 13, 12. 13 + 12.23 fD11,12. 13-113153+ 11. 12+ 11. 12.23
= (11. 12. 137= 12 12. 13) 13. (-11. 12. 1334
11. 12. 13 ∞∞, 1B.13 + 2. NP. 12. 13 + 11. 12 - 123, 13 +133: 1.13 - 1. 12-123
 seu fit 23=
quo vatore subilituli in 25 et 26, omnia habentur. Set sed quie exit
+ 2 113. 1
sed persequi
 distinctim operae pretium non est nam et haberi quilvel ocfficiens ex sola
consideratione labulae formam, Nam (3=  X + X + X seu X Est antem - 1= X +REXX
X
XX
cec
3
X
1XI
est X = fl e9 - 113 + 2.11. 12 - 13 = 13
modo facile rabebimus inveniemus et
jam Si X =
3
6
et n= XXZ. Eodam
sedet N = 1
 X = - l + 2X X = 2m - 1
X X = CE Ergo K X + X
 XX = A2 X X +QXXK + 2GXX -E X. XX = XXX X = + _ L I1. 13 Ergo
X
XX O + 3X
2X = 12- 2. 11. 12. 13 X. X. X = XKX DX = - 13 XX XX = XXX - 3XX X.
ergo X. X = 12 = 2. 11. 13
X X t. XXX + X X
3 1
23. 13
ergo XX X = 9 132. Ergo X. X = 123 - 2. 11. 12. 13+ 3. 13
+L X
+m
data
e
p
-
+n
X = - 11
Xx = 12
XXX
et = 13 = XXX