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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 4
# Folio 11v, page id 00068206:0022
# Scan: The same scan as fol. 12r (00068206:0023), where its text is given.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068206&page=22
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 129 lines, status machine
# Lines: 129 recognised, mean confidence 0.73
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

X xqX +r
XX ∞ qXa.
aX+btg3X
2
2
X X H qX +r
ax tozue 17X  Ab
14X +r
axt
ax +ZX
yg
b
axut bX + yX ∞ 4X + Y
ax + b Fy + bX + yx ∞ 9X +Y
ax - gX +
er axtoty
+ bty
axpbx2
X3 x axp 467
XXX
yy x X9 ta
bX  cy+ d Z tC
xxgetr
yx ∞ +r - Z
+
a
ra-Y
=Y7a) +r79 - rz
1aq (+raz
XA
Z
a - 9+ 7
a +9+Z- 2ag + 2a7-29
Sonse a atia a ra r
a-4+
=.
Y+C.
c t
2YZ
erzue
Ya -YZ a - 9tZ
+Z, a -9t
ra= raq +Z4 - rZ +Zat 39 +2
=2Za9 + 24 7 -
12
t
XXL
a - r
X x
Xx a +B
X x a-
a
b
+6+c
e
c
a -6 -c
aa
tem
a- F.b- 1
xa
X
1 qX + Y
X X 
aX + Z
ax (+ ZX
axtaZe +ZX 1 qX + Y
s
Nit hinc
demonstratia quod non detud formili radicus
Cubicae imnginarias habentis, sine imaginaris
sit aliqua  a +F- b + Y a - (- b p c. posito 
Cesteatiam expressionem sine imaginariis, fiet.
Yar lb 1 C - 3 a - f- b B C - v
Ergo
Ergo 2a p, C - 2CV F 3CY. seu v - CD + C7 22
X H qX+ raysut XH bX + CX + dX + C
X
bxrxen dure
XX c
bx +CXFx  ex H qX  X sxt
b XAbXrbdxabe qbX qcX qdxtqC
XH qX + rx + SX + t
bx Bx
bXab B ex+ )
at L. 6), C 2C J a- Lib + 3e a -b- 2ar. b ( (+ fb) atr. b
seu 2a 7 c - 3C + 3C V
a (t s- b) 1 C - 3ev + 3cv2 - v
= a(t s. 6)
X’H
X H bX + CX + dXFe
H bX + B.
X a - bB - x) X (seu X H
X p aX rx+ st
6+ c-9
X bX + CX + dx+ e
X5 bX + cx + dx +CX
X+p X   q X + YX + fX + t p  
- d C
B 6X Ap X L Bdx + p C
X - qX + r p d
CnX aH =
possibil.
seu v2- cB + C p E - C + 2a p = C + 2a. Ergo  + v +C Y S-C + 3a (Ego si 34 pE erit, v quantitas impossibilis aequalis ipsi 4C, - e42a
BC
12 3C
quod est absardim imo generalius adhuc ipsa C- 3CV + 3CV  2a cum requirat ipsam V solam ad constructionem eut possibilis C. determinuta per po 2C
di imporsibilem Adhuc talilius forre. ponatur a  DC. fiet C - 3CV + 3V  EB. Ergo C- ct GV 1 9V - 3V +2C B  v + 2C. Ergo C - 2Vp S. 2132G
sed omnium optine sic. quia jam =V + E  V. C +2 a et v est imaginam, e
Nilcil est
pt = CP+ CBH ZaV Madirembubicae affectae non posse exprimi sine imaginariis melius ita demonstratur, sit radius cubica non imarinarie expossa c. ejusvalor,
a - f- b
3C per Imaginarias Ya + (b + _ aequ. C. ubi una eademque imaginaria. compendio ea vocetur v. fiet: V +Y aequc. et Vv + Yaequ cV. e virvu
Sai. b
seu a, +S- b q + YV aequ CVY, pro vo valor ex aego 4. fiet a + 1 - b f YB aeqo ccp = cr. Ergo
 grecdinset tu pr cotatias qoen  se nas ri    ps s sumtitasi n flliaribu
+
h = (bs- aequ pa +9S b, seu n. - 3bH
qu
q- 3Ch + b
eqt
ZH
sem an qx, SY
concludendum quo
gaper
quoritar an    seuan  Y
seu an X HAY. seu an qX. 19 4r
possibili. quod est as absurdum
X B aX +Z