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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 131r, page id 00068201:0261
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enuntiari potest. Et quiliber modus habet tres radices. Unum tantum Nec
video quid abiod dici passit contra possit.
Porro ut valor ipsius
M non nisi cubica aequatione habeatur, utitd ulile in aequatione data surdesolida
effici praeparando ut sit e 70. seu ut absit terminus tertius; et ut ea prae paraoe
facta maneant d, et h. eigoem signi. Quod semper fieri posse videtur.
aequatio autem pro mostigando valore ipsius m, erit:
=aeg - maf 4 ram Vdath eha + 2a h maus F ma t
a
4 mah.
Quam praeter grimionem video non esse nisi peanam et erit:
rgugn 4n a Fh  =gam h fdah Y ta (F2 a hmag + m ag
Eno num si abest tenia
Haec method,s si bona est poterimus eam etiam in quadrato quadraticis
aequationibus experiri; sit aequatio X ax aY Bo: multiplicetur per A + m
fiet.
X A +ac X + dc B X + pX + aq X + ar X + as p0.
scubamus: EdX +DX +ab H AX + pX + aq X +aer X ras
+ d2 . +2abd. + a b2517
Axciletur quadatum ex latere: X + pX+ aes+ ab
X + PX + 2 fastab X
o + psasaeb X
fiet:
+ as
+ ab2
nas + a b  ae Y + 2abd, + a9 + 4 d - p
HI
4 paq +Ep A2 - p. L Y
 16 ad
+ 8paque 4p d + 16p d2
2p3
=16aY
4a d2.
fictas
ad eo
et 62
+16 p aq
aopaq
-64 pagar
ribpar
dga
16 a4 + 8aq 4d + 16d
=8 aqp
p
Videndum ergo an sedi possit, ut fit 1bp aq 48) aqu oupagat p topat
1
ita enitm aequatio reddi posset plana. Quem in finem cogiletur aequatio
fiei:
quadrato- quadratica facta ex cubica A X =  X +  Y. 0 ducta in X + mpo
+cl X
=ahm
+2t m St
Destruatur Y. ponendo M p C  p.
restabit aequatio: 1644) paq Lop.
Ct
1C
X+ X - bh. X
substitutis hacoribus:
+M X
X
+BW Ih + 10B1
ak
Unde radix. extrahi
+ah
et C0 1 D
Quare
necesse est i2 esse quantitatim negativam, seu Terminum penultimum aequationis cubreae
1
ath2
+1
error. debet
esse be 
1h
potest, et fiet
Co
datae esse affirmativum. Fiet autem bpi Ld et b 4p
16 p d qud - 49). et d7 49’ asa
si es . 216, 4, hd  s h0 siut ere sasit Ia 1 o
Cum ergo K. sit grantitas negativa, debet esse Acolpt
a
e st
21
2
C12
 as aedque scet:
+hC
A2H R - 1607
co h = 16c