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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 75r, page id 00068201:0149
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Martii 1677
de Martibus De imaginno exti semirrationa Re
hiis altiorum  radicum aequatiom
V-1 non potest reduci
ad 3-1
sint quatuor quantitates ex rationatibus atque irrationatibus composita
 a ibsc
C+ d se
ftgh lam i
e
27
V+1 1-1YC
quantum licet arbitrariae, videamque quamde i quot modis in summa ex ipsis
possit destrui irrationalitas.
Hoc ut fiat debent esse
+b sc + d se +gTh. + m in 10 Hoc autem rursus fieri nequit, nisi
vel omnes irrationales sint una eademque, et fiat: b sc + dse + gtc + m Sc po
vel binae binis coincidant, ut bsc + sc + Grh +mTh
Priori casu
fiet vl b p7 - d - g- m  et tunc misus fieri poterit ut sit-g- m p 0
seu ut sit 9p - m. et tunc fiet bp, - d
binao binis coincidunt, fiet rursus
videndum ad
posteriore, casu cum
b d et 91- m.
imaginarias
jam ex his estendam Aequationm quinti gradus  licet
quantitates continensem semper
quinq
per sectionem anguli res olvi posset
CErrortion ita compenitur ut mox dicatabsiguo N)C
Nam componitur ejus radix tota ex quatuor quantitatibus irrationali
suide solidis, quarum una hujus erit formae.
X + + (2
(x- (x - 13
∞+1X
ponendo enim
a
V+p+g+rt
+Vr +
+9. Vriis
Pras
qri
ar+Y5 + Yr-YseC fient tantam hae variationes tolerabiles
4
49 + C. Hq Y-4+O, nam quata V- q C non potest adscribi alioqui
4
enim omnis aequatio quadrato. quadratica necessario fiet et maginaria, quia
semper haberet partem imaginariam indestructibilem. imo videt ne tres quidem
refiner posse nam si +g- O est affirmativa, utique -q+0 eris negativa
itaque hoc modo non poterunt haberi aequationis quadrato quadrati cae
tresqu radicim tres partes. vera eas habendi ratio est, componendo eas ex
tribus aequationis cubicae radicibus. porro omnis aequatio cubica aut duas habet
sit aequatio (ubica: X X pX +9B0. erissit unaradio r . 9+ 7: 9+ 13 , - 29  p
erit aequatio X pl + qpo seu +X + PX (+ 9 p0. et dividendo per X. l fiet aqu
nova aequalio
41
Y-1
a5
1
1- PI -q
X + lX + 170. cujus radix erunt: +
4
(D - el et - 7it - b- 1
I: quod videtur absardum Y(2-1B Y-. sed idem p, 1 contradictio quia V1 H1.
dicamus Y1. plans habere
radices unam YD. alteram is- 1