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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 84r, page id 00068124:0167
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a = b
a + AAh. + V a = + b
ae
X
- gna +. rX - 5∞0
n + Va + 1
X + S... y.
X
X2 + 2 ax +6
3X - pX  c
X+axL.
= b no
Demonstratio hujus Theorematis a me
o
+ Yd
+
Yad
reperta: quod omnis radix aequatio cubica deprimibilis) XSc
habeat radicem rationalem.
Nam radix aequationis (ubicae
est: + V: 9+ 1 494 - = p
+
9- 3
V)
quod si ergo deprimibilis est, necesse
est ex his binomiis radicem cubicam
extrahi posse. Extracta autem
cia 
radice fientbinomiutu a + sb
et a - sb. uli quid quorum
summa erit 2a quae erit radix
X. X
rationalis. posito a esse rationalem,
ipsam a autem esse rationalem patet
seriqibus
-
7
9- L
cubrea
+ L
ex e eo quia in binomiis extrudts cabicis unde radio extrahenda est
binomii exsitrahendi
Ccubr
P est quantitas unde radii
extrari potest, nempe ea est.  p, cujus Tadix est = P Ex tali autem binomio
si modo radio extrahi potest, semper una pars est rationalis. Ergo ut
in in additumento ad schotenii lom. in Geom. Cartesi
1
2
r+
+.
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