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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 3
# Folio 6r, page id 00068216:0011
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Septrembus 1678.
aequi  tum
sis aque
vel C
en
Ergo
partee
de Rationali potestatum a radicibus. Schedat
Quaeramus ergo analogis in nunc quidem non in valore ipsarum
quantitatum y. 7. B. se  (nempe y sumta pro ab +ac etc.
et Z pro abc + abd erc. X scilice Y X posita a +b  + d etC)
Sed contenti simus hoc, ut reperiamus, quid sit rationale in ipsis.
generaliter scilicet sumtis. Seimus  id enim nos etiam ad
exitum perducet. et quidem fortasset melius quam si aequationem
haberem, pro ipsis. Scimus autem quid sit rationale in X, item
quid sit rationale in X. itam quid sit rationale in X. Et exhibet sese
analogia aliqua memorabilis.
Quod est rationale in X. X. X’ et roritur ex p. g. r posito XE- pX + gXE.
Uti Valor summae ex A
3
(Xp 1C
A
oritur ex P
intelligo Por A. B. C. intelligo radices
quod est rationale in ) ta a
 tey 48
uti valos summae ex p
Xa
oritur ex P p r3
37 oritur ex B. 92 R3
co 2
i
LA +X et
Revera tria sunt fundamentaliter analogica:
CEodet modo probatur tisdem positis seu si potestas a vel ad etc. est secundum exponentem radicis sit Xaqu tunc quod est rationale in X X X etc oritur ex p. qu. re posito XZ- p q et
ere
valoc summae ex se
et
Uti
cox
co con1
s s erc oritur ex P. 92. R et posilo D.  + erc.
C3
en e
Et uti
a a etc ortur ex X. y. L
b2
eu ete
Duo posteriores termini analogiae generalius
enuntiari longiusque extendi possunt, hoc modo.
et cu
ABr
cuc
A2C2 3
eu s
AB
en
et
a
oM
a
ac2
ur
erc
ab
A3B)C
en
i i hoc
a erc oritur ex X. y.
En
asi
a23
ei
abc
Cantum enim idem est ac si Eoco dV. C. ca FlX. L. 7. 
qr e )ete
a
summae
item 
et
valor sumam
ilem
uti
eu
sisit X aequ. a
y aqu. ab
iqu. des
valor summae
tam ex
3
L
en
 o
abc
ere)
e
ino falsa est har analogiae extensio, aut
intam 2. 2c et 3. 3 nam qui constaret si 50X
mi
nec consta responsus
2
en;
ilem ex
Demonstiatur haec annlogiae exlensio per substitutione
scribamus A. B. Cel