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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 3
# Folio 2r, page id 00068216:0003
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splemt.b78.
De rationali potesenta parte protestatum diradicibus siceda 
de C∞.
X det B8
de
Ra + bX + CX dX) C X +fX + gX
B + _X + Z X + 3X + 4 X +∞ X+ 6X
AbiX 46bX +SCX +6d X + +SX 69 X 02
4+6aX +5b 45C +5d +se 5f +59
+4aX 14 Hac +4d +4e gf +ag
X epx+q +Y
XAX+B.
quX abpX b92
t xp pos
p 192
XI + -pXPF q
+29
X+  XC p. aequ. 0
X P a
+2 tax-ab
a cp aequ. 0
seu aaequ + p.
X X - a p aequ. 0
X2 X - p aqu. 0
Jam etsi X - pX + qX = r aequ. 0. velis atsollere ad X D. X. X
tamen in secundo termino aequationis provenientis non potest esse nisi p. et g.
seu -p +2q. ut ante. Quia Y non potest ingredi nisi ingredia i rh. sed
ita non seduatur lex homogeneorum. Unde praclarus ejus usus apparet quem
recte servavit Vieta ,non ita recte Etantum novandi causa, neglexit sartesu
Est ergo = p + 24 summa quadratorum Radicum.
XoXix reas exu
X pX +qX rX+ S ExAVX- WX xX+ corq
XpN+ qHXexxX+ co
Hox  pCx Gqox r X+SEoN x t noW stX aoX +r
X ∞pX + 4X - YX + SX- LX + v aequ. 0
X + pX +9X +r X +) X +tX + v
X -pX +4X - YX +sx- lx + vx
+p = p +Y4 -pr + ps - pt + pFX
+9 - pu +9 - q + qs - qf + qu+
+r
+ tgy q tipco
-pV +qB -r Ar -r +DVX
+s+
-ps 445 - r3+ +sB sat5 + st vX
1 -pt +9t -rf +55 - +0 + tv X
+v -pV +qV -r +sp- V +
ip tx x tiqe p + tistr X +v aequ.0
+29)
1o
4, v
-2r315
+58
+216X X Lquv xt A +sX X +v aequ.q
-+10
vel sic ordinando:
-2pt3
+2915+
-215
X2+ pX
Iaequ. b
X X APX X Y) ipBX X
+9
trst
+25 +x
2b13
aqu. 0
X X +29X 
A scubuluo ingelento p le rq. 4 94
et ita
+sd
Ita melius apparet, lamidiia
modusque continuandi in infinitum qui hic est
-r6 ita enim signa semper alternantur, omnist inembra
pro secnd multiplicantur per 2 excepto penultimo lilerae autem ipsae. Sic patent:
2
qui quia ultinus est simplus. pro Termino  quinto incipos a quiulo aequatiunis datae, qui est 5+. dupliea cum signt +
fit a s+ inde retro ad r3, cui jungi debet p ob legem homogineorum, idque multiplica per 2 per regulam fit 2pY
inde porro perge retro ad g. sed quia cumalio onjungi non sit conjunge seum fit _ et quidem cum 4 be
altermationem, et simplum, quia vltmndue. Ita de caeteris som ergoogo haberetur productum siaequati
 esset X, vel xen.
X