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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 6
# Folio 3r, page id 00068219:0005
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X +F
X + lX + am X + a nX
C
X + lX + anx + aen X + PB
+ p... + P. + amp. + a np 
(+ ar  + a s X + a F
X
+ 9X
ta th2ga
8k
Martii 1675.
de extractionibus radicu
ex aequationibus ntrine
X
eX
pat
2h X + 9a X + 4a rh = 9a
ek
(xar). - 4a rtegaR - 1a hL.  8a hhq + 9ta
(+qa
At2).
X
+q’at
8h4
64h
nde ut exacte procedat extractio, fiunt aequationes duae:
os
8h245 - 4a rhq + 9’a 0.
Unde Y ⊓ 8h+ s( + qa
4 atr q
qua 46
et 64h at p 16 atr h- 8a rhq + ga
et F, 16 a h 9a  hg 4 9t ad
64h6
sito jam aequationem  in duas resse dissectam, quolibet nem
termino indefinite bissecto, et unum latus esse D. altrum similiter literis exprimi
nisi quod eae non nex his h. g. r. s. t. da pendeant. habebuntur
ad extractione ex altra parte duae rursus aaequationes, pro quibus
duae super sunt incognitae
f. 9. r. aut potius quae ex ipsis pendent
praeterquamo quod in ipsa O. adhuc superest arbitraria p. Et
in ipsa quoque initio data Cubica duae intelligi possunt arbitrariae,
nempe ex additio ra dicum anctione et multiplicatione; itaque
ab pro aequationibus ut collutitiis vel si mavis inciden-
tibu quatuor habebimus indeterminatas numeto octo scilicet
h. 9. r. s. t. P. et duae praeterea ex ipsa equatione cubica
data auctis vel multiplicatis radicibus pro arbitrio varianda.
Ope autem octo indeterminatarum qalnor aequa quatuor
aequationis exitum plana constructiona habere posse, non videtur
dubitandum. Unde illid denique condluditur, omnem aequationerq
rubicam reddi posse planam, quod cum it atsurdum nuhil
eficient tol arbitrariae