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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 223r, page id 00068201:0445
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X 2apX + a 
2ap X +arX + ap
= an
A posterioris aequationis latus conferatur hmic B2X +2abCX + a C et conferem
fier: P H b2 + ag. et bcH ar. et b 4 2b a + a q = an 1 C, aer
adeoque
12a b + a9b aro
= 14 an
sit jum aequatio Z + m Z + ah 7 + aet Z + aml B
+mat
X 4 (-m X) m X (- ame) X  m
 m.. _3m..  .
=n
tah.. dlim. + ahqp
+ a2 l.
+ eak.
F mah
= a2 l m
=mah
+ am
Hujus ae quataris productae explicata Z. terminus penultimus
est m si ponatur 0. et ita quaeratur
Int. habebitur aequatio cubicu qua signum penullini
termini non mutatur Uideo initilis.
si ex nan b r poser extrcti radiui quadratia
Ce
aequatio  optime resolveretur
nabret
sed haec sublatio trmini secundi incommoda est, quia facit m. nimis a alte attolli.
quadratia
radicis veniri possit:
sit aequatio:
X rp X +aqX + aer X + a0
divellatur in dluas partes hoc modo: X  pX + ag Xv+ ar X + as) C X + 2CCX + a
+ea +de
ubi manifeste ab mno latere extrali potest indix quadratica, quod ut fiat ab altero quoque Aconferatur illud latus
cum aequatione producta ex quantitate aliqua ducta in seipsam: X + fX + ag, B, pX t2s X + ragX
ubi conferendo, f B. et 91 4 aq + 2 - P
8a
et eri tapq + adpc - p3 - 8ar +5. trasgx +ag
et tandem, ad + 4a 59. - 4 a5gr + a r  ag
si ponamus a X  + agX A a  1
sie espatus ar
quod si poneremus AC sive RCMP. S m
ont Nam incaquatione nZ. n arbi troria
si jam aequationem quadrati qua raticum. rcapse cubicam est, fet. 
aMaes q
X  d
sed satis qideo trinc mihiti novi pro venire
aes
a g
Aliam tentemus viam: Aequationem quadraticum elevemus ad gradum
X B 8 alX + aemX + aenb. sive X  alX + amx tan et X SSalX +am X tan
videamus aqe explicando effici posit, ut ex X xffrati possi at amX rau extrahi possit radix ex
quantitate al X + amX +a, vel pro al ponendo _h,  h X + aem X + ar ponanuus
XH = y + c. et fiet: X b  + 2bey +c: adeoque radix x quadratica erit exstrahenda
Lebry + 2tebey + h c2
+ aemb. +amc
+ a3n
co sive  dividendo per 1b, extrahenda erit radio ex.
 + F y p h c. Quantitas comparanda cum facta ex
+ am .) + a me
ab+ an
nde conferendo ent e itic tam. et C ahic aglicam + arm 2
4h2b2
n. y +e in sessam seu cum
N + 2heV + C
a e
b. quam proinde ad caleulum iantilem fuisse patet restat inventio ipsius invenienda ipsa c, sed matum est, quod ipsa
quoque evanescit, nempe fit enim aequatio: 4hc+ ticam tamth + 4a mc f 4 aeriti necesse est ergo fieri
aequationem quadrato quadraticam secundo termino carentem in qua sit am rinti. Sitis judicari potest rem
procedere non posse, aliaqui si ponramus
X+ x tas sat + ag qedrando fier: hX c eaf + rhaque X
Ratio cur rem non putem procedere est quod
mula posser intelligi duas haber
utce, aequalei. Ino video posse quantiber formntam duas habto rradices egualee, auiendo
ucet eas e minuendo
Methodus qua regula vietae
aequatibuum quadrato quadraticaum
ad Cubicas potuit invenidi
Pone ZH X . fiet.
+nahi ras.