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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 216r, page id 00068201:0431
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Resumamus: X   qL 
(+ibe 2b) p
Pest Desmutionem residua aequatio poterit
iterum divelli in duas nempe;
1  as H 2 54 et a ta as
X5 b + c.
NrI p a 2b
+C3 -af
Ex quilus prior divisa per af + c, dabit:
a ita 1
it poime fo. 
unde le
ma - a f
at + c-a
= mEY
qui duo valores ipsius L aquari debent inter se, et
cum unius sit nominator sit a f + c -af, alterius vero
X1 AB n + nC, so nt  5 
Variis modis Varii modi tentandi sunt, quibus fieri
posit, ut radix ex factis extrahi possit, quae ex
factoribus extrahi non potest,
X FF B) m + Nn-na +
N m
m n ramu
Ne Ar
8f + c3- mr
Hactenus verissimus est calculus, sed jam video cur ipsa m
non posse possit tuto explicari pro arbitrio, ingredietur
D(+ a, +  +n 4F D (t) an ri  qr
enim in ejus valorem ipsa X seu at +C quod alteratet
e ud x ps anabe abn 0 an es aen
videamus d an divisi possit: ben Ban + Ca an
erit es a mAtq
sive n C+g + 2q n (+ 35  ) ( +4
valgrem. Formam ipsam aequationis datae ac fatis niulilem
XV  b 1() an + 2nabe + Ct0) a n
+ Aq X.
et m e L4. et m Y (+) 93
+. (12 ()
Sed cum signorum ratio suspecta censeri possit,
hinc resumamus adhibitis literis pro signis
emarna  marna sier:
N’H v’ m
fuisse divulsconem redivimus enim per circulum ad illam
epsam aequationem i quam jam ante habueramus:
a 1c n 3 4at texms at
1d ab + 1 a bs3 an
pr XN L s
XH a B an
+D in X
et aequatio novissima erit:
sit at +e, vel afere af, 2 af + c. itaque dividendo Xe V 
Utrobique per af +c fiet:
n a - af r
x 13ab
an
manae
+com+con
+ 2vam X
jam data est aequatio:
X aq X + ar
quam comparando cum inventa, fiet:
M  d4. et ma
outa, et me paqu
Altera aequatio collatitia est: sed sulis hcjam
ex generali cum ponitur X b+ c colligitur
hunc culculum fore inutilem.
Inquisitio potius omnis redire debet ad modos, comminiscendi
imaginarias, quarum summae, et cuborum summa, et
facti, imnus reales.
X 1O n + 13sen - 13) 1 - n
XN (3an +(BS-an, + 10 an-an
x
rationales sed factus  ex parte in partem, etsi contigent
quantitates acales non contniet tamen rationates
Huic malo an sic olviam ibimus? sit
des sen  et erit d n et d n In
cubicam tadirem fingere
sit b tulis, ut ejus quadratum ductum in de, faciat esse
quantitatem planam. sit ergo )t
quod ad b. itemque ut quadratum ipsius sit quantitas
Plana, quod an ila comminisci licebit? sit:
1I() n P.Sp + n.
b aa
a +tat
l  a + b  sarbu
ej b 10
bet 10 Lus arbs
Itaque si sit E e 1C an
producta ex radice cubicis quadratis
conferi polerit cum plana:
XrI 466 an +4 1bn
Ergo X  a b10 an + ct0 an
ponendo af p, 3bc. vel
b1 at  sequetur
destructio quam notatam
fnessisi
+a10) an