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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 193v, page id 00068200:0388
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nnta quod supm
 nunc 
M errovi in
eo quod poscum
Ido termino
aequationis
nac nova aequatione apparet non posse suml et  et  pro ubitrio
sumi, et satius esse proarbitrio An sic: aequationem ultimam separubimus in
duos, ee puamus 6 a e f pone Z H dP. Cumque posita Eo pro
arbitira habita sit A, pure ideo C per Ng. 1. ideo in aequatione 2. divisis
omnibus per
S habetur et p pure. unde aequatio sexta dat:
6a3 (t 6  a = 6 sa  aY SSs +4r7S
 et divisis omnibus per  tet:
sive  a = Pa = 4+ V
D  12
et pro 6 substituto
a PCa-a +2
17 = 8 aY sO, et quadrando utrobique
+8Y Gγ + 16r 14
jam per Aeq. 3 14.
1I 640 aV
∞a - V D p a 51
Unde patet in eambila face haberi, , et V. et
datae sublato, faciendum etram  0  aut fre Do unde rursus absurdam aut faciendum
I fore o
ei fuit a
l ataeus olo heret _) 0 quia 1
l aliaeus  tat manebit arbi Ruria
 2  nisi ponamus cd dividi per V. tunc enim E restituetur. Extra
parabelam, sumenda  talis,  ut G frat (0.
sumenda Eo talis ut A fint (0. 3 fiat 10.
Extra anrabolem
His artibus res haud dubie exitum reperit, sed ut omnia ad summam facilita
tem perducantur venit in mentem utramue aequationem datam pariter et
factitiam reduee ad Cubicam, et tum demum sublato rursus 2do termino, e
collatitia.
aora
Primum ergo posito e0 aequatio oia erit quae supra
X + a4.
+ a 2,
6 a3. 0. cujus loco per regulam
a Carresio taditam ponat aliisus ante et post ipsum traditam, ponetur:
 VV V ea14 + 2
y X
X + a d B
+ 2a 
aa
-6
sea
-a p 0. et habemus aequationem cubicam secundo
jam resumendum est data secundo termino carens:
a 5 I
 V
+-
+51 a , 0. ex qua eodem plane modo fiet:
=a5 0 Unde tollendo secundum teminum scribemus;
erit V
ponendo V ∞ - 2a7 erit
Cubicam eudem forme pro qua aequatione scribemus. S 4 S
56 (-32a 754) + 35 au42a - 8a Y
+4 a7 52) 45.
a 0
S.b X a3B S + aY ( 0. et ponendo S s AW
fiet NV X a + aY sive W N
  sive Npi  aS-
debet esse
Atque ita fier aequalion data: gb
ponendoque V e - D D, et Q⊓ 61
-57..
+ a0) (10 ac
020a, sive N ⊓ a Y 
= - 8 V+ a08
conferenda cum
ats- Ba.
a stiet aequatio collatitia unica.
xp
08
ats- B3a
1p27
27a7
+2a51.
=222
X -69 a
traevi.
Sed in eo hic erratum
quod ea aequatiocum
qua confertur ultima
aequatione popo
factitia proposita;
reducta enim directe
data non constinitur
Rectius cuncta procedent
1 et ita aequa
nonem datam ad
2d0 termino carentem
reducendo
data non construitur himino carentem.
Ponendo D et 6 et  2a=