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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 2
# Folio 34v, page id 00068215:0068
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pro i
+ p + q p0.
O + pDO + ∞53
fiet:
10
quo erit aequatio sexti gradus arbitrariarum ad summum quinque.
sumatur aequatio quinto gradus arbitrariarum etiam quinque, ope
unius nempo abti ex ipsius tollatur alio primus vel ultimue terminus
habebitur aequatio Eti gradus, et restabunt arbitrariae
Rectiu ita aequationem quarti gradus artitrariam attollermus sumendo
N
Y
lurc enim utique ex inventa haberi X haberi potest y.
prodibit aequatio gradus duodecimi, sumam jam aquationem gradus quait data c
y3...
arbitrariarum minimum 2.
sumatur aequatio grodus quinti data, e
mulliplicetur fer formulam 7 gradum et artitariarum,
X + pX +
41
X ppy +  A ita sit aequatio X+ X
An ita sit aequalio X X pX + 4X + rx, dy + C sumatur alia  X
o
ValY+CHdyte
quo ubique substituto habebitur aequalio 20mi gradus arbitrariarum fy +gy thus riy +l
numero ne plurituarum. numero 10. qua atique sumatur alia aequatio: V = in 10
quae ducatur in utum quindecim arbitrariarum formulam donec etiam attollatur ad asum gradum
Lomum
et comparendo fiet quaesi priori comparari potest, habems aaequati invento ipsis
in valore denique habebitur quaesitum.
X + p X + 9po
X  d. eut _C
+ b
+ P∞ +9 10 seu O + OD +9Do
an sic X A ( X + p X. + 9 10. XI. Unde substituendo pro X ejus valorem
habebitur aequatio in qua assurget y ad gradum 2stum, sumatur jam aequatio arbitraria
quarti gradus, et multiplicatur in formulam grodus 2, un
ipsius y per aequationem quadrato. quadraticam, et inde valor ipsius X. sed hoc jam video
ineptum. An sic potius: sit aequatio qindus quadato- quadratici, X +X4qX+ rX +5 0. sumatur
alia pura aX 5 + b 1) y. qua ubique substituta habebitur aequalio  in qua sola restabit y
quinti gradus crigatur compareturque, et poterit adq data quinti gratus gradus interveniente puro
+ e
ejusdem quinti reduci ad quartum. Idem aliter. sit artiaria quinte quarti data quinti gradus
ut X +pX + q. sumatur alia pun aX + g_ b
An sie X + FX3 +gX + hX + ipo aX
ar
3 et
ay +be. sit opy + pV F qF
dy+e
aequatio data quae ducta in CyE c. XI .  Ergo X + fX +gX + hx + ip0 dabir
6+ f0D +gOV.
Et sd hoc demue
Esto aequatr
v  V 1 lr + mv + R + l K + mK + n p,
et ponendo RF X + x - (. fiet KA
Ergo in unum addendo
Et per compendium
l
 int
C
X - i X + 3 lX -
+ LX - 2l∞
27
+ B
m X - nl
n
X = + I2X +21
+ m X
x+q
posito 9F + 5 1 - m. et rp - 2 13 + ml - n
 ml
 1
+
assumatur aliqua aequalio arbitraria: X pa X +b. Tollendo. X ita
ut tantum mancat y fiet 3 + 3by2 + 3bV
= 29 4 3aVs
1. qua aequatione ut tolli possint
termini intermedii, fiet
1(0)
2g
1. et ap
0
2V
4
Sapor
492
93
-49b
=29
+ y
+ 13
- 2912 (7)
+3bar
+qub
= aqr
=aeqb)
+aY
n
et y p - b + 2 qb 13bar - g b + agr + a9b - ar +
vel y
(11) 3
4r-17 V 59
293 27
+ 4qY = 9Y squ -
29
12
(3 + lR + m K +n 170 resolutam
Hlabemus ergo et aequationem
r
ope aequationis Xaxtb vel pro X substituendo K +  fiet: (13)
7
C2 + 2IK + VB a K + al ∞ vel K  + 3IK+ 5
+
36
(14)
vel per compendium K2 + cK + d po
(15)
et bp (+ 1)- dV + ct - d.
d
= a. = al
-
b
16
posito scilicet aF
2l -c
ita ut l. et d. aliunde quaeri fas sit
sit jam aequatio K + pK + + K + vK + WV F0. assumatur alia
3poH e K + fK +, g pF V seu seu K ⊓ e K + f K2 + g K
e
+c
Ergo +5 K3 + +K +
+0
7i
+f..
+
VX + W (70 aliter
.
S0 R + co.
+0.. +sfK +, sd
+ ef.
2
2
s co
) (20)
co