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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 2
# Folio 34r, page id 00068215:0067
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aquationi
14
 addatur aequatio  multiplicata per arbitrariam h
et fiet K + l K + mK. +n
+ h K + hcK + hd
= hy
equatione 18. K - e K2 - fk = 9
= co
0
17d
quae comparari potest cum
aequatione 18
Rursus aequationem 12 multiplicemus per quanticatem K + fier
K3 + lK + mk+ n
K + G
K3 +(BL +mRK + n A (22)
l
+K + lK3 +mK +n K
10
K + SK + +K + VK +W p0
igitur ut reapse comparemus aeg9. 21. et 18. ac 22. et 17.
in equ.
ita  procedi debet quaeratur _ co per y ita ut contra se invicem
et datae
pollantur, de reliquo s. t. v. W. sunt cognitae et reliquae omnes
assumtitiae. Comparando aequ. 27 et 17. per quatuor collatitias habebuntur
literae quatuor l.. 9. l. m. n.
comparando vero aequationes
21 et 18. primum ponemus co p, hy. ut literae co et y. destruantu
deinde ope reliquarum einde reliquas c. d. quaeremus per c. f. g. h
ex quibus tres sunt super numerariae itaque compendii causa, ponendo
(22)
(24)
1) 10. et eri 0
(29)
cdI - ly.
8
30)
3
S-l mpi + - Is + P
WH + Sv + s+l - 2521V +5 13 - 14
t + st. - + +2s
=W - v. -
+s+.
(26)
62)
(2
Cri m
nei v -s+ +15 -
+tl -512 + l
2
+ + -53. +s
+ v + U
sed inde patet, et facle praevideri poterat calculum istum esse
inutilem, seu non deberi comparari aequationes 22 et 17.
equ.
7
quae comparati potest cum
X si adtt ox + cX + d
+ P X  + 9 p
paX + pbx + pcX + pd
+py
+bX + CX + dX
+ yX
aN + abx + aCX + a
+ay
X + pb X + pCX + pd
C
+ d
pat b +a + ac + ay
+ 9y + iy
 a X + b X + CX + d
- e-a
- f X
=0 - a
e x2 = fX = h
1, - lX
= n X
= myX q = βy
V+ dy V+Sy
+ py
+ ab  + y h+ ad
per compendium X + e X + f X + h X f o
X
X
=
70
pa+b+a patbta
+7
+9y X + h + iy X + d+
eoa
e
fier:  X + B _ X + e
+A y. + Ey
10 +  y
rgo 10 sed jam omnino video methodum hanc esse inutilem
novissime enim necesse  est fieri vel X1) y + 8 vel X7 3 + gy era
itaque sic poteramus initio supponere
in aequatione X +  pX + 9 10. ponamus
Py + N
a y + hy +C
de + fy +g
ayt+ In aequatione data sudst aliqua assumtr
substituamque atrum
(I valorem, ouctuo alia cum incognita altius oscendente, utique prodibit
equatio altior priore, ut si in aequatione X + pX + 9. pro X substituatur y
Ergo X ay + 3ay by +3a stc
faciendo XpaV + by +c.
dyr + ey +f V
seu X, ay + 3a b y5 + 38Cy+ +6 abc y3 + 3ac y
+ 3ab
+ b3 in +3bC..
+3ay by +6ay bcy + 3ayC
+3bey+C
V +3d Cy +3d fy 46 def y3 +3 d fry +3efy +f
+3de) +5 .. 43ef.
+ B3y + 3bVc +3b98+0
et
X
jam
s
Ergo X + lX + n
+ m y +β7
a
et
edus