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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 23v, page id 00068194:0046
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1
Resumamus: dd aequ.  aequ
(4. 3
Ex aequ. 2. mit  aequ  3 aequ 3
se
(4). =
(4)13. 7
 ex nostrir. YL9 +m ∞ + n92 34 ) + g+ 3ng rEp
l
aequ.
Alg+mgg+ng3+ p gt vocemus Z. erit l+ 2mg + dn g2 + 4 pg qu 
ergo exargo Ter fet et 6 fiet.
seu fiet:
dy
qim video optimam et compendio sessimam rationem extraheniihs
modo sit
p
Bona est sed vel maxime ostendit
remnon semper socceder
revoonnm
de bet esse. lX + in AX + n X+ P Xem in ili priores diffrcultates
.
aequari quadato: C + redX +ECCXX A
+dd XX +2dex+ e A
(5,
dividatur hac aequatio in tres.
Px. C cex, et nx aqu’2dex,
per aequo erit e aqu sp. Et per cequ. 3 erit d aqu
Restat praestanda aequatio 4. seu lx +
et demique IX +m XX aqu ee HIcX + reC XX
+dc
Deber lx + mXx+ nX + pX aequadi quadrato ab  + ex + fXX assinta v inde 
seu seu resse aequ.  aequ  vet XX + 2GHXX Bon hc
Ht
Vv + 2 evX F EfVXK
+ ee XXtrefX+ fs 4
e
+ ee
)
hor 
Divellatu hac aequatio in tres. P X aego  et nx aego ret X. et mXXAlxugorVxA e
(6
Ungo
rec
Ex aequ. 2 est f aequ sp. et ex aequ. 3 est e aequ. n unde ex aequatione 4. fiet
P
aequatio talis: + m XX + lX aequ. 2. sp B XX +  vX + vV. Ex qua quonentus vator ipsius v
nn.
+p
 per v
Sed quomam aqu. 7. ad huc difficilior, nec in ea arbitiariae praeter vi indeterminatam
huc stotius lx  nxx 1 n X p d ae quabimus, quadiato a c+ dv + ex +s -
Hinc felciamus Y aequ Z+ C. fiet + m XY +lXego 2 sp  XX + n ZX + ZZ + 2CZ + cc
nn XX MCX
4
21 cX
Y
61
dividatur hoc aequo 8. in duas: in XX equ Z2+ 2CZ acc seu  sim Nego Z+C
Espc XY
nex
e P ZXX + n gX seu =nn X.
s
t
sed video nihil hinc cegi, quia icognuila X Zec in se ducuntur
2
C12)
nc ryo 2Sp  +n
p
p2
 aqu. extr quaerendo xper extinctionem fi et copendii causa faciendo ma i aeguq
in  fier +q Xx + lX  + 1= 2la V +MMon (8) P- Ex ln ~ = un v0
ece
2DI Xx _BX G
evic
L8CC
2
+i J = Enrp
de
aequ.
Ia ato
NIE.
P + v0
4, 4 - 2b sp
ubi a
aequam o gudiato, ubi iterae
ascenditur ad Cubr
nisi sit 1a- in +nnive divisibilis
per 49- 20. sp
f n + ap9
aequ =+  sP
sp
ddg
ed hoc obiter