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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 61v, page id 00068200:0124
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(2)
nempe M + bZ + PP+ 43 +Y yX 55 etc aequ X
+vy + wyy tey n
quem valorem ipsius X substituendo in aequ. 1. habebitur
aequ. 3. in qua solum supererunt literae y et Z. quae
aequatio 3 comparari potentcum data, aliqua 4. ubi
in aquoue necessario7 ad eosdem Tradus assurgit, ad quos X in
aequ. 1. assurgit, sed y admalto plures, sciliet ad
tot dimensiones quot fiunt ex ductu summae dimensionis
ipsius X in aequ. 1, in  summam dimensionem ipsius y in
aequ. 2.
quodsi comparatio nondum procedat, prius
equationem datam 4 transformabimus in aliam
aequ. 5 per mechodum differentialium. Posset etiam
praeter aqu. 1. alia assumi ab mitio, eisimilis, ins
quod ponatur co pro X. et in aequ. 2. loco X ponetur
X + d co sed sed tunc alte nimis assurgetur
Videndum aq liceat aequationemdatam 4 attollere multipli
caudo ut ipsi 3 fiat comparabilis
Est et alia methodus conjungendo curvam cum rationali et alia
C1)
incidit et haec: sit axx + bx aequ c + dy + egys +fy erc.
quadus inferioris.
quaeritur X dus per solas X ax et  dy. Est autem aliunde:
2axax + b dx aequ  d dus + hey dus +3f yy dy et.
+ bXdus  cay +ay sus reyyly er
aequationis2
ex  XX dus subsituatur ipsius dus valor per aequ. 2
plures alias hujus modi aequationes quaeram
in
ut
a XX y + bx y aequ 9+ dyy + cy t et unde fiet:
15)
fiet aequ. 4.
a xxdy +2 axy x +b xay + b ydx aequ Cdys + 2dydy t3ey tye
et ax + bxX aequ Cx + dyx + Cyyx+ erc.
unde fiet: 3aX dx + 2bxdx aequ c dx + dy ax + dxdus teyyax
fe x y dy erc.
Datur a)fxxdy + bsxdus per aequ 1 vel 3.)
sednihil
datur et 2 afXy x + b Fydx per aequ. 2.
 axx + bx aequ Z.
X equlZ+ mv. XX + bx aequ C
seu X, A X+b aequ  y. y+c seu Xaqu
sed nihul hinc. satique hoc modo.
hin.
V. VtC
X + b
Quantilas dey + fecyy + ge  + hh et y quanda
quadato, ab ly theeyus c quod est: llyu +
2l hec y3+ (Chh c2 y), aequ dey +feeyytCy  hhc
sublatis tollendis et divisis omnibus per y. fit: a
+9 e3 yy + fee y + de aequ. 0: et fiat ge- 2lhec aequ. 0.
2thec... . 11
seu fiat: e aequ 21h
Ergo y aequ. de. Et x seu yaequ
1- fee
sei ita ye erit 2dtih, aequ X ac proinde X fit
gg-4fhh
quantitas determinata contra scopum
idlh  d 2dingus
U fauhhus
qu
per dicta ad
paginae 2 sub
ine