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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 2
# Folio 8v, page id 00068047:0016
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Si sit equatio dx dy = uXX 4 3 + xyp et 5., ax x t ayy tutus et
Si sit aequatio dx: dy L WoNX 12O Gy +MOKy A MX + 21 yt 122;, doxxet qu vy t Z Nyt 1ry 1 342
videamus an liceat eam reducere ad talem quae leges homogenectum secvet secundum
data
indetermmatas per se solas, fat nempe X Si +_ y+
+. V. . Z+. v quia e
e +GGeEXC et y=
sed nec
licetefacere simulqus BC  - - Z+ vel x - ZZ ∞ p F. ZV, :, Z3 +. vu g. . 21,
fortisse non licet autem facere Xe =
y hoc modo, quia ita tam X  quams
Z. V. il Videndum. Et aerdeo cur non
liceat eo ipso eum, dan datur X per Z V, et rursus y per zu
et similiter A
per
V. cs
datur ergo X per y absolute quod ab surdum
sic, ut faciamus quidem X = . Z + . v, ., i q. L. Y
Qui desi sic. aquatio  ex Analogia, 1. fiat
quo
qualio multiplicatione per cuicem,
hac aequatio constabit
ex partibus aequigratalibus gradus 0 1, 2 erc usque ad
ulliumus gradus totius, quot ergo sunt unilates in altissim. gradu tob
assumantur literae per quas explicentur X et y. inde divellati
aquati i tolidem partes, quot continet gradus, ta in unaquaque
indetermmnatae servabunt leges homogeneorum.
video, quod  non licet tollere indeterminatas
sed
flitu sit
 fiat Z=
verurm id mali subesse
hoc sunt alterius loci
 +_ + EnZV. 1g2dy + P (1 X 117
ad
X. y addus nter sedrsmit hesade aliter. et jgi= _
aequatu pix
et v = Z. yA et V = X. y.
13 Lx per p, 8, ex ay habebiur
E X. y. lx. d =0
compainda dulae t dateuli suo montiganda sege data
per 2, 3, +, si pses
 tot institior
ad aequ.
Q
=X. 9
redu
dx. ly c
seu dxcey
ty
la erit ad quas
1D = a X. y.
Ax: dst
Generaliter calcum
y. a v X. y. a
616
tailes
F. 9. a
Eivisorem, tunc 
vel a alliyres dobeant 
.. Kuy a d nra gotu ny a d
in X.g. a. X. y, + d. Xapa
duci vel instituta mult.
reducibilis ad quadituram nemue ut e sit formela facta ex Ze
quae est
delligere licet, ut aequ. l.
Jam.
dentica
altera ex v sola.
Transformand entam  per X et y qualis g
duabus in
Contraria ejus qu
et Y; Hic cocra quae
asumendo valores ex et y. per
n
in in quaesitam
per Let formo in datam
trans
paer p et g. assumendo valores 2 ipsarum Eit W per X et 7
un ubi
ductis
Haec videtur methodus generalis.
pro reductone Cang. ad quadraturisq
 detur ex Z sola
plins usus
aequalio n
oot sunt gundo
dis
 jam munerator et nominator in ag. 8 data non habeant coem
l
scrvantibus inper solis leges homogeneorum vel formula facta ex
pe curcem, fiet aequ 9.
quarum
Ligo vel debet labere numeritorem et noratorem ejsdem gradus cum ∞g.8
.y
= d igta
galoe dx 3
C
x + XXp a dy. et ex 
(seu ar: 40 =- 9. d
LGC) 
t X X. y-
quarntum exozetu, a et dv = :. et tollendo
autem
reductu s
quae ut A
du. do
d22. d X. y. a Ex +