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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 309r, page id 00068196:0613
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2XXy = aaX
videamus an licent loble
a ponendo X = Y bZ + CY et y . WV+
un
2.
fiet 2bc2
1Z+ mv
sed Jam video non posse tolli aax samm nisi
sm hac expliceve, insi simul si al X _C
1
quod te non debes
C
uryde adg
Et
anisur
video interdum, etem ne pos
3
quidem ese idque cinterdr posse rraevideri
ba ulcum sit vel non
na
berbi
palia in  ee ausa qacunus
re suppositio detet sillilxyl.
casus e 1X
2)
2XX y . aaX,; 3aay = 2Xyy = dy : dy).. 9. y
ubi ad lolendam aa, debet ficiri 2x9- aa =0
et 3aa  2Xy = 6. quae dummen tolli aa tam
ex 2Xy -aa quiam ex B 2 Xy - aa
quae duo simul feri non possunt. Si tuisset
2xx Quoni Auia via abhiceri et reductao
aequationum inerementatium ascolatum in puras
seu adquadraturat, si implicatarrum ad explicalas
si efflei possit ut eeat dux nuo ex hans forcmando
ut cna exliteris novis ut habunt sit hogogenea cum a
assera vliircum   posito T. y dx; dy. sit
e ove
Eugo ponamus in easin mesenti nha
et rursus 283 ry aa n  2abZ. 8. Et tabores
sudstitamus in habemus fires aequatio rec fundamenta les
uhit pervabuet, in cibus d
et
osvalo
 que
 d
quaelibet inter se seval legus homogeneolum jam si
hinc tolli debent X et y. quod et succedit, sed cum toteo praeterea
debene dx et dy. Hinc opus est ex aeq. 2 duci differentialem, ut
quaeramus velem ipsius a, ex 5q. 3, qui sit 2XXy a axy =
EXX 3aa
X =
Nihil ex hac scheta quod non cimn
e-
posita ed consta
C. X  dx: sit  dx = CX
siet ce SXe=
b
X
y q.
bdx + cdus
Taxa mlus
A2 1 +
X = 8bZ+ cv +C y = 1Z+ mv + n B
Ergo
si sit 2xyy a a Xy: 34a Exg,:: dx: di
Haec hypothesis si servit Tollendis constan
tibus, solutm est problema, nam
circa dx: dus nil mutatur in summa
nam
 dx  bdZ + cd D
et dy = ld7 + mdv.
ergo
x yix = 1dget ndo dp.
sit ab una prorte
eL
bdy +CB dz
jam s ldZ + m dD, : bdZ+ cdY = O (seu Z. D
fiet. laque amdo = bZ bOdZ+ cOdv. Ergo
av = ( - b0. seu dv =  = bg. v , ubi let,
Z
CO= M duz
 et z: V significat
cy:  M constante
omnem terminim
utcunque Cpinatum ex  ratione Z: Y, quo casu
ostendium rem semper reducta ad quadraturas
c
Imo res etiam reducitur ad quadraturvis
si cilli possint constantes ponendo ee
X = 2+ b7Z+ CZV + eVV +f
et y = 1ZZ+ mzr + n vv + p. se
sed video nihil gos has Et ita porro modo
scicet _ Z et V servent inter sa homogercitatem
ex cepta litera + et P, quae in axidu evanescunt
idem est in alturiau.
verte