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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 310v, page id 00068196:0616
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2XXY = aaX
videamus an licent toble
a ponendo X = Y bZ + CY et y . WV+
un
1Z+ mv
200 E bbZ2 F + 2bcZP + CCVY = aa 1677
fiet 2bc2
sed Jam video non posse tolli aax samm nisi
su hoc explicaive, insi simul si al X 
1
quod te non debes
C
Et
angisur
qideo interdum erem ne po
3
quidem ese idque cinterdr posse rraevideri
ba ulcum sit vel non
na
erbi
palia in ment aua quarcunque
et suppositio delet 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 simu 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 hansforcmando
ut cna exliteris novis ut habunt sit hogogenea cum a
assera vliircum   posito T. y dx; dy. sit
Eugo ponamus in casin maesentia rushc  ovo
et rursus 2B, Hy aa  2 2abZ. 8. Et tabst scores
sudstitamus in hobemus tires aequatio res fundamentales,
i pervabuat, in ribus d
et
osvali
 fucel
inibude
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 cima
e-
posita ed consta
C. X  dx: sit  dx = CX
siet ce SXe=
xb
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 du dxe = ddZ + cd∞
et dy = Cdz + mdv.
ergo
ex 50v = 1dg+ ndo dp.
sit ab una parte 
eL
bdy +CB dz
jams. ldZ + m LD, : b dZ+ cdV = 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 quadraturos
si cilli possint constantes ponendo ee
X = Z+ b7Z+ CZV + eYV +f
et y = 1Z2 m Zv +. n vv + p. se
sed video nihil gos has Et ita porro modo
scicet _ Z et V servent inter sa homogercitatem
ex cepta litera F et P, quae in axidus evanescunt
idem est in alturibu.
verte