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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 171r, page id 00068199:0341
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solei potest C + fy+ ondu = 0 posito C, f, 9 dari ex x, et dx dissimulari
assmititia dibitraum
quaeritur sol utio ipsius 1+ m7 +ny+ ddus =0. differentibtur ipsa  aequ. d. et
prodibit productarum firi prodibit de dfy + fdue + gddus 2 Multiplicetur aequ. 2
dodu
per g, fint lg + mgy+ ngus +gddu0 quaecomo coincidentietur aequationi 3
habetur de = ly et df= mg G= df: m  Ergo ob f + dg  = ng siet f + ddf + dfdin)- nat
pergo res reducta est ad Ge. f βf + V df +  das si fiet posset  data fieri n = dG: M) esset
ddf: f: cognito A sed dof das: f summari nequit sane si fessent progressionis Geonatrae
tcet
1: + = b bb B bt
to
btot bb.su
ub. 
- b,
6
b
ddt  Ib
b.bb Hub ec et debet 
ubique applicari
b bb cu ad logietitim
sumper
uls
gulo
et prodit rectan
un (de semper
idem quaecunque sit progetia
ipsius f etsi non Geometrila
Hinc spes est aliquid effici posse ea methodo, qua
scuper noemo du = per X, ax, ddx seu qua
incognitas invicem separo et quidem rationalter
in fallor Res prosequenda
difficila maximi
quomod summetur,  dx dx, ancon-
sipienda area, ipsius dx indx; san ipsius
dx dxdx applicati ad elementum o.
qatmicum quod constans si X sint
Geometrica
_ Gy+ Xx, : aa = ty: dx
si esset l + m + n + gdd et fieret v - qy
foret l+ mqu + ngdy
c do = qdy
ydque
n dgsy. + 2glg ctus +99eay ddv. 4dcy
cydagus
2 dydus
sud hic relationem desiderala ajda
efficere difficicus forat
proposito
aa dy = yu dx + XXdx
. 2 cdu
ac ddus = fyy ddx + 2ydydx + XX ddx f 2X xdx
aadradus - aa gy = acdus -Xxdx, :dx = a addus- 2ylydx Xxdi
dux
Edifterentiando erut, si tpldx -o erit, fiet acdus dax- xdxdax = aa dx ddy. 2) dys dadx XE extax Et
aadu J. yy AX + Xx dx
aaidus  29 dxdy + 2x ex dx
et y = aa dxddy = 2X dx-aadu adx,: dydx
fit  gy = a axaxdulus 4a ax ax adys -2a dxdydexdtys
et yy= a ddgdu - aXx dx + 4aa xdrcx dd + a Xxdx + 4Xaa dx dus pax ta dydus dx 2: du a
4 dxdx dydy
=aady- xxdx,: dex 4 dxdx d cx
= aady =Xxdx C d)
(et
et XX = a ddyddys F et yus dxdxdydy - 4aa y dxdy ddu,: 4 dX
et XX = aadye - yydx, : (aX)
seu dx = a ddy ddy - x dy dy + 4 aa d dyddus aa dy
vy
yy dx
dx
yAxtx
O a Sddyddus- Sdydy +4aa shyddus- aa suy
qu
axdx
ita enim nunquam nisi  ejusdem affectiones inter
x
y
=
si fuisset sammandum
ab ipsor yydx, ut scilicet non assurgeretur adx
se conjunguntur
oporluisset concipere gu multiplicari in elementum
quod constans est posite
esse o + y progi. geom. et tamen quae inde prodeunt
log. ipsius y, seu in dy: y
leliam alias valent
An ergo rursus per hoc divitere
tibus mulliptina
nisr
do - dy. 9
 y - ab dus = 6 e b 1ab = dy: y. t patus = b dyd 1f Ergo dy = b dy y
commuge duav;aa
oportet. An potius sy. gavia
d
Idus = B lydys: gy dag = b dy f. 5t, et. Haec posito v esse progressionis
quod utique semper licet,
= yy: dy = b d sdy y = 2yy. quomodo hoc.
arithmeticae, seu v =
1X s = (2V
Sdy: y
ylus = B sv lyiy - b obo) ( f cty.9  1g. g s. 2t (ty. 9) 5 yito
V b 
(1e, o  jam (BV = b. V: 2d. Ergo Sydus = bv: 2 = yy: 2, quod
ab
Vabemus ergo Methodi comprobatione
avdo (ignus  fygeu y vod Cdydus 10 b4
 quemadmodum oportebat.
ydu:
agan
Bdduditus lydu Zdyous Fvidu ce Eep Exdyay. Ay 1n
yy dgtue du: y dy ddy-yydv: ay
eno sdud yiggis
lagaliadu = 3 y a =. Ergo fadu dag - die 
Ergo Cayddys: y = et dedo F ydo: a= v dodo y: a = aa cydus y: yya = dydus: ya
a
sed videtur haec non lice. Nam si (u Examinemus in Siydus
Neraeg. C fct X= d d dy- ydvea tgdus = qu dvdvin d d.  (6: na Ergo sdy dus lxd fB
deberet abesse a A F y: a = b
tD: ran =C, dB yy: raa = dus )624
sed ret non succedit, quia si esset sdydus = ydy: 2 foret res non succederet cum dus est constanis
et du 3
yy
qun cunset otrercis ae a dus B t soti rui sregt aus Ayed.
et Plytus = dvdo: aa
quaeu  sit
+aax t axxd X + 4X aaX dG
aady3 dy + xXdX dy2
+a (per dx, du, dix, days)
0 assumatur forrmuta
prostante, quae sit
a ay. dx +. aX.
Xix, Zdo + vdzue : 20
Saxdco = exio - scodax
Saydys = ydy - Syady
Sadutyt2. flu  
e
Saxazue = se
Syav = Z0 - sutZ