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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 13
# Folio 11v, page id 00068084:0022
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quousque continuandum in m istendunt datae in b et c et f.
sit do de = ttu posto h dari ex _ X. faciamus do = dy: y1 et
fiet dydus= gyl eh faciamque B = ers fit du 1 y sy. fi sey
do = (2 a V
13Z
q
= Edy.ps et dudo = dydy: y = tau
seu dydy= t1s
Sed video comparationem non bene procedere, si absit simplex dy. ergo pro
dus ponamus Ergo ponamus de =  i x Plax et fiet de+ lax = h dx
seu dodo + 2l dudx +NI dxda = h dxdx. seu fiet
dodo + 2l d EHI, = 0 ubi l et h dantur ex X. sit du = dy:  y
ax
=h et fit dydy + 2l y dydx + =H yy dxde =d
ergo ergo in b dxdx + caxdus + fdydy fiet b = H yy c = 2ly et f =1
axax.
adeoque fit 10 =0 1=0 12 = ( H - h 13= 0 ek.
30= 1 31 =0 etc. fit d50 = a
cvanescunt n
Inaeque vero tertia fit 12. 51. S1 (- 21, 51d51
taciendum ergo ut conservetur  aq. 2.
u
si
sit ergo V = d dv =
yt4
dy-2d4
Yy + ∞2y9+q
dydu = d7 dz, X X
fit dus dy - x
h.
20=0 21 = 2l 2220 ek
 seu 50 gtans.
in 59. 2 oa
∞+ 30 dst) dsi sed hac nit lacramur
ubi q pendet ex X
sit y = Exy + By +D
p
fit qlydus Xy + 4 dydys By + Hydus )) =ceCF
Xdy +ydx F Bdy + 47 ex
2 Y...
nut sit Xy= By+XC L Xdy + ydoet  Ody 3, C h (uy   tR
rdy dx
ergo licebit.
itaque si volumus in vulore ipsius dycdis, abesse 
axdx
numeratoi s R absolutam
fiet hdY axY + d)) K = 0
a, ubi d3) non fario 0)
pusiliretur ad vy dxax
quia alioqui non haberetur yaxax sed statums
CF C seu V) = -K: h. sin ila fare t oystum
veum facio K verum facio hV +k-d
Resumamus ergo sit dydus = d2aZ, hq +K. sit  Z =  q y frit aZ= xdus +dx
et et
+4
D2 sit Z= _H βX + γ y +b
fiet du dq= Xx dydus + = X 9 dydx +ggdp
Sige +
= (X
64
in fir d2dy βBdx + 23) dxay +YY dydy
in sE (A a +K ettgut = B X + V y + B + 4βX
nX 1
3 Xy
313X93 + 6B (3YYXY
BBBBXX
1V60yy
+ 12 3YB Xy 12β(16Xy
(3 YVDXy2
+
YXy
Et fiat BBK +  1bβ +q BB3FC
et7
= 0
sed nec sic possu efficere, ut obsolutum de pura on
x coefficiente carens evanes, at
do do = eh dx sint d e V = Y6o t bIK 4 62y + 62 X9 60 + f1 + 6, y +62yy ac
Ey + yg
sed omisso prius numentore hoiatore fit fiet do = 600d60 + d6i y + doc yys erc te
+ 61  267 +363yy, dy sen fit dudo = 460 +24460 dbi y et, dxdx
+
61. 61 + 2. 261. 62  etc, dy = hax  ergo 160 = h. seu quae
difficullas est par propositae. Ergo addendus et nomiaa v = 60 +017, :70 + 71y
lebv