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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 283r, page id 00068196:0561
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Reassumamus ergo
o= dzue y + Zdy
U data sit equatio coy + ady + 12ddus = 100, assumatur
L
100
d dy + vddy S  (2
02) 10Wy = 11 lodys + 13 loddy = 100)
10 = 43. 10 6) eb Zr du, : 11 Z v: 12
fint 10V  12 dZ et 1Z + ndvZ uV Has duas
aequationes, ut solvamus assumo q c0 + B8 v= 10 + =g
Ex B fiet, 12dao + 128 dr + 12 rdg = 10c0 + 10+ 9 et ex 9 fit 12co t 1XG + 1ndeo + 12td9, 2 d 110 4 1t
10+8 - 12adeo (15)
ido urq- iadco Ergo ut tollamus _, sit
 = (per 13) + 1l0 = 1 at
1010H - 12 tar = -12rr. 12rd L. ur1
sit t = Pr: a. fiet: 1a Ber - 12 a βrdr = ncarr - 12 aBrer 2 β + 11 a B YY uhisi F r fit (1o  HY=
14C
pondum solutam
=12dr 
Et patet
ite idem prodibit, si pro t: r substituatur B, quod est in potestate. Itaque exitus hac via
= 12a rr dB
sed video nihil agi et evanescere r, et d quari per ae quationem
An sic procedemus  10y + 1 dy +12 ddy = 100
non habetur
tantum Ergo opus est ut faciamus 10y + adue summabile
su
fial y = 8V et fiat 10DB + 119do
11 dgV +c do - c d
Sit - 108 + n d = 10g. + u dy - 13dus
+ 13 49
1)dy = Vdy + dy dy + yddys
10y + dy
10 By + 1 β dy + 12 β ddus = 100
posita c constante
10y + 11dy + 12 ady
sit v- - 12
10 39 + 1 βdy = - 12 βddy - dys (d (1β) + 100
du ly = v(Z dys: G3 = var + ldv
ep = + 12dp Ce + Mpleo + 12rd9
10t - 12 d4
4) = - der
β - 11 + d12
- d ( B) dy erit   d(. () 10B = d (n β) = dd (11(3)
sit  si esset 10 = d 11
y = B _ Z. fat +0Z + 5 b
vy 2 u dy
10g c0
+ 12p co. + 129deo + 12t de
+12dgc0
c - (2dC = 12V
12 p + 1rdq - 19, 10t - 12 dr - 12 dp- 109, 12F - 12 dt = 121
deo (12p  (12r r12dt - ut) + 10. 129l- 12. 129 dY)  des (ert (10t - 12dr) + 12r (nr + 12s= 1. t)
F 12r+idt +uL - 1 2p. + 12d9 - 19
10t - 12 dr
t12d 124u toque
1219r + indC et r 1012 ql. n 2 gur
10 a2 tF - 12. 12 t dr + n. 2er + 12. 12rdt + 11. 12 1F
a
co
 unpur ta= p pr ut g 1alus
du = dv b
ddo = dudv b. b sv
dav = audo + ddo
dduo fit v = B N 
toa D
a + 12 X
Bco
12 Agco
12 d p + c2pdv + tadg =0