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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 115v, page id 00068199:0230
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generalius sit 100 + 112 du + 12Y yy =0 siat 200 + 211y + 212 dy + 221 yy = 0
seu +200. 112 4 211. 112 y (+ C. 212. 112 dy 4 221. 112 yy destuatur gy, faciendo
= 100. 212 _ X - 112. 212 de - 121, 212 9y
221 : 212 = 121 : 112
fiei y - - 200. 112 + 100 212 et dy = - 112. 211 (l 112. 200 + 124200 + 112. 2114100. 212 + 100 d 12)
112, 211.
ergo (100. 112. 112. 211. 211 + 1120
112311
y=
=(112 d 211 + d112. 211) (-200. 112+100. 212)
112. 112. 21. 211
- 200. 112+100. 212
112. 211
=
C
112. 112,. 21.211
sed hoc sic nil lucramur facile
 f +202. 112 + 211. 112y = 0 fit differentiando ti2 groo + du2 R y + 2H. 112dy = 0
= 100. 212
ubu pe 12. dy ponendo galerem - 100 - 12199
1 10 F y + 12dy destrmatur v. 22ydy + 12. 21ydy
30+ 219 +21 dy
10.10 +,.. 
fit m 10
+200. 1126.
- 100. 212
= 100 (221. 112
121) =121. 212
7aeq. )) Fist al (200 2)
d (103. 212)
200 di2 +1I2 d21
= d100. 212
- 10Dd212
sin sic potius se aepelatur aequ
in aeq.) pro ju = substitiatur = 100 - 12dys, et prodit
121 121
+ 21I. 12y 4 - 1125+ 221 112 gdu mult per 400 + quy
121 7=12. 212
compendio 300 + 311y+ 312dy mult per 400 + 41y
fiet fil 300. 400 + 31. 400 9 + 31 quodu
4 g00. 41y + 8
31. 447, +312, 11F ydy
+dtt 12) du + y d (211. 112) + de 221. 112- 121. 21 ) gy ∞22 1 12 r2 124) rgily
si aequentur 312. 412 et 2. 221. 112 -2. 121. 212 si at =112
e habetur 41I et frd 1. 300 400
+ d (200. p2)
et 12l. t1V)
+ gl (218. 112)
211. 112y
2
e 41+ = 2.
d(20012) + d (21. M)y f. a(El. H2y + d (~2t. 12- 121. 27) 9y
d (100. 212) - 311.400
+ d (L. H12) G -. 300. 40  300. 411
= H2 f2ut. 1)
121 L- 131 2V
= 317, 4019 = 311. 411 3y)
+d (2I1. 12) 100
=312. 400. 212l. Gy
habetum aequalia mova sie differenlialibis
coincidentiavida
a g
112
comparanda ipsi r200.112 + aru. Burly + 221. 12 yy
100. 2
quatur
= t21. 212
Habemus tres aequationes, et Hteras 200, 211, 212, 224. Maber insam eo
quae ad curquid destinendum infervire potest
sunt simplices
100 4. 1117 + 112dy + 121+ 122 dH =0
20+ 211 y + 212 dy + 2 : 1 + 222 d =0
ipsae autem aequationes
per P+m
Explisando y todatur 10 in una
et explicando  ollatur 210 in altera
abebimus duas aequationes plane simcles istis, niso quod absunt absoluti. Jam
tollatur nempe
+311V + 312 d  si possemus tollere absoluto erum
omnia essent in subvo, sed res redit ad ae quades his ipsis aequales similes
estrta
=d (100, 212
1F20. 11)
o
206. 112
= 100. 2l1
= 100 (27. 12