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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 86v, page id 00068196:0170
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10 y + 1dy + 12 ddy  =0 y = b fit dy-rb  dgb et idus - d b dedv b
1 209+21 dy
Godvb +  dedob
 20y + 30v + 27, 20y+ 30v + 230 -0 407 + 41dy +50V + Sidv + 450
a20 y + 130V + 20 dy +. 30dv +d230 6 ope 2 et 3 tollatur dv;
 sr - d ( )y
30
fret + d20. 51 y + d30. 51N + 0. Sidy +(3o s1dve+ 51d230 72) Haec aequatio differentretur  y
=40. 30.y - 9130 V A. 30 dy 30 51dr = 450. 30
d ed 20. 51) y + d ( 50 26
40. 30
fiet d (tro. 51) y
40. 30
d ( 30 39 9
50. 30
+d50. 30 Hfro jy
= de. 51
100y
= 40. 30 dy  d50. 30 dp
+ d (=20, 2i) dys
= d20. 51 dy
 40. 30 dy
a (..7
 a-41.3
+ d50. 302 20 dy
= d30. 51 d 30
 Uedy
1e ly
fit . 1 20. 51 - 41. 30 = 12C , ddy,
+ d 270
+ 138 = c
absolutus differtur in finem, quia
Ibi litera qu quantitas quae non alibi
10 y + 1dy + 12 ddy + 13 =0 I = so t d12c) fit Illendue = 10C F 1rdle + Ed d 12 r2 d
y = 9v dy dg0 +9ar ddy = ddgu + 2des dv + c ddo
1  29 - 20 + 21 d + 22 ∞s - 0 sit 2p = py et dp = dpy+ pdy
et sit op dpy +7 20py
21dp7 + 2p dy +22 20
Fit disfcontiando deopus + 20 pdus + 2 pddy + 12 =0
conferatur ipsi 10P y + 1P dy + 12 e ddy + 13e = 0
20dp y 21 dp dus
dedp y 21 dp dus
21 dap y du p.
fit e = 2p : 12 = 20p + 21 dp + du, : U fit 1. 21p = 12. 20p + 2. 12. 21 dp + 12d21
fit 20 = 11. 21p - 2. 12. 21 dp - 12 d21, : 12 et 2 rp: 12 = d20 p + 20 dp + d21 dp + 21 dep, : 10
seu 10. a1 p = 12 B d20 +12. 20 dp + (2 d21 dp + 12. 21 ddp
2o aequalio data 40 Y + _ dep + 12 ddes + 13 = 0 fit 3 = sit V = py, fiet d p - apy + pdys et dd p. - dopis  reptus B
et fil 10py
1dpys + a dpys
20y+21 dy + 22
+B1dy + 2 ddus +d22, 12P
JXo Vdrogt ld2oy +20dy
217 Fadps t, 12dp dus + p ddus + 13 a5
20. 12 p + d2j. 12p = 11. 21 ap + 2. 12. 21 dp
et d2o. 12p = 21. 10p + 11. 21 dp + 12. 21. dap.
seu d2o =  10. 21 + 1. 2 dp + . 2 ddp
a 21 de + 22 ddy +23 sit V = Py fiat dv- apy+ pay surl + 21 dp y + 21 pdus
20 = - d2 + 1. 21 dp + 2. 21 de
12 P
C
1e, 1)  dp y. + 2 rdpdy + 22p cllys + 23)
Haec aequatio comparetur datae  nultliate per e, toega Hedut eddus + 13 = 0
228- 21p +2 22 dp tnusfuanatae 104y
10. 22P9
+114y
pa 2BI 12dd  +reragdus + 12 4 ddus + 13
1221qdp et 1. 22+ 12. 21 p9, fit 
11. 22 pdg = 12.22 gddp
12. 22 P ddque
2.12. 22 p de
fit 2 = 10p9 + updq t npdau -nquap
2
124 dp
2. 12. 229 dp
 e 12. p9 = 2. 12p d9 - 2. 129ap 129 + 2 12 A9 X 2. 29.
107 sit 1opp _ e rfild p
seu  12 ddp = 12 dp
+2p4
si esset g = B froiet 10p + Upp dp = 12ppdpst 2 ppe p . 418
a 1  (1+2.1 8 dp) = 10 1 dp + 12 dap
5 1 10   1t  dutr da +(aglia) Ap a t l 12) Lpcue - 10p p ee t. d lp
L (11 dp + 12 dp) = 10 P F 11dp + 12 ddlp 2. 17 -. P05 10
fint  udip. + 12ddp + duup + deap = 10 + 1t p + 12ddp  H
ab = sot, ddb- dx l. + dedvb
= ubi pro dae substituatu
vator ex ∞e4. 2, et
pro V, ex aq.1.
= d ( 30. 51230
50. 30
+450. 30) d (230)
= d30. 515
30
+ 20.51 ady
= 41. 30My
t et
+ 20. 51 ddy
- 41. 30