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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 85r, page id 00068196:0167
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pry.4
10C1 + 1 edy + 12 eddue + 13 = 0 fiat 10 ey + 1 edys + 12e ddus F13 =6
debet. esse 10∞ = d(ne -nde - dne)
e = 20, 51 - 41.30 = d20, 51 - 40. 30 + d (20. 51 - 41. 30) + (d 50. 30 - d30, 51)
0
12. d20. 51 + 12 d (20. 51 - 41.20) + 12 (d50. 30-d30. 51) 20 - 71. 20.51 + 11. 30. 4)
2051- 41.30
12
40.20
a Exdd 26. 51
d12 d2051
30
G0.51) + plo 3o .7 d
- 30.50 = d30.51
C
0
Decta aequatio sit 10y + 1 dy + 12 ddys F 13 =0 multiplicetur per e, et dividatur in binas, fit
12dc
+ 10Cy + ne dy + 12C ddy + 13C (2) 00fy+00gdy +ooh ddy
Assumatur aequatio quaerenda 20y + 21 dus + 230 = 30y + 31 dy. quae differentiata dabit:
12) d3oy + 30dy
+ d3idy =31 ddy
-00f y = 00g dy = 00h ddus
+ dec dy + 21 ddy = d230
a, d2) + 20 dy
a
 Identiticentur Aequs Z et 4, primum sinistrum sinistro, deinde dextrum dextro.
in deptris per is fit f = 10C - d20a, 1: 00. in sinistris per cyfit f = d30a, : 00. Ergo C = d30 a + d20a, :10
per ddy 1 = 12C - 21 a, : 00
perctdus, h = 31 a : 00 c Ergo e = 21a + 31a, : 12
per dy g = 20 1tC - 20a  per
dea
per dy 9 =ne-20a, :00
: 11
perdy, g = 30a +  Ergo C= 130a d3i a
d31a)
valorem cum tertio, et secundum etiam cont cum tertio, habemus ex et 3 pumo et tertio Sta +50 114
e
Ita contrahuntur literae, et f. sit
Eex prime et tertio d50 = 50 + d51 Et ex secundo et tertio 5 = 50 + d51
10
sit d fit d50 = s ex 1et 2. Enjo 51 = 12d50 et d51 = d() d50 + 1dd50  Ergo fiet
10
ita saltem aequationem datum reduximus ad faciliorem, ubi abest abisolutus; et quae proinde fingendo
d50 = 50 + d( 12) d50 + =
0
101
11
11
10-1
ui eio =: V b. reducitur ad differentialem primi gradus
sed idem obtinuissemus sinetot literis comparudo 1029 + 11 edus + 12e ddu + 13C a = 0 cum
differentia ipsius 20y +21 dy + 230 =0, quod est d2oy + 20 du
+230 =0
duidy + 21 ddus
fit C = 10 d20 = L. 21  - , 20 +, d21 fit 7 = 1 d20. Ergofit, d2o = 1 20 + + d (1 0)l2o r: 2 dd20
seu 20 + d() 420 + n dd20, 4 =0 ut ante ita 50 1a 20 et 21, ut ante 50 et 51 et frustia
multiplntur literae a, d 2o y + 20dus
10
fe 30 ~ 104y8
deidus + 21 dilus
udp y + a pdus
(multipliantur literae
11 alxus +2. 12 apdus + 12p ddy + 13 =0
fit 21aa = 12 pC et d21 aa = 12 p de + 12 edp + dir ep = 11 ep + 12 e dp - 20aa, adloy
fit 21 aa = 12pC et dEtaa = B pde + 12 edp F der ep
fit 20 aa = uep H12edp) = 12 pde (= 12 edp) - di2 ep. Et d 2o aa = 1 p deft i eap, + d ex - 12 pd de. 12 dp les pd
Si dit + dd 12 possent aequari 10, primum in alliuma aeg. tolleretur ex
dupdest dne ap. + de12 ex
10 ep ( n eap, + 120 d dp
ceinde per de et ddx, tolleretur reliquum p. et iavenretur restatet aplap
sit aequatio 3C + 315D + 32ed d + 33 =0 debet 30 e = d31 e + 31 de f3 rC + B2de +Zrdde
fint 1B = py et fiet Xe py
Anthu potius v- 47 3ledpys 43epdy
3eapG F.32edp dy + 2e pddy +33C.
 sodco et ddl  bat. l  dcono + d ddco
d. b
so
-0 et debet esse 300 - (31 edp dus ep
Bcende Creaptrane
232 deap
sud hoc quaesotis dificullate aequalia
1050 + 11 d50 + 12 dd50 = 0 sit 5D = b fit 10 + udeo + 12 deo du + 12ddco
I 40=
 12dedus + 12dedue ∞
ndire dy. + diredys
rursus
+32 Cdd p
32 p ddc
2.g dp de
2B2edp
pde
2832pC
dancep