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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 54r, page id 00068198:0107
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Fortasse servaretur Analysis si primum poneaemus esse datas
ady
aequationes 100 aa = Mav + 2 ay + 112∞ F mrgy = + = 0. et 20oaa + uav + 22VV = 9 = 0
multiplicetur illa per l et haec per m, et conjungento fiet:
100 laa + iu lav + 1rlaq + 1. Lvo Y 122l gy C5= = 0 l:m = - 212: 12 = - 1: 1 seu H = 2
Si 1o at + (m1) _g + (129  + (112) a dv + (122) alilus) 1) et 200 at. 7 B + 212  adv ) 
+200 maa +, 2um a  + 212m qv
16(121) uilx
fial (9) = yr t v. At ex 14. 1. fial 100 cdex H(1) D (112) adV + (122) adu fiatid ant (11) 2) s
H hv + (22) h do
Git
e
(112) + (n9)h (22)
ADh A, at atque adeo effici potest quaesitum
Unde habetur aequatio per quam datur
sint jam duae dalae ambae continentes y et dus et v’et do, Ras con-
jungendo  formetur una in qua absit 3 et dy. Quod fiet
simili fimi Ie thodo.
deinde ex data, una et producta formetur
nova ruisus explicatione in qua absit v et av mydx
Sit aequatio data 100aa nav I nray 100ca x + i adx + ex + UEadve 122 as
et 200a ux + 2U Ddx +212 adv0 sit  ay+ E et aduadue
sit ay = aco + hv et ex aequ. 1 L+Et ady. adu + hdo + vds
Et exaeg. vfin +100adX + 1 Ddx + urand t + 121 aco dx + 1aadv + maado ∞
+ 12IhVdX
+ 12a dh
6200alx Z Eulvdx
e
+122ahdv
4212aldo
l= 12aF 122h,: 21k
Ergo ut destruatur vax fiet
111. 212a1, + 121. 212 hext 122. 212 adh = 2 112. 2ua dx + 122. 211hdx, cujus aequa
ut destruatur du, fiet
adeoque et  et podibit aequatio
+ 121 a cd dx + 122a4do = 0 ita 5g. l et 2, reducta est ad 2a
tionis ope habetur h
 habitis ergo V per aeq. 2 et co peraey. 4
100.212a DH. 200a fL122
+ 100. 212 a fdx
- H12. 200aQ dx
et h per aeg. 3 habefur 7
100a dX + 11I vdX + 121y dx + 112 adv + 122 a dy 0
= 122. 200 Ahdx
1. Et 200 a dx + 211 v dx + 221 y dx + 212 adv + 222 a dy = 0
quaeritur aequatio
in qua solum sit  dx, v, do fiat aV = a e + F gy et siet: etay = e
sit
+ 109a dex + 1I E dx + magZ dx + 112 au d8 + 1120qd
+ 121 a dx
+142a yeg
127 ala 
Eoodasdx P2n af dx  21fgqx  212 aaf d8 ( 212 afgdis
x
ree
212 af sdg
=222
1
t su pererit aequatio sed
Et supererit destructis  aequali
+ 100. 2 aadX) - + 11I. 212aG dx) (1, 2212 aa d8) =0
- 200. 112 = 112 211
= 12. 212
et faet aequatio ipsius Et ex aequ. 1. fiet
+f.
et 100aa dx = Igydx  + 112 a gdy = 0
in + p a es dx +121 a ydx ( + 122 dadus
+ 112aad8 + p3 aydq
in aequ. 7 abesset 22 et 222. ipsa potius
lteremur et fierec
fiet f- 12a: 212 lor inum
end male
et  ravo lort 9
et 111. 212 gAx + 121 212 a dx + 12 213ad9
aequ. 112. 21gdX + 112. ∞21 ad X + 112. 222ad
fra ito habertur fet g
+ 200a adx + 211gydx + 112 agdy =
+MI a SIX
2et agex
212 aydque
+212 a4 d8
et ita habatur 8 = 10. 212 - 112. 200
dabussemus e
1∞ 211 = 111, 212
seuodatur 8 per X, habetur et 9
Haec via ergo mihi praeferendu
videtur priori s licet
essent 221 et 2228 essent 0
 in 5q. 2. Ia enim opsa
ipsa aeq. 2. non amplius est opus
in aeq. 8 vel 9 tolli potest dus
ope aequationis 
nemm-
sipraepararia aliis datis tale
i paequationibus  et 2 debe habeetiam q haberetur absolute nec risi una foret opus
(1 prius fuissetae ratio secundum V et secundum ∞  et pro 121, 122, 221, 222, affuesserit
112 222 = 122
tu
 (121) (24) (221) (222) ita pro D ponendo ey, pro 121 fieret (121)C pro  22t fieret (21) e
praeparationem, ut si
sed quia F imoltoit g. esde a non pilet ad habere hanc multiplicatimetu s praectat
exilicare, et qsed forum per Cr
cedi
et V per a8 92 ita res oplime
Hac optma latio
antils
reper