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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 118v, page id 00068197:0236
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plutis aequationibus simplicibus d differentialibus duarum
duabus
literarum d multe  habentur silutiones non simplices nujus
sit  gtf  fZ 1gdZ  t.
sit fv +Gdae + hZ+ KdZ _ =0, et lV+ mdv + n Z + pdz =0
literae.
fiat Z=  e B= Z = b et v = y . unde ex aequationibus propositis
fiet fiy +AX gd ref y tagdus tak dx tah =0 et aly tamdy tapax + n =0
Oxy
Mdxy
fiet - dx = fy + gdy + h.,:, gy + R = ly +mdy +n,:, mytap, quas duos
pg
Valores ats aequando, fit + fmgus (F om ydus + ah mys tagpaus + actep
+at py +agpdus + achp
-gl yy( gmydu leagnus 
aKly = atmdy -aa tin
2 quae aequatio identificanda est datae; possunt autem  poni
aequales a, quia sunt arbitrariae superfluae imo licet etiam h et n
facere quales libet. Possent esse f - a et h =0 et 1 =0 et n - a
fieret av + gdv F KdZe = 0 et Mdo + az + pdZ = 0
et fiet amgu + Lapu + popdus + qar  = 0 sit data aequatio du = xxryuse
+ gogy- ftmdy
K = +XX: a
fiet m = a knt XX v XX. K
ax
aa
seu agu a dy +axX = 0
P=9 et ggAXx = aa
seu g9 = aa - xX et fit av +  (aa - Xx) dv + XX dX = 0 et adv taZ = 1 (a - ) dz -0
sed prostat conscrvare generalilitem, fiet sm. gl= aa  hm+ fp-gn - Kl =0
qu - Km = = aa hp - K n = XX quaerantur f, ny K, m. g, , In, p
+= ta gl,: m a l tgn hnc: p f g - sm- aa  = tm = aa, : p rCLAtm Sp, : n
na limu honp taan,, nin + pl =K
K= Hta- aap4 aat, . lm s em
etm _ = Ap. K P = Km: g fot a~ AB(Kg m: g = l. f sege g
sit p = Kl: f et nhl. f p= Kn: h fit l. f = n: h = m: 9
Pok- Lf fit m: 9 = f: l = p: K = hn ita nulla liter opurrit bis
M= gf.  1 = 5g: m h = nm: g p= Km: 9,
superest aequatio hm + fp = gn + Kl in qua substituemus hosualores fiet
num + fkm  gn + fgK. m seu C mn + fkmm = ggma + fggH
R = m -ggmn, :, f99 = fnm = - mn: f. Euo p = - mm n + Fg
Habemu ergo l = fg: m h = mni
p= K f :b p. Kur.gHo mo p-mma
abrys + aac dy aad dy 200
 datam generalem ats) i aadus + aasibus + a
k = pp. H sumamus D+
n + hp- ag,: t l= fm ac, : g an n hp. af,: K
n= prost
h= . ae +KR i Cgt:, ad t km
p=  ad 4Km: 9 undejus ecalores tstomamus in sa
l= fm - ab, : 9
in aeq. hm + fp - gn +KC = ac
fet aem tkemn + adf + KFm - gn + fk ( - ab k = aC
siet aegm tgtema + Ldfp +Ksmp ggpu = fKlp. abtp- acgp
D
 ad +Am
et fiet aeggm + ggkmn + ad f qu (ad Hem) = adgg GKmn + K(fl. ab ad akin)
aacd + act
m
d + 2adtem tskmm-adgus = asimo +Ad kfLaabd s H fretlm abtrm
ad f qu (ad 1Kt) -+ (fKC l. abk - ac9) ad T Km) +ggm (ae + Kn), : gg (ad +Km)
a eggm  gytemus
fit n=
jaciendo p- 0 = ad +Km et h = o = aetKn fit M = ad. K, e n = - ae: H gm = ac 5f. M- ac: 9
possumus hanc aequationem partia in duas simplicuores
et se l adf- abk igk
en