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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 21v, page id 00068196:0042
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Hinc apparet modus aequationem hansfeeo mulandi in difficliorem, quod ulile
aa hay + mydx + G n dx ex y fiat svax et pro dy fiat vdx et
pudibil hrdx + M RVdx + msvdx dx + ndx = o seu hv + m sedx +n = 0
inde differentiando fiet hav + vdh + mvdx + am (vdx + dn = 0, et
pro sodx substituendo valor, - hV -n,: m fiet  mhav + m, vdh. + nim bdx, ndn hvdm
seu nih. do +
hv dm
Sit ponamus log. bi a esse 1.
f
eam
maecedente fine paginae, etiam gradus fit
attior
egut alyamania  ny + ap- aseu per cumpendium ag+ nytap= o, unde diffeccaliand.
ag de. b + Caadque b t ndy +yan t adpX? jau B = = ny ap,: a9
ddaqs
et siit agnysde tagapde + aanydus +da ap dg. nag ) aaydn- aaga dp
a9 b: a)
et explicando regnu trapusse qu
vill
reanyduscgndus + a p dg
a
9 aep
Fn
etrsus dm=m
sit aequatio aydys + aβdy + Jydx tad ex = 0 quae multiplicaliper 2Cgn + aeq dabit 12gcd x sat a . ad
gyan
2aFgnydys + 2a (Bgnydy +2CY gnyyex t Za cbguis + R B9dy + a 9AX
fi Ex gyydx fit dl = 2c) dx: aa ex dus sit n g = gpl - agn, : aB = grul - augnri aa B
+a) Gy x
unde ex ydys fit ant +  2 a Cp = 2 cBndpl: B - Bn: B seu p = apl 2BB+a  seu p p  rantndra
+ aq ydy
e
aat - ZaBC
Next te sit  m blypaxagnabgnax-aa gnpaapdus argneaa gupta  ac  a
Ex ax fitBBdm Bepdus Ha ap = Dt opdX- abgn ax Unde habetur 
-2aBpac dgndx - aApae VyxaX + afea ondx=
et proppouendo valaen nia frit aa BVnx-  Dsgap ax- a Brtipag- a B pg5 an- a  para Crrpnal
at Brundus-2aβCBrgunax Ng pnaX + Vr gunax =  ernat gun
si q et dg 
Et potest compendii causi fier
luas et 2
cyytalyrnaai  nytap =o seu aqs thyrap: ofit a de b randytajant auap
Ubi illud pulchre evenit,, ut posin ubique non extet
et pro be substitiendo valorem fiet any de undq ayan-a =. junde- rcgag ratsrag lacem
nisi n et an unde habetur an, d. Y
aq 
Resumatur calculus:
acep y ds + a lpaus raangyal + ea pydm
y+ a pam
Eydu - aide
et f zaenyydy f caralydus +
sit aequatio ag dus + aβdys +V ydx+ ab ax =  quae multiplicata per  re ny t aaque dabi l
ndy
2aCnyydus + 2aβcnsLy  + 2) nyydx + 2ac bnydx
+aq qydx + aBgax S
Unte per - yy dx est dl = 2C. aa) B  Vdx seu l = XC: aa) s)ax. Ex hyfit 9 = lp - an, : C
+aqydu +aBgdu
unde ex
iy dy fit, aut Bl a βIn + 2 aβCp = 2βBCn + aalp= Bn fit p. n = aB l- 2BBC + a) :, aal- 2 aBc
Ex de fit mat
E Ex ex fit arnam,agran- astr - a BIrndx - a Bn ax. seu dm = ad Brda + aa Bn di + B lynax -accDn dx
i et quia ljam inventa est potest compendio dici p = In: a et ap = rdn + nuY,: a
a Brn
Restat gux unefini ata an + BaadF+ aa bl ax-aa aa Bdx paur XI( a B du) - 2 ac CD ex r f-)a dx
am =, agHn: a) tadm F at rn dg - agden) N- tgrn a on Dil gn dx u na Degndx,
in dm = (- a d9) +  den, O dx -ad dx
Yn
a
pursus am = 2acd 1x +  aa g Y dip A  duf B dg. 
aegl
aa (5
vil
a
videturres haberti
sed verorne sit enor
sane habetur san et satn
rn