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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 16v, page id 00068196:0032
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=32
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s
vy aydy ta  aβ dy + Vydx + aB dx =0 multipli.
cemus per  hyytanut aan, fiet rete sane
ascendemus rasus nimis alte nempl ad yhaqu quod est sine suo
itaque hac ferae tpartculae fiant
at partes aequationis compares fiant, summabiles
ompare 1t
hic nou sufficit sed si assumamus gy hyy+ anst aan =0 et
fiat yudh + 2hydus tamdus +ayam taaan 0 ejus multiplicatae
per ad, addatur ejus sumnia multiplicata per pdus 4 gax fiet
hPYydy +ampydy + aanpau thayylx + amquax Laangdx 2 -0
teach yydu tamaq taa yndh ta isam +atan
sit aequatio data asydu + a Bay +V dx + ab dx =0 quae multiplicea
tur per ayhrp: a+ar, et fiet
hpyydy + hB β ydus + aar Bdy + hBVygax + hpBycx
ie
+arvyax + aaordx
identificando, fit ra perame est enise et ex jydo fit
radr idque
sp-aat a Y fit in Exdyfit
noa
sae non diferentiantur
et ex ydy  fas r- amprraah tp Biaa
inveniam primum D, qY quia 
racteon, ex dy fit Y = np + am;. B
adeoque fit aanB + am = aBmp + 244β
sit r= n nodx + aa dn g: bax ado
 Bngdxt aaBdn
Ex yl
priore fit P = ZaaBh - aM∞:C
exposteriore fit 9 = npB dx tam Bdx
Rursus Exgyax fit 4- hpH a
alinpodx+ aahmddx ahBdn
adeoque b= aaptimaxta Bndh BBhan
itaque habemus aequationem ex duabus
qua a h, m, n assurmunt ad
superest aequatio ex y dxiubis substitnem
autem
sine p. se tac
L
sida A Y- an B et
sed rura g2 pibau easdn Ba
q a
eiu duos ipsius quatores aequando sal
rectat aequatio
 p=d, video gia ex
 dat a_: Ra
paulis prolixior, nec salis
Si
at aequalto absa
fit aldy: y copalimus- adan
+ jam + a dn
sit ab AmB et
in line pay. praced. dia
etvebet essezax
ggennus, s et uu
apan + andp = utm
nex
a et rursus exax
nd ex tam bex
u En
aan + BBh- aBm
aa Bdn: Bndu
latax. Unde
CBhnp)do- aBndh
in Bhtivax- annodus
valoribus ipsius p, in
quadratum.
ralores 9, Y et P prius
enthennana fieret
esthc adeoque YL 2h
seu g. 2B hbex aadn: nax
gan Lrlinpax pahan
a B+6+ EahaB aYhVdX
mrovime pracadentes dabitur
s
evanesere
restat fit calluu
+mi +an-. unefferentiando
uvan suclessum
e
+m dy -0 seu aldus- fll: ) ingy- l: Dan Hitab
a rudnt ayem 
sim data agamgag mBau +myydx mbga
adereamaem dur t aneniax
p
devidaturae quatio peoducta per ns
ponel iptris angrem prbgaru
seu datur nim sed misus fre
Wmux +nzax, fit aanin t adpop = lohmax 
ta
aa