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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 76v, page id 00068198:0152
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B 5y+ 9dy + , 10 2ut y +  +..
10F. 10 -ad z. 5 = a Z. 9 fit 12 = 5 47 - l9 Z -  9
a
1Z - Bt S (5 s et W = a b3 5tg
Ergo fgradus a f9+ gaus, ab sstig summabile est
1g dato rationis ad 5, se sit q s f - l cg. a, fiet
(9+ c3y + gdys, a ben summalit
Cby + ab dus eut summille = Z  d (27) - te bey
sat g habeant inter se rationem onstantem
ul f9 + gdys summabile
V) = cHfix Cb x + V ay
A2 B2 y + B dy est summalile sit ues hine avi
= 17B2. 5
dole dy + b dsay
= b + 1 2u, .g = V: h
8y + 8 ly
Ay +8 
+. Idy
Se 1y + Siu
Gy + qdy + 
de y + 9dy
didus + Valus
av b dus + b daque
5y + g dy +hacys
videtur id semper comparatione illa
obticeri ut obtineatur aequatio  differentialis
in qua obti absit terminus absolutus seu homogenens
Ex gr. Nempe ex  aequatio f y Hdy +9-
reducitur ad v + h du =0, quae est solubilis. Et
aequalio y + fay +  ddus +g 20 reducitur ad tatem
V + ldo + m ddv =0 sed talis non ideo est solubilis
idemque est in altioribus.
An licebit sic procedere
ay + flys + gddy = 0 (quia res eo reducitur) multi
plicetur per ly +mdy fiet
alisse Estag+ l9 ylbus  hijtus + gndy ddus =
tamydus
quae comparim potest compositae ex his
vadn yy tun ydue
+adpy du + ap yddus tap dydus
adqu adgaydus + aglyddus
se
P = du g: a
im - 4 ag. 9 p = 1g. a l = dn = ap. 9 d et sp - du dy +. g tln
restat duf. + aaq = an + gddn
sed ita tollendo q vetriemus _ ad d.’n
 dyt aue alysagus eben + l iby + in =0
Aay + Bdy
aq = gan + a dq
sis aadu + dius + amy =0 ~ ns amy + amfdy + mg ddus = 0
fit al = ng et aa + adl + alli9 = 0
a d du
ml dys
medus ytm + ndus + d dys + ldlu + adu + P =0
a
mpu Alx ay + al ddu + Anp ~ agy + 4fdy + 4g dus + agh -
my + l du tan
aam y tamdus ubi circa termnum ultimum non est difficultas
taadn = o-
fec mpraam = ag (98q ncam + ag 17 + b 4 2sq =0 es.
= 49: 0
tadl dus
p ren + radm - raque = 0
sit m = β9 + V+, erique n = adm = β d9 + quB + yat
et t aqualuo s 9d  (4  t + agaq + als 9- at 120
pe + rpHt + redq + rq uB + 1)) it 3
tiat gp + aβB + adu - af + rp C + ra B = 0 1 ut evanescat 9 1
it habebuntur , et )
et ag + rβ =0, ut evanescat dq
et fiet aVt + rppt + W at = 0 unde habetur t
porro valore m et dm s quem assumsimus substituto in
aeq. C fiet aequatio in qua sola superert incognita 4, quae
non ib qrae non ibit ultra, 9 et dq, et ita si nihil
in calculo turbamenti est, habelitur 4 adeoque quaesitum
et fBZ + fat -hdz = haec aequatio multiplicata per Y abjiciatur priori, fob,
sed sic video deveniri ad βB, dB,
q. N redit ad hoc
dZ b. y + b cdys
vac
ag: B et p = a Bt ady - a57 : (9- 8 et
sit aβ+ a d9 - af +rd (3 =3
et quia YB = ag hinc tollendor
ccenditur ad βC B, d
Hoc
sucedere
Ex pau praeceedente su mantus aequationes:
fZ+ fpX + sBaz +G afa at - 07
(Z + f do - gdz -0 fv - h dZ = 0 fiet vet si v. - βZ + at;
ac 
rat