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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 87v, page id 00068196:0172
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=172
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EF in omni aeq. simplics duam differentiali duarum
alem
sit pamy et f nv
32dcomus + 3tdeonB
33dcopy + 33dco gV
32dm 1) +32dub +32 may + 32 nd
33 aps + 33 dgV +33 pdy + 334
Jomus
fiet 3on +,dce n +H 9+ 35dc) + qeduty dqu - tont 42 dcon + 919 + 43 des 9+ Fnt 13 
Ex his duabus aequt siuul tollamus V et de
30. 42 un (+3242 dconn + 3Ig2ng + 9f. 33. 4 2deb n9. + 32 qunlu 33 +undus
aequ.
32.40 nn (132. 42 dconn) 32. 41 ng
33. 4149. (+ 33. 43 deoq4ue) 3340 ng
32n F339
32. 43 deo n9 43. 439d932. 434dn
+. (32. 43 d0 ng F32. 42ng 152. 43 ndque
33edqu
qutmy
=d(iem 9 . dsiet
1328 mdy +33 C9d
4359)
33C p dy
43f p dy
4359dv
ex
42f
1354
endo et demendi
boli tot
ope ducrum ipsius deo valorum collamus de fit df
ita evanescit do, nec
oumF 3Iep-3Eam -3 Fdpe H32. em + 32 edmtz ndert
du2tmtaefum+
destmamus in hac aequatione tan ds,
quam fdf. ot af, fent
33. 42 egm 2 47 e
dexomiratores Y
(32. a2 emnds) + 23 42 e puds (42. g2. fmnat) + 4. 47 fnq edt
espetne
sed hoc nonlicet
peuaere et (et silitu Ls) Dum11 3 p - g 2n. + 439
3em + 33 ep +42Sn t 3sp- 3 eq 435 47 32e+425 = m2
43P
a
B3Pp+ 43fY
22t
32C+425
Faciemus 32 em +33Cp + 4u so + 43sp = 32 en + 33 eqtarfn + 43f4
ita fiit p= 4 sed ita Clial sieiet n = m
2
m
g2arem +33 V ep + 42 Lm + 43~. fp = 3raent 33 acq. + 4rafnt. 13 afq
ut 42. 438
R = 32 N e m + 2G ev ep + 42 v. fm + 43W sp - 33 aeq. 43af9
-42 43f9
hrac re g2af dui
seu n =  m + 37 e (qop a9) 1B (33 C + 435) C  p - a9). d estruntur spont m Cfi
42n 4 439 sit n l m  + 43pF
23ac - +2af
re 4et + 3re + 42f -0
eaemet  Lepe tes C3pdete negut cqne
e as2e Scde A1 sp 42 p= 43 pas-a sa massut aqa
Ar CN h Sep BCer dae ((3 d 3) P + (41 - d4) (33de + ~) p- 9
sed ita simul esd destruitur du et fiet
hoemgofm
20 en fB fes + d32em + 32nde a= 240fta d4fm
supersunt 40fn aa +d42 fn
et fit n = M
de
a43p93 fap +43p d
32em = 33C p + 42f m + 43 fp
32 en + 3309+4
q2m + 43p- 4397: 42
=32. 43 ep
Z243C
 faciamus potius denominatores in data ratione sit
etAm +4
et fit n. m +
+
my Esc lum affictis per dys  do- 0
a23 ex +33 Cdp +
v sabi super posilis destrecris
Bie
deo = - 40 5n- a15
532 42. en mdf) f, 3. 42 Cgmdf +42. 2. fn md5 + 42. 435m q. ed
quarum ope toltamus n, et p, nempet
et fiet +33 grep + 42 a3 fp
37. 42 19 = 42. 435)4
am -42Fd
lodem modo e
32. +3 emgts (137 42 e 9p d5) + 4 2.43 5mg df (+ 43. 43 fp9 ds
quicquam lucrimur
rent asmentu 
ded =  40
si licet
32. 43 en paf (+33. 43gpds 42. 43. fn pas (+43. 43fqpdf
a
qn +4Bq
Et de reliquo t frat ex y totleado ibi supersiositis destinctis
n do
qufdeotus arfdcono. arfm dus +42fndo
40fnv
grtn
Bt
dremt3s ex +Em p+3) y + d (32 en tcq +g Sn 14) sy) B
rant
et compositam fentemus compiet  (rem reprartmta3s
33dcd e q
32edn
n
1.
smassiplicasam addamu in 
33. 42 deong 43. 434 9) 337 42 gda
hinc per illam
Quod si aequationes eddnts tractabilem
gredomys +32dconv
+330dcopy
+2 edmys
33CdpG
+3legV
475P
teral eiferam anguiao; itaque
+30 + 31C5 =32 d( + 33dG -d et 404, f 418 +42dip + 13d9
+3 alco  133dco G
20 siniliter tedous etc
31. 4349 (+ 33. 43 deo49 36.43
30my + 3onv
31 epys
ortns
42co 43dco
si= mg+no et g - py + qV. fiet et dyp - dmgs + dn v. + msus Ando it d - dpst dqu + Pdy t9 do
abemut aequativnem
Et obtinai uaes novam quantitatem de
30mys = 30nv
1py +31qV
finc
tmd
42 n
(31 - d39) e + (41 - d43) f - 33de - 43df ) p-
(d32 - 30)C + (d42 - 40) f + 32 de + 42 df
3 a, p -9
quos binos ipsius m valores aequando
M = (_ (31 - d3.) C + (41 - d43) f = 33de = 43 df
d32 - 30) e + (d 42 - 40)f + 32 de + 42 d
(33 e + 435) (a p - a9 a, :, v - a
fit
23 aC - 42af