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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 75r, page id 00068198:0149
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uo y rudus + ikov. + 121 dv + 100] = 0q sit v = e et fat  r. 120 (1 9 t pay
210y + 21 dy +220V + 221 d + 200 =0 Ha aequationes expli +121 d βY
mulsipliabur prior aequatio aequatio ex
tat
tera pera . ...... e.F fie d. componendo
ut iam tollamus tant dy quantque, fiat
siat Y =  221: 121
pec licet siu
ide
tur
succe
e
et X -1II. Z2Iaa = 121. 221 aβ + 211 a + 221β=0 sed hoc non succedit, qa evanescit (3. du
ad totendum L Y = 220a: 120
Hoc sid summos terminos cellere posumus, ut y et Z, sed nil non satis hoc pacto fiet
quo valore substituto in y, fet qua coefficiente ipsins y ut tollatur fiet = 10. 22Oaa - 10. 2oaB - m rroad B +
2
210aa + 2o Ba + 221 dβa = o, fiet - 110. 22e a (= 120. 22 B. 121. 220d βB + 10. 2W0 a (+ 10. 20() + 120. 221 d β = 0
itaque per quadraturas habetur dβ, atque adeo et β. Et fit  B- (110. 220 - 126. 216, :, 120. 22 t 2to
Restat aequatio. ( MI. 220 a - 121. 220 (3 + 211. 1oa + 221. 120 (3)  dy + (221. 20a = 121 220a) d Z + 2 ∞. 120- 1dbnlosas
seu compendio S dus a G dque + H dx  dq = du + Bx, :a .Hfic valor substitnatur in duabus
fiet 10ay + 120 aZ 2 et B dy
120 3y
100 adu
ax
rationib
(+ 200HIa 
10ay + 21 adye +200 adx
G y+ 4202 + 4pay 1400aL
erunt y, Z, et a, quae aequatio sic differentiari potest, ut in ea suit
121 d βy
vol compaadio 310 y + 920Z + 31 dy + 20d a L0
ita tarum duarum aequationum ope
habebitur
tollndes dus
tollatur Z, maneat y, du, dz, a, dx, eibi pro dz ponendo vilorem dz = Fdy + Gax
habetur aequatio quaesita in qua solum extant setus, una cum x et dx, quae potest solvi
ne procedendo ita, et quaerendo
gratione in qua du et d y et Z golae evaniflant omnia, sei tatur
et ita quaesitum consequemur
un
nes 
luffe tamend
y
verea
Ex aeq. X. fiat 210. 41- 1211. 416
et n f. y 1 dy + =c fori coincidentes
= 300 qul a
3I1. 420 - 320. 411
311. 420 - 320. 4 ( 00. guL - 311. 400 7 a
 1(310. 411 -311 410) 1 + 310. 4u - 31. 410 dy Y d gro- 3200
=liz =) Fdy + GG.
la2st a . 13. 2B Lra oo Unde apparit evanescere aequave 
dina
311. 420- 320. 411
31. 420- 320. 41 = 111. 420a + 121. 210 (3 F, 121. 220
a me trrer teaue
tat simpeditus sicessu. Tentunde san liceat officeret constantem
10
multipliretur  +210aay +21aa dy +220aa Z + 221aa dh+ Eebadax
+220βa y +21 Bady
Z et dz.  et sunl tollere y et du foret
verte ad
l +22 dBay
uiie
3.
dem qiu
quatu
ande
ZH. 20