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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 11
# Folio 3r, page id 00068106:0005
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Xx +yd - d
u
X. 
2
= Y, P, C dys - E v vaz- 2 dv = 22 + v co
a b a b v
bv
qu
aq ter
eovdco lodo
= b2  5 2+9D +hco
0
cd +V
vi
e = ( Z2 V cocovar
det extore eo, ine locova
tunc posset resolvi problema
nam posset srnt que formula
u fazue et
f5+259ZV +qVB +, bZco +coV + bevZ + CeVV Tontingus ed aequalis
coco tciv+ r
faciamus aa sit Xx+ yy - dy
px +44 = dy
aa
dx
aa
ax
c
niuilo
sit aa - X0 et vdco + code
dus vdco -codo 2Z + co
X = 2 _ =  x rdzue - Zdv vn V
a
vdz- ZdV
 fiet vdvazu +vdo = Z do
seu vdzue -Zdv  - vdo fit ~ - n B - log. V seu Z = ~
on
seu deo =
dy
vo
Z2voz- 73 du
e
 v
dv, - 72∞4  -2 d0) - - dv
2 n - logu
(2In - log. v
Et habetur solutio
X = Z y co du adco = codo -  ZZ + Coco
sit XX + 7) = x a
a v x vsz - Zd
se. Vdeo - Wcodo = 7Z vdz - 7 + locovdz- cocozdv
Ldid
aa
seu Coco + vodo co + vdxil
seu
vr vo
deo
= v dr + 4V vdz - +vZdvt  vr-rium
vaze 2d0 V4 sul Zan
-472 vaque vaz F 4 7 V12 7 du
4. vdZ-
du
2C  Vdz- Zlo = + V v +4  dusz - a v  devav + 8 Z2 xdvaz. 12 dv - a17
- ndo.
Sedu tunc notandum sed tunc si velimus adhibere hane Methodum et facere
VdZ - Zdv =0 proditit aequatio identica
Quod summe notam
dum. sed quid si utamur se mi-expplicatione
tfu in aeq. () faciamus
V deo - vvcodo = ZZ VdZ - Z3dv f CoV
et
vuda + ... - vdu = 0 seu vvdo + .... = 0
fiet
fiet vda +931- Z201Z = sed non nanciscimur aliam in qua absitao
nam ista prodit bis
XX = XZ dx - atque fr. l  rrvay y - x _2+g =
2 Tay
+dZ
seu 2tZ + y d7 = dy1 ZZ + 28y +yy, dy = 4 a q dy
2547
sic si possimus deo etiom  in datis jam unius formae
adsit ita ut una aeq. supposita evanescat et ea aequatio
sit differentialis, habetur ilidem exitus
Quando alures sunt termini ipsius co,  assumamus
tres quatuor literas, v Z co, 2 ea praecantione ut non assurgatur
altius quam nunc inde divulsio instituatur, ut duo termini, nempe co etro
evanescant. hat etimus modum tollendi d litera restabunt tres literae
cum siis differentiis, sed in hic redit puor difficultas
da
Z
la evanesceret
ci, et haber
dua aequatione
varum ope
ausicendo aco
habere tur og n. ter
v, du
=, bdz - Zav)