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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 4r, page id 00068199:0007
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sit aequato angentialis vedut  dy: dx =  yy+ xx, : aa
fiat  X: a = dZ: du et y: a = dv: d0, et fief
ddv: dd Z = d2dZ dvdv + dZ dZ 3: deo dec et dco = S(a vav. +dq d Z : da vil1
ponamus de esse constantem, et faciamus (post tot alia irrite tentata.
da = dv (ddz dZ fiet dae di: (d v: d2) ddque + ddv. sddZ: dZ = 0 seu sddz idZ = - dx dd
et deo =- ded v adZ: dZ d2 Unde (dv: dadZ) : iddx ddx
et tandem dv. = dudvdZ dZ + d7
1 da
avdv +d ZdZ3:, dar 2
Td2
quae aequatio est
poteramus et facere. da= salZ, sed hac illud brevius
poteramus et facere aliud quiddam, oeib. gr. ei =d  b Sadzi d2 sed illud brevius
tractabilis
idem est ac isi fecissentus y: a = P: (dd7. 4Z et X. a = dZ: de sadzi Z
et deiZ dae (ddZ: dZ constantem, ita fieret
dy: cx = Z: d2 qu sddqe. d 7: ddZ:  sda Z. Z = - dv : dqu (d z:. d c
= dodv + dZdZ,: dudv (qu) sdtz. dt
jam f
jam fZ ddv sdaZ. dZ + (dv: dZ) adZ seu Sdd7: du = - du odque - dvaldus itqalla
p
quo vabore subsoituto fit dvidque = dedx + dqudqe,: + a v diZ. d2ddv. seu
du d7d7 dedr + d7  = adv: ddzue ut ante.X
seu
ddv: sd Z = (d v  dZ):, duav: d2 dqe + 1 du: dz = e: a  et fiet:
ui
ddv: daZ = et: e aa ee + a Ergo ddz: 1Z = de,  :, (C:, aa eet a) - e: a
siu dez: dz = aa ee + a, de: et - ae - ac
17 = deo X: a, ddz = dco dX: a, et fiet  dx 3X = Adzue. d2
dued lco: dv = yeca 2= (ddZ: d7 daret y3a = )dX: X, quod non licet
X  lg: ax = XX+ y9,: aa
3 = y: a =  Z. v rat
gi a = vZ: aa  et X: a = YB + ZZ: aa fut 
tiel dy : dx =
vdque +Zdv vlx + 27dZ
qoia
 XX  = R +eX Y pIIX + 2, y,: g
30ca LSHXF3Xy
X: a =
yy 3 = 201 a + 21X + 221y
u I 301a + 311X +321y
a
_ XN S0 x yta 3: a = 6 60 101 + 4 110X + 101y 0
dy  3a. 8dC - Cd8
dx
 9d5- D a
110 dx + 10c dy
210 dX + 201 dy
101
(d
∞
X = 201 a + 210X + 201y = 2
2014 + 310x + 301y 4 1
(d+ V
X
y = 0
3004 + 310 X +301
 X = D
2
8do  . C7814 = 700+D + 9 DDdD- DECAY- D13
tat 29fy d8 = 900d e d+8 = ( - tl)
seu ag= C dD: Y sd msque 740 = 8 3γD = DOCdZ -V d
459 NdO DD+
possumus facere aeqsation srle onduas y panere parte
fit de
si du soustans erit et nodx+ yydx couslans
ponere constantem
et fiat O = Xxadx + 2X dxdx A Z yyddx + 2ydydx
dlyaa = xxdx +yydx
Xa = y: g = x: 2
X: a = dv: d2
d dy sa vag 5 de- vaZue Z2
de
=aZaV d∞d13
n
d
XXXyy, : aa = Z: a 2X dx + 2ydy,:, aa = dz: a
l’av
aadu - gydx = XXdx sit X = Z.7 fint d = yd Z- Z ly: 9y
aaous  p Ergo Hd  G dus - y dzu X Zy dys = 2 7yd3- 7dy
g: a = Zpr: t X a = +: F dy: dx = plae -vat, :, + 42- Zc+ -∞v + Z2,:t
 Lde+ Hva = tordz + +Z247 - Zrnat - y3d +
X: a = 7+ v ia
Ria = (X
yia = Zv: aa dy: dx = Zdv + vdZ = Z2vr
312+ 31V + 30a
a, 312+31V + 30a