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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 134r, page id 00068199:0267
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101  + 11 X X = 12 Xdy
iy
3dus ydx
sit WXX  = 20 +2) X + 22Xy + 23XX et diffecentiando 214X + 2Exdus f 13Xdx
1
jy
fiat 10= 21 = 10 et 22 =11, et 23 = 4, 12
9 = 20 F21 X + 22Xy + 23XX + 24XXy + 25 X + 26XX yy +27 X3y +28X, + en
differennti
audo fit
y3
sit aequatio.
Xgy
yd ydy yydx
diffecea tialisdata 1 des + 12 X ly YT3 x dx + 14 XX dy + 15 X
12
Xy
iy ydx gdus. qydx
dy
gydy gyxex
sit aequatio differentialis Homoepplota data
yax
Sstay
100 dx + 110 Xdx + 101 X dy F 1IIXy dx 4 120XXdx + 102XXdy + 121 XXy dx + 112 XXydy + 139X dx + 103 Xdy + ey
dy
dy
yydy
y dy
ydx
yda
yydus Xyydx ydus yax
sit aequatio ordinaria assumta
200 + 210X + 21I Xy fl 220 Xx + 221 XXy + 230X + 222 XXyy + 231X27 + 240X, + et
Xyy
quam aequationem differentiando fiet
- 20 dx +A 22oXdu 2II XaG +, 221 pydx + eX
ily
2) dx + 22xdy 1 23Xdx + e4Xxdu +2. 24 X ydy + 25 XCdx +26. 2. XXydy L27. X du + G,. 3XXydx + 28 4 X dx , et
dy
dy
ydus ydx
dy
4y3
221 Xdy + 3. 231 XXydy F 2. U2 X KyL, + 25)OXd. F 31X dus
3. 230pp dx
gydu
gydx Kyydx
Xyyax yay Vx
O = 100 220=110 211=10) 221 =111:2 =102 230 = 120:3 231 =121:3 =103 222=112.2 240 =130:4
sit aequalio dydoi dz = ZZ + vv,: aa Fial Z = xty et v = xyi fiet dZ = dxtdy et do = xdytyax.
et habebimus xdus +ydx,: adxt du =9a (X X + 2Xy F gu) + xxyy: a, seu fiet
- axdus lgax  aaxX ax FaaXy dx + aagydx F XXyydx.
odx
da yy dy
dy
du aa xxdy
 210 = 220 =190 = 0 211 = 101 = - a 221 =111: 2= 2aa = aa quod est absurdum
coincidentia aequationi
Ergo ope aeqque. C et D tollatur au, fiet aequalio sine dus, ex, data =
Hoc in gentrali etiam reapse tentandum
Za= X R D: a = (dx:y Z. a = fag:u dv.: dque = dx: du = qu. six: B = qu sdy: y
vel salten ejus multiplae
v: a = y: X
XX
Z. a = (dy: y fiel X dy - yax: dy = yy + qu sdy, et fiet
X
dy) 2Z d(+): dys - 22 d3 = qu say unde pono
du
du ddZ = a() d-
dydus: yy
CX
y X
2u299 dZ - 22dd Z = 2 sdy dy
an
Et tollendo ay s
differenio differentiatem: qua abest a. Ponamus ab eadem
etam abesse simul assumi relatiorem inter X, y, dx, du,ddx, dt ys
vaerendus et modus problencam a curvae ex proprietate
Vangentium reduo cendi ad lineas positione datas quaesitam tangentes
l
0
Sax Snus
yay