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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 27
# Folio 14r, page id 00068072:0027
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Hare aequationem Tangentialem alibi brevius solvi
aydys+ e B d) = q e a
axax
ax
X
  X
a
sit ej: a = f ddZ: dZ et s: a = Sadz. do et dy: dx = dv: d2
fiet dydo B a = Ds dd
deaz Ca
aZ
+ Cdd2. et differentiando fit
.
au
e 2dZ a2 dvddv- avdvdzue ddze, +B did cd v -  Bd7dzu d vdaz
detZ di4
aequ. DddZ + s ddze unde fiet
de
au
dazdvdv 2fd VdZ adque + ABd dvadx - 4 BdZa dBdo dazue - dedo + n 1E 7
sit B = 0, fet et ddv20 firit v = OV, d d+ 3 d37. sed
ita de:du corstans, ergo et dy: dx. quod absurdum
sincido muneat, fit 2 dtaF 2dZdxado - 2 dp adzue = B dzdu dxd
ao
Ra)3adZ
dd ddv 2ddZ = Ed v3 + Od2dZ dv + X d33.: 2d2 doax 
seu d.x iddue X 2 d v: AZ + B. dz: dv + X d7dz: dudo
gade aos =  dx + B de + A,i dpdo = rel (dv: dz)
d.1Z
a2B.
sit addque
d73
L devidu
ret (V. dq) - (d n idZ)
sit du.dze = +:a fiet m
Cadz
a
et
e
2b
earra
oa
hba
l ae
azaz
a (av: d2) dudv. dz d3
9
4
 2(Hdt
fiet (adZ = B D2 (99 +2912: D) a + (1): C0) aa
seu (
d
daas ee q
u de
Baa (ddz = = 99 + 21 a9 + 13 aa (de
2 S
bBC
49 + 24 aq B: aa = log (4
logsd.
2
Daat a Baao Bt-ga
sit Bt - a = G et t = 9+  (r: B) a
ddz
seu1
e
8.2
+ 0.2)
A2: 6d sed logdz = y:a et av: dz Lg: d
9-
et hoc loco du.  sed  = F: a = (9: 4) + A: D
sed hot loco dv: dz = dg: dx = relf: a; yia) ergo qu re
e
es
ergo q= ret ) vel (X:a; yaa) a.D. Ergo hic valor proq
g.a pro FdaZidze substituatur in aeq. Cd et habebitur
et
relatio inter Cx,7, a