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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 65r, page id 00068200:0131
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de evolutione curvarum
Ellipacae et Hyperboneae
didem sio curvae carice
s rduct ejsegeram raterenaleer
oc nl
Erbenverticem i axem VB
sit curva conica VDE centrum habens  (Elliptica fig. L. Hyperbolica fig. 2)
firmumi tencatur alicubi ut
si
circumligetur ei filum, idque  sti in E, liberum in V. atque  ita evolvatur
et extendatur, in eodem semper cum curva plano, ita ut  extremi liberi mota
describatur curva VF. manifestum est durante descriptione filum describens in rectam
extensum, ut LF aequale esse arui evoluto V; ipsam autem fitum extensum DF
semper tangere cutvam evolutam V in D et perpendiculariter occurrere curvae
volutione descriptae VF in F.  jam ex puncto F demittatur in axem
perpendicularis FG. quae erit curvae VF ordinata. denique ipsa H LF prodncatur
lum axi occurrat in p.
sit currae conicae triangulum Characteristicum
GWL. currae triangulum characteristicum FDH. Manifestum est haec duo
Triangula esse similia. seu GW: WL: GL:: FD: DH: FH. sunt
autem jam sit CB aqo  Y. Et BW, y. et (G sit Z et GF sit v.
erit GW aequ dx. et. N L aego dus, et FD aequ de et D Hequ. dz.
Ergo fier A x: dus s:; do: dz sive dx aequ do
ut
dus
d
Ex unius puncto curvae puncto ducatur perpendicularis, ad alterius ordinatam Bt
est FM aequ = C B + CB, seu =X + Z.
seu ML aequ
et fiet:
pursus
+X
c
=X
=
v.
erit F: ML: i GW: W : FD: FH
itemque ML aequ +) BL (+) GFa
2 aequ = aequ =. Ergo = x dus  = Z aqs aequ (4) y ax 4) v ax
Y(+)v
dX
=Z 1C (4) ay (+) do
Ay
dn
az
av aequ (= x
= Y (F)v, c+ x f tque
FR N y2+ v (+) 2yV aqu
)du 1dv ac, F at
- = tx
1
Ix
aequ
itu 
Fx +Z. x eibus
d
(By) y uqu.
Tex dus- au aequ 
aus
ax
qu. 
l