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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 141r, page id 00068200:0283
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curvae generatricis, est illud in quo se datae curvae
perpendiculares secant.
van y.
IVLPNF
2V- N (y)
_
SiP
(P)
A 82P
si si1V. P = 2V. PB ppB(p
22
Ergo  1P - P  dp = dx. Si B, Si P - , B2 F
et loco (y) (P fiet:
5
∞+ dy
P+ ax
Z A Sip- dp + dx
jam S, P aequ. . ergo fiet
vel multiplicando per erucem.
127
2V2PH(p
1V2V dx
r7
1V. P - 2V2 P, .V2V+ 1 P P
(y) A V + dus.
y
3 + dus
B Sip- dx + x
p + dp
A P2- xt ax
pZ dus - dpy + dx y A ap Z)
fiet.
sie si jam faciamus  ex dp  dx id enim
aliquando ob arbitrariarum assumtionem fieri potest:
ax. sine y aequ
fiet du
sin faciamus 
de
sed missis assumtionibus arbihariis fier:
licet
d 2)-dus pZ H V ax -  ap.
 Z y, dx- dx
y 1
ap y - dy p
datur et Dq aequ 9.  et Q1V aequ. X.
VSp Vp - 5 P.
1Z
dx-ax y2
dps dyp
5 aequ QV - V5
Ergo QS p X - p + PE aequ BY
et fiet: X - 2Xp + 2X p Z + p - 2p Z + pr 2
du + ady-dy aqu. d
Nota BB
et dp p dy, dy y ds u
IX
P
quae postulat quadratarum hyperbolae
seu
en
ursus jungatur. DB quae est data et sit aequ. d.
Ix
du
2  F 9 +24743
. seu p H y dus
dx
jam ds dus adque-dx
fiet dx p dy + vdau - ydx
do
du I
dei
l
du dx + y daus - y dux
substitutisque vatoribus dx. p in ipsorum locum in da duabus H
aequationibus quibus valor ipsius Z explimitur, tolbi, tolli poterunt
Z et p. et solum supererunt X. y. de dgys. yadx. adqus.
compendii causa ponamus g+o, rrsus se quad + sit quad oqo B. P si
seu Z+
cus rebe  cigieus centro
b
u
sed spunet
ipsi 
BN
DF
D9+SB
cx a x
SB
1pa P p
Si P