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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 19
# Folio 5r, page id 00067981:0009
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ve quacum vero cuilibet puncto curvae
CC respondeat suum punctum, e nempe centrum maximi circuli curvam ineo
puncto intus tangentis, seu convedinem metientis, operae pretium erit
invesligare lineam centrorum, ED. Quod ex dictis non est difficile, exem
pli causa, fi in foctione conica, quin inverrimus esse,
7 aequ. X + p + 4p, seu Zaequ X +a + ax  q +X
unde compendii ausa +a +q vocendo b et 29 +a vocando R
fiet Zaequi LX + b. seu xaqu 29, bg
seu  xaqu. 4Z- Bq. b)
Et quia supra diximus esse vaequ Zy- xy -y.
a + ax
- q
erit
seu vaequ 27 4Z744b7
Yaequ. av fiet y aequ. va Faez p + a bv
1b - a-
 intor tatunc ut
a + 4Z
a
as
sed tevx
t2bC
et compendii causa pro a   b scribendo f et pro h- 4+ a scribendo g.
et pro  b -f scribendo 1. fint y aequ  ZV + f0. 97 + l
Et inventos valores literarum X et  substituendo in aequatione ad
Conicam: X rax +q X aequ gy. fint 2247 - 2agb, + 949 + 2a9 bZ + 49 bb aequ. . .
h hht
aeu aaque vo t 2at zun +5fiv,: 9977 4 2.q  I
1h
ht
ht
quae est aequalio ad curvam EG
si conicassestio esset parabola, fieret a aequ. 8. et baequ 4 g. et haequ. 29 et fag.
et faequ.q et aequ. 9 et et laequ. +:9
et ficret 2Z + a4 + _ f aqu aequ.
 aZ + a4 f a
yy
a Z + aq aequ. -aa ZZ vV  Z3
aqat E
44
Y: Z- x p.: y. p
ent vigu FCu 17 7
si curva sit par ACC sit pambola erit AF seu Z aequ x+ta seu xaequ Z a
erit _ PF ad BP seu ad _ a. ut 
In genere curvedinem cujuscunque sectimis Coniaem sis inveniemus Ducatur pen
seu gy tpo +ov, ZZ 2ZX - ZP exX + 2xp+ pp equ e. qui quia dp aequ. + a dx
fiat diferentialis aequatio 3 A7+ vause d Zdx +Z ax p X AX f a xAX Aa Xx + adx + xrq eadxaqo
q  B  1
ydy + vdu q dx +22 tx 1 ad axx par f a p dx aeguro et quia veram repy
fiet x. du  2 ∞3: 
11a
tiet Z.x aequ Z.x p + Z xap g. seu ap + p +x aequZ
seu gy 129V+ ro + ZZ 2ZX + XX aequ. el. seu cujus differentialis yy + vdqus 
 ydy tVdy  1Zlx + xdx aeq e ( Cyes se axel y rrez X : 3 g. p.
Et quia ob Triangula PFE, PBC similia FE ad pF seu vadze X.p. ut BC ad pF seu ut y ad p
fiet pV aequ Zy = xy - py. seu y tv+ y:: ZX.. p. Et pro p ponendor valorem
a + ax firt. a0 43xv ay +GYV aequ. Ly x cujus aequationis aequalio
differentialis est + avem tadu fantus aequ Zdy- x 4- ydy. seu Ret
a dx: du in Y 247  y a 1 ap: x f 2 B At supra Lx dy 1. y: a + ax
tiet za ya vaa  aa v + a Z  + a xu faa x - aa vx aequ xy t a ry
q9
seu p B+y aequ y. Z. X. et Es autem p aequ a + ax et dp aequ = a ax fiet
deidys.
:
P dy + a dx vty aego Z. X dy  ydx at  dx aerio Zp Ergo firt: 
YY P + G q vry aequ Z. X = 978. ab Ergo paulo ante Y +y aego Y q. X.
Ego per p + 3 v27