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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 5 (shelfmark Lh 35, 5, 5)
# Folio 1v, page id 00068023:0002
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rax+ + 1 + 1 Z. Et pro circul quidem
pro Erculo aut Hyperbola Ciculari fit. 
2aXFX
1
a
cli Curvae a (ircularis ducendo in ejus distantiam a diametro, seu in rax-x, fit
a sive a. ac proinde habetur superficies circa diametium. Ducatur in X, f
ea -X NC qua unde a X p 2ac0 = XCd
raco
distantiam a vertice, fiet a fX
cujus quadratura pendet a Quadratura Circuli, ac proinde: X 
v
a + cor
At p Elementr Hyerbola, Curvae Hyperbolie
est ad figuram
ducendo in erus
sinum, fit. a + AaX + 2X, quo est cujus propessio est ad aliam Nyperbolam, etiam
circulo symmetram.
latera rectum transversumque, aequalia habentem. si duus in sinu X, fiet. Pax a
2a +X
Unde patet nihil fere habere o hic quidem Hyperbolum cam simplicem in quo emineat prae
composita Si Elementum Hyperbolae vel Eltia sis ducatur in vidinatam, fiet.
a + a 5 2ax + qx 4 2ax + a X, quae progressio est ad Hyperbolam pro Hyperbola
ad Elliphui pro Ellipsi. vel Ellipsin, ita scilicet ut sit semper ad Hyperbolam, quando curva
est Hyperbola, sed quando curva est Ellipsis tunc distinguendum est, nam si +a
2
= a 4
est quantitas affirmativa seu quando a, major quam 9 latus rectum quam transversum, aequatio
est ad Elliosin, sin contra ad Hyperbolam, sii contra ad Ellissim se ad Ellipsin.
etur ergo centrum gravitalis curvae Ellipticae ex supposita circuli et Hyperbolae quadratura
eaudem Elysui  curvam Ellipsicam modo minorm modo ad majore axem referendo
tam eundem calculum resumemus, ponendo aequatitarm ad Conicam esse:
sidine
d qua est ad Ellipsim vel Hyperbolam,
, a y
a repo b=LI 1a 4
et Circulum, parabola et recta exclusa
qu + a q0
Unde
9 2
+2Zβ +β differentia.
8
rende transponendo:
s
et quadrando (ad (4 ac
11
EC
v
fier: proxime major ordinata:
2. 1204- sar age 
  ..+... +...
r
(  a70) +  + 2yβ Y arp a gr + 3 6
e
6
 Y 1 aet aya vel quadando
k
et destructis destruendis, atque ordinando: fa
qu saetq Hujus ergo figurae veneraliter habetur quadratura. Ejus quadratum
at
quadrato ab a, et addatur, fiet:  + a unde radio: a a 7 q
a
3 
Unde
adq aqu
4
Z
Sed jam praevideo quod nihil hinc
Elementum Curvae Hyperbolicae vel Ellipticae.
novi, magni momenti ultra calculum priorem; tantum ob circulum patebit: Z
9L
E
 unde GL G GCGW, quod
W0
a 497
v
GC 1 BG
circuli quadratura pendere
ex
demonstrat summam omnium perpendicularum aequari momento curvae
ex axe AB., at GL⊓ SC∞GW
Aestimemus valorem ipsius GC in Elli Hyprtat. G fiet 16 a X + a,  fra2rEA
sive a X + 2a X + a + 2aX + a X, quae figura pentet ex est
Hyperbola
porro Z
79 - 9 + a
rpq)
X+a ⊓ qu X + 24 X 44 _ autem ay 24) X + X + G 3 
sa y
+ at
 e
GH
+2ofer. X + Syqu q
GH.
cun e, s hl pedet à cetu gruntes treuto