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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 28v, page id 00068022:0056
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fiet: (quaeramque surita AH pro absussa at DB pro ordinata, equaeramus 
D7 pro intervallo langentis quam vocibim .  nempe fiei Xa7 saque V fXA
a
sive A; hujus aegreationis pricti junctae ope tollamus
X +) terminum Z. dempe primum qu, pro 4q2, substituendo ejus
62 sive
diva
volorem ex priore, qui est. X - 2a7. 1 0 fiet:  (a Z) + x (aZ B Xd. et eris
ZY X = X 2, et 32
aequatione substitati fiet:
214Y - 2a+ =  X + 24 X A - f H A2 qua
X
aequatione exprimitur, valor ipsius A. aequatione tati: 2 a x - 2 ad = X + 2 X A - xd aX
itam effeciem sed revius forte ita rem obtinebi my
Z2
= 26Z + b B b - x et +Z + b p, 5b- X, et ZH + A  + b
 pro Z fuestitucudo X suestituendo X +(B. fier: Z F propima Z p f S62 . 1. B a
auferatur illa ab hac, fei: + Nb2= XE = 2∞ - p)
1b- , B () unde
+ b2 - X) - 2x B - B2 - 2 (b. - p - 2 2  - (  br =  ( bZ ∞)  W
sive b 112 + 2+ B ( B,  b   2 +( b2= X. sive.
WW4 + 4Xβ V + 4 N B
64 - 2 
262 - 2X V = 2 xB = 1.   WV2.sive:
26 - 2X = 2yβB = W p 2F.. et quadrando utribique
4b 2 b X - ob x B - 4b.u2
e
(-8b X  4X +). -8b 3X + A8 X B.. e  quod si jam
addatur ad W. addatuo β, Tadix summae reprae sentabit etiam crementa
llipseosi sed haec quoque compositiora quam velim.
exitu, quia ibi A habetur jura
ope tamen ipsius A facilius habetur
satius ergo erit ad raligus propedi aequationes. Sumamus scilicet aquationem. 6- bx t.
et quaeramus EA  3. e HX, ponendo AH, BX prfordinata; et  D pY pro
absca nempe fiet, - Yb Xh p Fy, et
BT W
b- b
hp-
Xu a X, sui W  (t x
62- b 22
addatur (, et producti radixo fiet:
figurae
Y6-LX
bg2 = b 7
E42
b--
ejus quadrato
lX b
superest ergo ut hujus curvae dinrensionem tentemus b aX2
Nimirum aequatio fit:
b2XV + b- b
ficit
250 g0
6- 2 42
Hinus figuiae momenta g habentur ex quadratum Hyperbolae. Ejesdem  etiam
habertur ex quadilum Hyperbotae fit enim g 
quae pendet ex quad. Hyp. At 
br -
vel inculi si
8) fit pus
aua est quantitas
bqu
-k +E9)
hyperbolae si negativa. duo ergo as
curvae harus momente habemus rum figmae ipsarum 9t
fiet: mno mentam omnum g ex vert
summae ipsem _ X, d cinquiu fier:
b2 X B = bx
e
puncto ultra vrtieri
BX
1∞~- BXVF 1.
quae pendent ex quad.
ducantur 9 in b + xb
versus vesticem, Bmmetum
aux. + b + XI Cb - X B
Curva Hypeib olicae homogene homogenea est hoecfinura. Sa + 
XS
postenor similis facile reddi potest homageneae curvea Ellisti . dividendo per d. cognitam:
Elementa curoa Hypertalicae ex posteriore etiam sic enuntiari possunt.
1X
ai H 1 +
per partes.
in nfinutus facilimus ita +
∞7 1 +
2Z+
v
Item haeci Sex +a quae
Si.
(1.
a+X
a taa Uurur si licet extractione
er  sed ut prgessio frat