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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folio 30r, page id 00068073:0059
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Merae pretium pam erit investigare carvam Centrorum gravitatis
Hyperbolae, vel saltem curvam pro momentis unius parlis
e
E, itomentum ipsius ABC ex AF est Xy dx seu erib
X5y
Sx Sax+bX d quod divisum per aretum pen
per Suaxiberdo dat  FN ditantiar centri
gravitalis ab AF Eg  Sed quia FNquaeu
tur potius ex AF seu Y, ideo retineamus potius y est
cem: adx + 2bx dx oqu 2y dy. Ergo fit
ax aequi
et dx aequ
c
2y di et fiet FNaequ.
V et
a +2bX
a. et Z0qu Syy- ee seuerit; orZyy- ee
2b
2y dy
(a) + 2b7 a
et fiet FN seu n aequ 
Ep N selte aequ  yy dy- 4
266
seut Naeqo Z
3a5 y7a7
Cydus
62
d 
e
2b
+a+ = yy-ee
syydis
dy, 0F.
X
it
a seu GNaequn. aequ
2b
7
3asy7dy
5y7
a
2b62
est autem Z aequ St ys ee quod alaequemus quadrato, seu faciomus valorem
b
3
yydy + Y dn
seu Lar pyydus aeqo Y. Eratque: 5ydY aeqo L
3an
an
ann
descrbatur adc una curva AP. et cum ea procedatu: eodem modo
et faciendo BPaequ r. habebitur taudem relatio. Inter  et g.
Qua habila ut veniatur ad veterminationem sumatur
fix
ar aequalis cuidam quantitati.  compositae ex Z. y. n. Y, ut invet.
dx. Daequ. r.
C
(3
az
4).
de aeque
et ope aequationum 2 1. et2. habebitur ad huc semel an
et aequationes 3 et 4 aquando habebitur aequatto contriens solum ay. dy. _ yg. Y.n
dn
sublatis ar. du. Jam datur ralatio inter dy dy. ex natura curvae tempe de
or
 y
ego
bZ
dus L
V. Z. Y. n. ubi ope aequalionis Lee + b3Z aqu. yy et ope aequ n aequ 2 Collentur 3. et Y
 dy C
ex aqu. 7. remanebitque aequatio habens solum literas y et n. habetur ergo n ex datays
(10)
in hoc casu speciali id est quaesitum.
aequationes sidenticae. Momentu isit
 id unum verendum ne prodeant C
centemus Momentu ipsius ABC ex AB est C
erit Bp aequ. C. sel aego r. fiet, d ago sydx. seu YaCde aeqo dx. seudxrredra dx
ua t eter
rd) -rr 2t ita porro placet calculum ub solvere.
L ai