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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folio 29v, page id 00068073:0058
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Hinc quia
2
Sy dx dx aego X sydx- syax  per aequ. 2
et xydx aequ. est 2 X) = 2 Sxxdy. per aequ. 1. hinc fiet
Sydx dx aequ. X Sydx - L XX y + L sxx dus
si detur reratio inter momentum Trilinei ABC ex AB, et ex
vebitur linea in quam cadit necessario centrum gravitatis iiclinei
e v.y.
et inter
s
Eit cognita reratio inter sxy dx et inter  syydx
Cydxan.
1
quae si esset constans foret:
a Syydx aequossydxdx seu ayysdxogo b sy dx (dx et rursus
fiet 24y dys aequoy dx. Ergo ay aego bx
sci si haberetur Ssy axax itemque sy dx
idem est si habeatur relatio inter Sxydo et inter yydu
Multo magis hoc dicendum
Quando habentur haec mor
menta, ut in Hyperbola bubi xy aequaa RCb
et faciendo
Bxy dx aequ aax et syyax aequ)a dx seu
AB sit a.
ax 
a+X, y aequ ag seu ay +xy aequaa
aa XX aego gy. fiet aX + bxX aquyy. pet
syy dx aego = axx + 1 bx3. datur
ergo momentum Hyperbolae ex
axe AB. Pu X faciamus Z+ 9.
tret aZ + aq +bZZ + 269Z + 99 aequ’yy
aZ + 269Z aqu. 0. fiet: qaequa et habebinus.
aa + aa
26 4bb
s
ib
2b
crbarnus ee +bZZ aquyg. erit 8: 27dy cenu seedus +yydy
seu momentum ipsius AEFCA ex EF est- P ecy +81
10
eb
5b
13
2b b
yy de erit aequ 9 L eedque + = b73d. Et Nomentom
ipsius AB, exAB 
 etZ + fb23C
EC
Momentum ipsius BF
x AB est EF est: 173y a qua si an feratur Momentum ipsius AEFCA e
e
exEF habebitur 1779 - 2 eey + es. Phomentum ipsius ABC ex Ex
L
20
possumus ergo semper rectam ducere in quam cadat centrum oravitatis
portionis Hyperbolices ABC. Nam sis id certiu esset L. foret EM adma ut B ad e