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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 38r, page id 00068194:0075
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LH 25, 12, 1
Bisectio Hyperbolae, ope Hypeoctaends (abreae quia cylindem Hypetolicae est mo-
mentum Hyperboloeidis Cubit, lina ergo seu momentm ejus ex basi, Ergo distantia
centri Gravitatis ejus aHyperbolveidis ab axe, quaehaberi pt ypol
Hypeibolae cylindium biseeat.
a = xy. idio yx y - a c YX - a  = X - aB
e
7 =
a = xy.. Ergo a - y, et 4 y. MX - xy a a
7
a
a
BC
asm dn quaeratura hypertoloeclis rubica ) Nam Et quia summa omntum
ad basin Tummaeomnium xy ad axem. seu vibus a, ad axem Hinc quadratumr
ult.
aGX. Ergo quadruta omnium es seu summa orumys = a. Eyl. Hyp. Quadrato omnium X est:
hypeibololidis uebicae a=yax
X= a hinccylinda Hyperbolocedis. , ∞ a5- yx. porro quadrata omnum
Y quae basi parallet, aequntu ad allitudinem, aequantus quadra omnibus
in y. ad abtit basin. a. Ergo summa omnim a ad alt. Homn. a ad bosm
Contra X in y. ad altit. quin y = sa erit yx- saX; aequantur
aequalis.
scilicet oibus X ad basin Hinc quadratura cylindri Hyper
voloeidis a= Y X
a = yX. Hinc a= X (Glinde hyperbolocidis a- y X) ad ast.
F = Xy = a 1, Xseu aX, sOH s seu cylinde Huptato
locidis, cujus X aequatio aX = y
Mt y a YS Cylinde hyprtolocidis cujus aequato y 2 a sei
YXa ali. Sdcu cum XCY adbas. ser a- yX. Cylin.
der Hyperbolvendis a = yX.
Hac melhod. quadrari possunt Hyperbolocides in unversum
omnes.
ota