Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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18939DE CENTRO GRAVIT. SOLID. dem, cuius baſis eſt quadratum a b c d, & altitudo e g: &
in pyramidem, cuius eadé baſis, altitudoq;
f g; ut ſint e g,
g f ſemidiametri ſphæræ, &
linea una. Cũigitur g ſit ſphæ-
ræ centrum, erit etiam centrum circuli, qui circa quadratũ
a b c d deſcribitur:
& propterea eiuſdem quadrati grauita
tis centrum:
quod in prima propoſitione huius demon-
ſtratum eſt.
quare pyramidis a b c d e axis erit e g: & pyra
midis a b c d f axis f g.
Itaque ſit h centrum grauitatis py-
ramidis a b c d e, &
pyramidis a b c d f centrum ſit _K_: per-
ſpicuum eſt ex uigeſima ſecunda propoſitione huius, lineã
e h triplam eſſe h g:

140[Figure 140] ponendoq;
e g ipſius g
h quadruplam.
& eadẽ
ratione f g quadruplã
ipſius g k.
quod cum e
g, g f ſintæquales, &
h
g, g _k_ neceſſario æqua-
les erunt.
ergo ex quar
ta propoſitione primi
libri Archimedis de cẽ-
tro grauitatis planorũ,
totius octahedri, quod
ex dictis pyramidibus
conſtat, centrum graui
tatis erit punctum g idem, quodipſius ſphæræ centrum.
Sit icoſahedrum a d deſcriptum in ſphæra, cuius centrū
ſit g.
Dico g ipſius icoſahedri grauitatis eſſe centrum. Si
enim ab angnlo a per g ducatur rectalinea uſque ad ſphæ
ræ ſuperficiem;
conſtat ex ſexta decima propoſitione libri
tertii decimi elementorum, cadere eam in angulum ipſi a
oppoſitum.
cadat in d: ſitq; una aliqua baſis icoſahedri tri-
angulum a b c:
& iunctæ b g, c g producantur, & cadant in
angulos e f, ipſis b c oppoſitos.
Itaque per triangula
a b c, d e f ducantur plana ſphæram ſecantia.
erunt hæ

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