Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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16929DE CENTRO GRAVIT. SOLID. l h eandem habet proportionem, quam e m ad m k, uideli-
cet triplam.
quare linea l m ipſam e f ſecabit in puncto g:
etenim e g ad g f eſt, ut el ad l h. præterea quoniam h k, l m
æquidiſtant, erunt triangula h e f, l e g ſimilia:
itemq; inter
ſe ſimilia f e k, g e m:
& ut e fad e g, ita h fad l g: & ita f _K_ ad
g m.
ergo uth fadlg, ita f k ad g m: & permutando uth f
ad f _K_, ita l g ad g m.
ſed cum h ſit centrum trianguli a b d;
&
K triãguli b c d: punctũ uero f totius quadrilateri a b c d
centrum:
erit ex 8. Archimedis de centro grauitatis plano
rum h fad f K, ut triangulum b c d ad triangulum a b d:
ut
autem b c d triangulum ad triangulum a b d, ita pyramis
b c d e ad pyramidem a b d e.
ergo
124[Figure 124] linea lg ad g m erit, ut pyramis
b c d e ad pyramidé a b d e.
ex quo
ſequitur, ut totius pyramidis
a b c d e punctum g ſit grauitatis
centrum.
Rurſus ſit pyramis ba-
ſim habens pentagonum a b c d e:
& axem f g: diuidaturq; axis in pũ
cto h, ita ut fh ad h g triplam habe
at proportionem.
Dico h grauita-
tis centrũ eſſe pyramidis a b c d e f.

iungatur enim e b:
intelligaturq;
pyramis, cuius uertex f, &
baſis
triangulum a b e:
& alia pyramis
intelligatur eundem uerticem ha-
bens, &
baſim b c d e quadrilaterũ:
ſit autem pyramidis a b e faxis f K,
&
grauitatis centrum l: & pyrami
dis b c d e faxis f m, &
centrum gra
uitatis n:
iunganturq; K m, l n;
quæ per puncta g h tranſibunt.

Rurſus eodem modo, quo ſup ra,
demonſtrabimus lineas K g m, l h n ſibiipſis æ

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