Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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14416FED. COMMANDINI
SIT pyramis, cuius baſis triangulum a b c; axis d e: &
ſecetur
plano baſi æquidiſtante;
quod ſectionẽ faciat f g h;
occurratq; axi in puncto k. Dico f g h triangulum eſſe, ipſi
a
b c ſimile;
cuius grauitatis centrum eſt K. Quoniã enim
1116. unde
cimi
duo plana æquidiſtantia a b c, f g h ſecantur à plano a b d;
communes eorum ſectiones a b, f g æquidiſtantes erunt: &
eadem
ratione æquidiſtantes ipſæ b c, g h:
& c a, h f. Quòd
cum
duæ lineæ f g, g h, duabus a b, b c æquidiſtent, nec
ſintin
eodem plano;
angulus ad g æqualis eſt angulo ad
2210. undeci
mi
.
b:
& ſimiliter angulus ad h angulo ad c: angulusq; ad f ei,
qui
ad a eſt æqualis.
triangulum igitur f g h ſimile eſt tri-
angulo
a b c.
At uero punctum k centrum eſſe grauita-
tis
trianguli f g h hoc modo oſtendemus.
Ducantur pla-
na
per axem, &
per lineas d a, d b, d c: erunt communes ſe-
3316. unde-
cimi
ctiones f K, a e æquidiſtantes:
pariterq; k g, e b; & k h, e c:
quare angulus k f h angulo e a c; & angulus k f g ipſi e a b
4410. unde-
cimi
eſt æqualis.
Eadem ratione
98[Figure 98] anguli ad g angulis ad b:
&
anguli
ad h iis, qui ad c æ-
quales
erunt.
ergo puncta
e
_K_ in triangulis a b c, f g h
ſimiliter
ſunt poſita, per ſe-
xtam
poſitionem Archime-
dis
in libro de centro graui-
tatis
planorum.
Sed cum e
ſit
centrum grauitatis trian
guli
a b c, erit ex undecíma
propoſitione
eiuſdem libri,
&
K trianguli f g h grauita
tis
centrum.
id quod demonſtrare oportebat. Non aliter
in
ceteris pyramidibus, quod propoſitum eſt demonſtra-
bitur
.

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