Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. 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
16. 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
10. 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-
16. 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
10. unde-
cimi
eſt æqualis.
Eadem ratione
Figure: /permanent/library/4E7V2WGH/figures/0144-01 not scanned
[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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