Valerio, Luca - De centro gravitatis solidorvm libri tres

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PROPOSITIO XXX.

Omnis octaedri idem eſt centrum grauitatis,
& figuræ.

Eſto octaedrum ABCDEF, cuius centrum G. Di
co G, eſse centrum grauitatis octaedri ABCDEF.
Ductis enim axibus AC, BD, EF, communis eorum
ſectio erit centrum G, in quo axes bifariam ſecabuntur:
omnium autem angulorum, qui ad G, bini qui que ad
verticem ſunt æquales, qui æqualibus altera alteri rectis
continentur; ſimilia igi
tur, & æqualia erunt trian
gula, nimirum EBG,
GDF, & ECG, ipſi
GFA, & BCG, ipſi
GDA: igitur & BCE,
ipſi ADF; pyramis igi
tur EBCG, ſimilis, &
æqualis eſt pyramidi A
DFG, quarum latera ho
mologa ſunt indirectum
inter ſe conſtituta; dua
rum igitur pyramidum

44[Figure 44]
EBCG, ADFG, ſimul centrum grauitatis erit G.
Eadem ratione ſex reliquarum pyramidum binis quibuſ
que oppoſitis ſimul ſumptis centrum grauitatis erit G.
Totius igitur octaedri ABCDEF, centrum grauitatis
erit G. Quod demonſtrandum erat.

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