Valerio, Luca, De centro gravitatis solidorvm libri tres

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1
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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