Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO XXX.
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<
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>Omnis octaedri idem eſt centrum grauitatis,
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& figuræ. </
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<
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>Eſto octaedrum ABCDEF, cuius centrum G. </
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<
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>Di
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co G, eſse centrum grauitatis octaedri ABCDEF.
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<
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>Ductis enim axibus AC, BD, EF, communis eorum
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ſectio erit centrum G, in quo axes bifariam ſecabuntur:
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omnium autem angulorum, qui ad G, bini qui que ad
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verticem ſunt æquales, qui æqualibus altera alteri rectis
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continentur; ſimilia igi
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tur, & æqualia erunt trian
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gula, nimirum EBG,
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GDF, & ECG, ipſi
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GFA, & BCG, ipſi
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GDA: igitur & BCE,
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ipſi ADF; pyramis igi
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tur EBCG, ſimilis, &
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æqualis eſt pyramidi A
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DFG, quarum latera ho
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mologa ſunt indirectum
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inter ſe conſtituta; dua
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rum igitur pyramidum
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EBCG, ADFG, ſimul centrum grauitatis erit G.
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<
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>Eadem ratione ſex reliquarum pyramidum binis quibuſ
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que oppoſitis ſimul ſumptis centrum grauitatis erit G.
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<
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>Totius igitur octaedri ABCDEF, centrum grauitatis
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erit G. </
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<
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>Quod demonſtrandum erat. </
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