Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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monſtrauimus trium octaedrorum, quæ ſunt in pyrami
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dibus AFHK, FBGL, GHOM ſimul, centrum gra
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uitatis erit in axe D
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K
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: ſed & octaedri in pyramide DK
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LM, & octaedri FGHKLM centra grauitatis ſunt
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in axe DN; omnium igitur quinque octaedrorum, quæ
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ſunt in tota pyramide ABCD ſimul centrum grauitatis
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eſt in axe DN. </
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>Quod ſi rurſus in ſingulis quatuor præ
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dictarum pyramidum modo dicta ratione quina octaedra
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deſcripta intelligantur, ſimiliter oſtenſum erit quina octa
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edra in ſingulis quatuor abſciſſarum pyramidum, velut
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quatuor magnitudines, centra grauitatis habere in axibus
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quatuor prædictarum pyramidum: ſunt autem hæc qua
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tuor compoſita ex quinis octaedris inter ſe æqualia, pro
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pter æqualitatem octaedrorum multitudine æqualium,
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quæ æqualibus ſunt pyramidibus ipſorum duplis ord ine
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diuiſionis inter ſe reſpondentibus inſcripta; igitur vt ante,
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quater quinorum octaedrorum ſimul in axe DN erit
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centrum grauitatis: ſed & octaedri FGHKLM centrum
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grauitatis eſt in axe DN; vnius igitur & viginti octae
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drorum in pyramide ABCD exiſtentium ex hac ſecun
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da diuiſione, tanquàm vnius magnitudinis in axe DN erit
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centrum grauitatis. </
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<
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>Ab hoc igitur numero vnius & vi
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ginti octaedrorum in pyramide ABCD exiſtentium, ſi
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mili diuiſione illius reliquarum quatuor pyramidum primo
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abſciſſarum procedentes, & eundem ſemper gyrum, quem
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fecimus à quinario repetentes, poterunt eſse in tota AB
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CD pyramide tot, quemadmodum diximus, deſcripta,
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octaedra, vt eorum numerus ſuperet quemcumque propo
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ſitum numerum, & omnium tanquàm vnius magnitudinis
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in axe DN, ſit centrum grauitatis. </
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<
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>Sic autem facienti, &
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reliquarum pyramidum demptis præcedentibus octaedris,
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dimidia octaedra ſemper auferenti, tandem relinquen
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tur pyramides minores ſimul ſumptæ quantacumque
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magnitudine propoſita. </
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<
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>Totius igitur pyramidis ABCD </
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