Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ipſius OR; ſed & AO erat dupla ipſius OR; æqualis
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igitur AO erit ipſi ON. quare vt AK, ad KD, ita erit
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AO, ad ON: igitur in triangulo ADN, erit KO, ipſi
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DN, parallela. </
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<
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>Eadem ratione ſi iungerentur rectæ BH,
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CF oſtenderemus & duos reliquos axes LP, MQ, eſ
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ſe axi DN parallelos: quatuor autem prædicti axes in
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ſiſtunt plano trianguli KLM, ita vt DN tranſeat per
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centrum S: reliqui autem KO, LP, MQ, terminentur
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ad angulorum vertices K, L, M, trianguli KLM; igi
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tur ſi tres æquales magnitudines habeant centra grauita
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tis in axibus KO, LP,
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<
expan
abbr
="
Mq;
">Mque</
expan
>
compoſiti ex ijs
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tribus magnitudinibus
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in axe DN erit
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expan
abbr
="
centrũ
">centrum</
expan
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grauitatis. </
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<
s
>Rurſus
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quoniam E ponitur
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cẽ
">cem</
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trũ
">trum</
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pyramidis ABCD,
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erit idem E centrum
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octaedri FGHKLM,
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idque in axe DN: eſt
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lb
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autem idem
<
expan
abbr
="
centrũ
">centrum</
expan
>
gra
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lb
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uitatis octaedri, & figu
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ræ: centrum igitur E
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octaedri FCHKLM
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erit in axe DN. </
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>
<
s
>Quod
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ſi quatuor reliquæ pyramides dempto prædicto octaedro
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ſimiliter diuidantur, ac pyramis ABCD diuiſa fuit, erunt
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rurſus in ſingulis quatuor prædictarum pyramidum ſin
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gula octaedra centrum grauitatis habentia vnumquodque
<
lb
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in axe ſuæ pyramidis: quæ pyramides cum ſint inter ſe
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æquales, earum dimidia octaedr a ipſis inſcripta inter ſe
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erunt æqualia: ſunt autem eorum centra grauitatis in axi
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bus abſciſsarum pyramidum, DS, KO, LP, MQ
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axis autem DS: eſt in axe DN; per ea igitur, quæ de-</
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