Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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liter igitur vt ante oſtenderemus, vnamquamque qua
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tuor pyramidum, quarum communis vertex S, baſes au
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tem triangula, quæ ſunt circa pyramidem ABCD, eſse
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quartam partem pyramidis ABCD. </
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<
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ctum S, cadat intra vnam priorum quatuor pyrami
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dum, ſiue in earum aliquo latere, ſeu triangulo; neceſ
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ſario erit pars æquali toti; tam enim tota vna pyramis
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quatuor priorum, quarum communis vertex F, quàm eius
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pars, vna quatuor pyramidum poſteriorum, quarum com
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munis vertex S, erit eiuſdem ABCD, pyramidis pars
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quarta. </
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>Ex abſurdo igitur non in alio puncto à puncto F
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ſecabunt ſe in eaſdem rationes quatuor rectæ, quæ ab angu
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lis ad oppoſita triangula pyramidis ABCD, ducantur.
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<
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>Manifeſtum eſt igitur propoſitum. </
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PROPOSITIO IX.
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<
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>Omnis pyramis baſim habens triangulam di
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uiditur in quatuor pyra mides æquales, & ſimiles
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inter ſe, & toti, & vnum octaedrum totius pyrami
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dis dimidium, ip ſi que concentricum. </
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<
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>Sit pyramis ABCD, cuius baſis triangulum ABC,
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ſectisque omnibus lateribus bifariam, iungantur rectæ FG,
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GH, HF, FK, KL, LM, M
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K
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, KH, HM, GL, LF.
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<
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>Dico quatuor pyramides DKLM, LFBG, KHFA,
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MHGC, æquales eſse, & ſimiles inter ſe, & toti pyrami
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di ABCD: octaedrum autem eſse LFGM
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K
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H, & di
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midium pyramidis ABCD, ipſique concentricum. </
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<
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cantur enim rectæ DNH, BQH, LN: & poſita BE, du
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pla ipſius BH, iungatur DOC, in triangulo DBH, &
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ponatur DP, ipſius PE, tripla, & connectantur rectæ LP,
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PH. </
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<
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>Quoniam igitur E, eſt centrum trianguli ABC, </
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