Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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ad centrum circuli tranſeuntis per tria puncta K, L, M, quod
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ſit R, ducatur recta AR, & ER iungatur. </
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tur æquales rectæ ſunt AK, AL, AM, quæ ex puncto
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A, in ſublimi pertinent ad ſubiectum planum: & punctum
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R, eſt centrum circuli tranſeuntis per puncta N, O, P; cadet
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recta AR ad ſubiectum planum perpendicularis. </
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ratione recta ER ducta à vertice E, pyramidis ENOP,
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ad centrum R, circuli tranſeuntis per puncta N, O, P, hoc
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eſt, per puncta K, L, M, illis congruentia, cadet ad idem
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planum, ad quod linea AR, perpendicularis; itaque ab
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eodem puncto R, ad idem planum, & ad eaſdem partes duæ
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perpendiculares erunt excitatæ, quod fieri non poteſt:
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punctum igitur E non cadet extra punctum A: quare la
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tus EN, congruet lateri AK, quorum EF, eſt æqualis
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AK; igitur & EF, ipſi AB, congruet. </
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tus AG, congruet lateri AC, & latus EH, lateri AD, &
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triangula triangulis, & pyramis EFGH, pyramidi ABC
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D, & ipſi æqualis erit. </
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COROLLARIVM.
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<
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>Hinc facile colligitur omnia ſolida, quæ in py
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ramides æqualibus, & ſimilibus triangulis com
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prehenſas multitudine æquales diuidi poſſunt, eſ
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ſe inter ſe æqualia. </
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>Quocirca omnia priſmata, &
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pyramides, & octahedra, omnia denique corpora
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regularia æqualibus, & ſimilibus planis compre
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henſa inter ſe æqualia erunt. </
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PROPOSITIO VIII.
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<
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>Omnis pyramidis triangulam baſim habentis
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quatuor axes ſecant ſe in vno puncto in eaſdem ra</
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