Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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pagenum
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73
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<
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>Sit pyramidis quadrilateram baſim habentis fruſtum
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ABCDEFGH, cuius axis KL, atque in ipſo centrum
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grauitatis O. </
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<
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>Dico axim KL, ſectum eſse in puncto O,
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vt propoſuimus. </
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<
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>Ductis enim AC, EG, quæ ſimilium
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ſectionum angulos æquales ſubtendant B, F, qui late
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ribus homologis continentur, fruſta erunt pyramidum
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triangulas baſes habentium AFG, AGH: ſit autem fru
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ſti AFG, axis
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TP, & in eo eiuſ
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dem fruſti cen
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trum grauitatis
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M, & fruſti AG
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H, axis VQ, &
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in eo centrum
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grauitatis N, &
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iungantur TV,
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MN,
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Quo
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niam igitur eſt
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pyramidis fru
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ſtum, quod pro
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ponitur; omnia
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cius producta latera concurrent in vno puncto, qui eſt pyra
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midis vertex: fruſta igitur, in quæ diuiſum eſt fruſtum pro
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poſitum earum ſunt pyramidum, quæ verticem habent
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communem cum pyramide, cuius eſt fruſtum propoſitum:
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tres igitur talium fruſtorum axes, vt pote ſegmenta axium
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trium prædictarum pyramidum in communi illo vertice
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concurrent: quilibet igitur duo trium prædictorum axium
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KL, TP, VQ, erunt in eodem plano: TP, igitur, &
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VQ, ſunt in eodem plano. </
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<
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>Eadem autem ratione, qua
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vtebamur de priſmate K, centrum grauitatis K, baſis
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EH, eſt in linea TV, & L, baſis BD, centrum grauita
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tis eſt in linea
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Pq;
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reliquæ igitur KL, MN, erunt in eo
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dem plano trapezij PTVQ, ſeque mutuo ſecabunt: cum </
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