Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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à centro G, æquè diſtant, erit EG, æqualis GF. </
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<
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>Dico
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portionis ABCD centrum grauitatis eſſe G. </
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<
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enim figura, vt ſupra fecimus, intelligantur duo coni re
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ctanguli GNO, GPQ, vertice G, communi, axibus
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autem eorum EG, GF: & cylindrus LM, portioni cir
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cumſcriptus circa eun
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dem axim EF, cuius ba
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ſis æqualis eſt circulo
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maximo: & ſumatur EH
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ipſius EG, pars quar
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ta, itemque FK, pars
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quarta ipſius FG. </
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<
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niam igitur conorum G
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NO, PGO, axes FG,
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GH, ſunt æquales, re
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liquæ KG, GH, æqua
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les erunt; centra autem grauitatis conorum ſunt K, H; pun
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ctum igitur G eſt centrum grauitatis compoſiti ex duobus
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conis æqualibus GNO, GPQ, hoc eſt reliqui ex cylin
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dro LM, dempta ABCD, portione, ex ante demonſtra
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tis: ſed idem G eſt centrum grauitatis totius cylindri LM;
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reliquæ igitur ABCD, portionis centrum grauitatis erit
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G. </
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<
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PROPOSITIO XL.
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<
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>Omnis portionis ſphæræ abſciſſæ duobus pla
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nis parallelis centrum intercipientibus, & à cen
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tro non æqualiter diſtantibus centrum grauitatis
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eſt in axe primum bifariam ſecto: Deinde ſumpta
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ad minorem baſim portionis quarta parte ſegmen
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ti axis, quod minorem baſim attingit: & ad maio-</
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