Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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portionis circulus, cuius diameter AC, & vt EG ad GF,
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ita ſit GF ad S, & S ad FM, cuius ſit pars tertia FN, &
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ponatur ipſius BG, ſubſeſquialtera GL. </
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<
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>Dico portio
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nem ABC ad cylindrum KH eſse vt LN ad BF. </
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>Nam
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vt FG ad GE, ſiue ad BG, ita ſit EG ad PQ, à qua
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abſcindatur QR, pars tertia ipſius FG. </
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<
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>Et plano per G
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tranſeunte baſibus cylindri KH, & ABC portionis pa
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rallelo ſecentur vna cylindrus KH in duos cylindros DH,
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EK: & portio ABC, in portionem ECAD, & DBE
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hemiſphærium. </
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<
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>Quoniam igitur eſt conuertendo, vt PQ
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ad EG, ita EG
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ad GF, & eſt ip
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ſius GF pars ter
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tia QR, erit por
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tio DACE ad
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cylindrum EK,
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vt PR ad
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Rurſus, quia eſt
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vt EG ad GF:
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hoc eſt vt PQ ad
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EG, ita GF ad
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S, & vt EG ad
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GF, ita eſt S ad
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FM; erit ex æqua
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li, vt PQ ad GF, ita GF ad FM. </
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<
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>Sed vt GF ad RQ,
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ita eſt MF ad FN, tertiam ipſius MF partem, ex æquali
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igitur erit vt PQ ad QR, ita GF ad FN, & per conuer
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ſionem rationis, & conuertendo, vt PR ad PQ, ita NG ad
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GF. </
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>Sed vt PR ad PQ, ita erat portio ECAD ad cy
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lindrum EK; vtigitur NG ad GF, ita erit portio EC
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AD ad cylindrum EK. </
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<
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>Sed vt GF ad FB, ita eſt cy
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lindrus EK ad cylindrum KH: ex æquali igitur vt NG
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ad BF, ita portio ECAD, ad cylindrum KH. </
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<
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oſtenderemus eſse, vt GL ad BF, ita DBE hemiſphæ-</
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