Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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tij ad quartum, & ſic ſemper deinceps vſque ad vltimum
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XF (duplicatæ enim ſunt talium cylindrorum rationes
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earum, quas inter ſe habent diametri æqualibus exceſsibus
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differentes circulorum, qui ſunt ſectiones coni, & baſes cy
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lindrorum, ex quibus conſtat figura cono EDF circum
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ſcripta, ſumpta progreſſione proportionum eodem ordine
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gradatim à minima diametro vſque ad maximam EF) ita
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erit cylindrorum deficientium, ex quibus conſtat figura
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circumſcripta reliquo cylindri AF, dempto ABC hemi
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ſphærio, minimi, cuius axis DL ad ſecundum minor pro
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portio, quàm ſecundi ad tertium, & ſic deinceps, vſque ad
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maximũ
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XF, communiter ad conum EDF, & prædictum
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reſiduum pertinentem, ſicut & eorum baſes circuli deficien
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tes, quæ ſunt dicti reſidui ſectiones. </
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<
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>Cum igitur tam maxi
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mi cylindri XF communis, quàm binorum quorumque reli
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quorum cylindrorum circa conum EDF, & prædictum reſi
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duum inter eadem plana parallela conſiſtentium, quorum
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axis communis in BD, commune centrum grauitatis in axe
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BD exiſtat, erit ex antecedenti punctum K, quod pono
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centrum grauitatis coni EDF, idem reſidui ex cylindro
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AF, dempto ABC, hemiſphærio centrum grauitatis.
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<
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>Quoniam igitur quarum partium eſt octo axis BD talium
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eſt BG quinque, & BK duarum (ponimus enim nunc K
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coni EDF centrum grauitatis) qualium eſt BD octo, ta
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lium erit GK trium: ſed KH eſt æqualis BK; qualium
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igitur partium eſt GK trium, talium erit KH duarum, ta
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liſque vna GH; dupla igitur KH ipſius GH: ſed ABC
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hemiſphærium duplum eſt prædicti reſidui, cum ſit cylin
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dri AF, ſubſeſquialterum; vt igitur eſt
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hemiſphæriũ
">hemiſphærium</
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ABC,
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ad prædictum reſiduum, ita ex contraria parte erit
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lõgitudo
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KH, adlongitudinem GH: ſed H eſt centrum grauitatis
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totius cylindri AF & K, prædicti reſidui dempto ABC
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hemiſphærio; ergo ABC hemiſphærij centrum grauitatis
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erit G. </
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<
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