Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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cylindri AE ſubſeſquialterum: coni igitur ABC duplum.
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<
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PROPOSITIO XIII.
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>Omnis minor ſphæræ portio, ad cylindrum,
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cuius baſis æqualis eſt circulo maximo, altitudo
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autem eadem portioni, eam habet proportionem,
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quam exceſſus, quo tripla ſemidiametri ſphæræ
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excedit tres deinceps proportionales, quarum ma
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xima eſt ſphæræ ſemidiameter, media vero quæ
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inter centra ſphæræ & baſis portionis interijci
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tur; ad ſemidiametri ſphæræ triplam. </
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<
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>Sit ſphæræ, cuius centrum D, ſemidiameter BD, mi
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nor portio ABC, cuius axis BG ſegmentum ſemidiame
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tri BD, baſis autem circulus, cuius diameter AC. </
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<
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EF, cylindrus, cu
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ius axis, ſiue alti
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tudo eadem BG:
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baſis autem æqua
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lis circulo maxi
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mo, cuius ſemidia
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meter BD. </
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<
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portionem ABC,
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ad cylindrum EF
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eam habere pro
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portionem, quam exceſſus, quo tripla ipſius BD, ſupe
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rat tres BD, DG; & minorem extremam ad ipſas, quæ
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ſit M; ad ipſius BD triplam. </
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<
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>vertice enim D, baſi cylin
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dri EF, cuius diameter FH deſcribatur conus FDH, cu
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ius intelligatur fruſtum FHKL abſciſsum plano, quod ab-</
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