Valerio, Luca, De centro gravitatis solidorum, 1604

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              PROPOSITIO XXXIV.
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              <s>Omnis minoris portionis ſphæræ centrum gra
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              uitatis eſt in axe primum bifariam ſecto: deinde
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              ſecundum centrum grauitatis fruſti circa eun­
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              dem axim, abſciſſi à cono verticem habente cen­
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              trum ſphæræ; in eo puncto, in quo dimidius axis
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              portionis baſim attingens ſic diuiditur, vt pars
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              duabus prædictis ſectionibus intercepta ſit ad
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              eam, quæ inter ſecundam, & tertiam ſectionem
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              interijcitur, vt exceſſus, quo tripla ſemidiametri
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              ſphæræ, cuius eſt prædicta portio, ſuperattres de­
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              inceps proportionales, quarum maxima eſt ſphæ­
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              ræ ſemidiameter, media autem, quæ inter centra
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              ſphæræ, & baſis portionis interijcitur; ad ſemi­
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              diametri ſphæræ triplam. </s>
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              <s>Sit minor portio ABC, ſphæræ, cuius centrum D,
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              ſemidiameter BD, in qua axis portionis ſit BG, baſis
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              autem circulus, cuius diameter AC: & circa axim BD
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              deſcriptus eſto conus HDF, cuius baſis circulus FH
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              tangens portionem in B puncto ſit æqualis circulo ma­
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              ximo, & fruſtum coni HDF abſciſſum vna cum portio­
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              ne ABC ſit KHFL, & vt BD ad DG, ita fiat DG
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              ad P: ſectoque axe BG bifariam in puncto N, fiat vt
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              exceſſus, quo tripla ipſius BD ſuperat tres BD, DG,
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              P, tanquam vnam, ita NM, ad MNO. </s>
              <s>Dico portio­
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              nis ABC centrum grauitatis eſse O. </s>
              <s>Nam circa axim
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              BG, ſuper baſim FH ſtet cylindrus EF, cuius cen-</s>
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