Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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PROPOSITIO XXXIV.
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<
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>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. </
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>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. </
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<
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>Dico portio
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nis ABC centrum grauitatis eſse O. </
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<
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>Nam circa axim
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BG, ſuper baſim FH ſtet cylindrus EF, cuius cen-</
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