Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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conus
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B
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æqualis eſt conoidi IB
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, vtpote inſcripti co
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ni IB
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ſeſquialtero, cuius itidem ſeſquialter erat conus
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B
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; reliquum igitur coni <37>B
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dempto cono
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B
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æqua
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le erit conoidis TBX fruſto TI
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X. </
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cubus ex BD ad cubum ex BI ita conus SBV ad ſui ſi
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milem conum YBZ, in triplicata ſcilicet proportione la
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terum, ſiue axium DB, BF: ſed quia YF eſt æqualis BF,
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propter ſimilitudinem triangulorum, eſt vt cubus ex BF ad
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ſolidum ex BF & quadrato ex F
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, ita quadratum ex FY
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ad quadratum ex F
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, hoc eſt circulus circa YZ ad
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expan
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circa
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, hoc eſt conus YBZ ad conum
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B
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ex æquali
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igitur erit vt cubus ex BD ad ſolidum ex BF, & quadra
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to F
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, ita conus SBV ad conum
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B
<
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: ſed vt ſolidum
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ex BF, & quadrato F
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, ad ſolidum ex BF & quadrato
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F<37>, ita eſt ſimiliter vt ante conus
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B
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ad conum <37>B
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; ex
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æquali igitur erit vt cubus ex BD ad ſolidum ex BF, &
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quadrato F<37>, ita conus SBV, ad conum <37>B
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: ſed con
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uertendo, & per conuerſionem rationis, eſt vt ſolidum ex
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BF, & quadrato F<37>, ad ſolidum ex BF, & quadrato,
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quo plus poteſt F<37> quàm F
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, ita conus <37>B
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ad ſui reli
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quum dempto cono <35>B
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; ex æquali igitur, vt cubus ex
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BD ad ſolidum ex BF & quadrato, quo plus poteſt F<37>,
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quàm F
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, hoc eſt, quo plus poteſt Q quàm P quadrato
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ex R, ita erit conus SBV, ad reliquum coni <37>B
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dem
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pto cono
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B
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, hoc eſt ad fruſtum TI
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X. Rurſus, quo
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niam duo cubi ex BF, FD, & ſolidum ex BF, FD, &
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tripla ipſius BD, ſunt æqualia cubo ex BD; erit id quo
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plus poteſt cubice recta BD quàm BF, cubus ex
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FD, & ſolidum ex BF, FD, & tripla ipſius BD: cum
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igitur ſit vt cubus ex BD ad cubum ex BF, ita conus
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SBV ad conum YBZ; erit per conuerſionem rationis, &
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conuertendo, vt cubus ex FD vna cum ſolido ex BF,
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FD, & tripla ipſius BD ad cubum ex BD, ita fruſtum
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SYZV, ad conum SBV: ſed cubus ex BD, ad ſoli-</
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