Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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relato: huic autem proximus, & æqualis cylindrorum in
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ſcriptorum ſit NM baſim ipſi communem habens circu
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lum circa EFM: & conſequenti circumſcriptorum GQ
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ſit. </
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>inſcriptorum æqualis PO baſim habens ipſi commu
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nem circulum circa GHO: ſint autem circulorum qui
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ſunt baſes cylindrorum diametri in parabola per axim:
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quæ quoniam ſunt communes ſectiones cum parabola per
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axim planorum baſi conoidis, & inter ſe parallelorum,
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erunt etiam ipſæ inter ſe, & parabolæ baſi AC parallelæ,
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earumque dimidiæ vt EF, GH ad diametrum BD or
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dinatim applicatæ. </
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>Quoniam igitur in parabola ABC
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eſt vt HB ad BF ita quadratum GH ad quadratum
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EF, duplum erit
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quadratum GH
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quadrati EF: qua
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re & circulus cir
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ca GO circuli
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circa EM at que
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adeo cylindrus
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GQ cylindri E
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L duplus, pro
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pter <17>qualitatem
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altitudinum: ſed
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& cylindrus NL
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duplus eſt cylindri EL per conſtructionem; cylindrus igi
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tur GQ æqualis eſt cylindro NL: & ablato communi
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NM cylindro, reliquus GQ deficiens cylindro NM
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cylindro EL æqualis. </
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>Rurſus quia eſt vt KB ad BH,
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ita quadratum IK ad quadratum GH, hoc eſt ita IR
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cylindrus ad cylindrum GQ: ſed vt HB ad BF ita
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erat cylindrus GQ ad cylindrum EL; tres igitur cy
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lindri IR, GQ, EL, tribus lineis BK, BH, BF, eodem
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ordine proportionales erunt: ſed tres eædem lineæ ſeſe
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æqualiter excedunt; tres igitur dicti cylindri ſeſe æqua-</
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