Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ita N ad O potentia, & Q ad P longitudine: ſit au
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tem N media proportionalis inter EB, BD, at P ipſius
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O potentia ſeſquialtera: quo autem Q plus poteſt quàm
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P ſit quadratum ex R: & vt cubus ex FD vna cum ſoli
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do rectangulo ex BF, FD, & tripla ipſius BD, ad ſoli
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dum rectangulum ex BF, & quadrato R, ita ſit HK ad
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KG. </
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<
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>Dico fruſti ALMC centrum grauitatis eſſe K.
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</
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>Producta enim quà opus eſt diametro AC ipſi BD æqua
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les abſcindantur DS, DV: necnon ipſi N æquales
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DT, DX, vt ſit TD ad DS potentia, vt EB, ad
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BD longitudine, & deſcribantur conoides paraboli
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cum TBX, & conus SBV, quorum vertex commu
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nis B, axis BD: ſectis autem his tribus ſolidis plano
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per axim, ſint ſectiones hyperbole ABC, & parabo
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la TBX, & triangulum SBV, quæ figuras deſcribunt;
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quas planum baſis fruſti propoſiti circa LM ſecans vnà
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cum tribus ſolidis faciat cum parabola TBX rectam I
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,
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& cum triangulo SBV rectam
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Z: conoidis autem TBX,
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& coni SBV ſectiones circulos circa I
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, YZ baſibus,
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circa SV, TX parallelos; vt ſint conoidis TBX fru
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ſtum TI
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X, & coni SBV fruſtum SYZV. </
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<
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>Rur
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ſus producta I. M, ponatur <37>F, æqualis Q, & ab
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ſcindatur F
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, potentia ſeſquialtera ipſius IF, iunctis
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que IB, B
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, B<37>, deſcribantur tres coni <37>B
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,
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B
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, IB
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, quorum omnium baſes nempe circuli
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erunt in dicto plano ſecante tria ſolida per punctum F.
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<
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>Quoniam igitur circuli inter ſe ſunt vt quæ fiunt à diame
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tris, vel à ſemidiametris quadrata, coni autem eiuſdem al
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titudinis inter ſe vt baſes; erit vt
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F ad FI potentia, ita
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conus
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B
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ad conum IB
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; ſeſquialter igitur conus
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<
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B
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coni IB
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: ſed & conoides parabolicum IB
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ſeſqui
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alterum eſt coni IB
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; æqualis igitur eſt conus
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B
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co
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noidi IB
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<
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>Et quoniam in parabola TBX ordinatim
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ad diametrum applicatarum DT eſt ad FI hoc eſt N </
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