Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO XLIII.
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<
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>Omnis conoidis hyperbolici centrum grauita
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tis eſt punctum illud, in quo duodecima pars axis
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ordine quarta ab ea, quæ baſim attingit, ſic diui
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ditur, vt pars baſi propinquior ſit ad reliquam, vt
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ſeſquialtera tranſuerſi lateris hyperboles, quæ
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conoides deſcribit ad axim conoidis. </
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>Sit conoides hyperbolicum ABC, cuius vertex B, axis
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autem BD, qui etiam erit diameter hyperboles, quæ co
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noides deſcripſit, ad quam rectæ ordinatim applicantur:
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eiuſdem autem hyperboles tranſuerſum latus ſit EB, cu
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ius ſit ſeſquialtera BEI, & ſumpta DQ quarta parte
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axis BD, & DG, eiuſdem tertia, qua ratione erit FG
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duodecima pars axis BD, & ordine quarta ab ea cuius
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terminus D, fiat vt IB, ad BD, ita QH, ad HG.
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>Dico conoidis ABC, centrum grauitatis eſſe H. </
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>Sumpto
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enim in linea AD quolibet puncto M, vt eſt EB ad
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BD longitudine, ita fiat MD, ad DK ipſius AD po
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tentia: & abſcindatur DN, æqualis DM, & DL æqua
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lis DK; ſiue autem ſit DK minor, quàm DM, ſiue ma
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ior, ſiue eadem illi; omnibus caſibus communis erit demon
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ſtratio. </
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<
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>At per puncta M, N, vertice B, circa diametrum
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BD, deſcribatur parabola MBN, & triangulum KBL.
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<
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>Manente igitur BD, & circumductis figuris MBN,
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KBL, deſcribantur conoides parabolicum MBN, &
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conus KBL, quorum communis axis erit BD, baſes
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autem circuli, quorum diametri KL, MN, in eodem
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plano cum baſe conoidis ABC. </
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<
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bifariam, & ſingulis eius partibus ſemper bifariam in qua-</
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