Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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cum quæ tangentium concurſum, & centrum fi
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guræ iungit interiecta. </
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>Sit circulus, vel ellipſis ABCD, cuius diametri con
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iugatæ AC, BED, & figuram tangentes BF, GF, con
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ueniant in puncto F; (parallelæ enim erunt vtraque alteri
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coniugatorum diametrorum:) & recta FE iungatur, & ex
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quolibet puncto G, in recta BE ducatur ipſi AC paral
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lela GLKH. </
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<
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>Dico rectangulum GKH bis vnà cum
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quadrato KH æquale eſſe quadrato GL. </
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<
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>Quoniam
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enim rectangulum BGD æquale eſt rectangulo BGE
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bis vnà cum quadrato BG: & rectangulum BED, eſt
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quadratum BE, erit vt rectangulum BED, ad re
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ctangulum BGD, ita quadratum BE, ad rectangu
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lum BGE bis, vnà cum quadrato BG: ſed vt rectangu
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lum BED, ad rectangulum BGD, ita eſt quadratum EC,
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hoc eſt quadratum GH ad quadratum GK, ex primo
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conicorum, vt igitur eſt quadratum BE ad rectangulum
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BGE bis, vnà cum quadrato BG, ita erit quadratum
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GH ad quadratum GK. </
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<
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>Rurſus quia eſt vt BE ad EG,
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ita BF ad GL, propter ſimilitudinem triangulorum; erit
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vt quadratum BE ad quadratum EG, ita quadratum </
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