Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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46
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ro ita demonſtrabitur. </
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">Ducatur à puncto b ad planum ba
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ſis ac perpendicularis linea bh, quæ ipſam ef in K ſecet. </
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">erit bh altitudo coni, uel coni portionis abc: & bK altitu
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do efg. </
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">Quod cum lineæ ac, ef inter ſe æquidiſtent, ſunt
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enim planorum æquidiſtantium ſectiones: habebit db ad
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bg proportionem eandem, quam hb ad bk quare por
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tio conoidis abc ad portionem efg proportionem habet
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compoſitam ex proportione baſis ac ad baſim ef; & ex
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proportione db axis ad axem bg. </
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">Sed circulus, uel
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ellipſis circa diametrum ac ad circulum, uel ellipſim
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circa ef, eſt ut quadratum ac ad quadratum ef; hoc eſt ut
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quadratũ
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ad ad
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quadratũ
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eg. & quadratum ad ad quadra
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tum eg eſt, ut linea db ad lineam bg. </
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<
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">circulus igitur, uel el
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lipſis circa diametrum ac ad
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circulũ
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, uel ellipſim circa ef,
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hoc eſt baſis ad baſim eandem proportionem habet,
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quã
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db axis ad axem bg. </
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<
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">ex quibus ſequitur portionem abc
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ad portionem ebf habere proportionem duplam eius,
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quæ eſt baſis ac ad baſim ef: uel axis db ad bg axem. </
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demonſtrandum proponebatur.</
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16. unde
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cimi.</
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4 sexti.</
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2. duode
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cimi</
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7. de co
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noidibus
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& ſphæ
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roidibus</
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15. quinti. </
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20. primi
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<
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">THEOREMA XXV. PROPOSITIO XXXI.</
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<
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">Cuiuslibet fruſti à portione rectanguli conoi
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dis abſcisſi, centrum grauitatis eſt in axe, ita ut
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demptis primum à quadrato, quod fit ex diame
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tro maioris baſis, tertia ipſius parte, & duabus
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tertiis quadrati, quod fit ex diametro baſis mino
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ris: deinde à tertia parte quadrati maioris baſis
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rurſus dempta portione, ad quam reliquum qua
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drati baſis maioris unà cum dicta portione
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duplã
">duplam</
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proportionem habeat eius, quæ eſt quadrati </
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