Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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communis baſis ſit poly gorum inſcriptum circulo quidem
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æquilaterum, & æquiangulum; in ellipſe autem, quod pro
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Archimede deſcribit Commandinus, ita vt & à cylindro,
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vel cylindri portione priſina, & à cono, vel coni portione
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pyramis deficiat minori ſpacio quantacumque magnitudi
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ne propoſita: quo modo autem in portione cylindrica, vel
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conica hoc fieri poſſit, eadem quæ de cono atque cylindro
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Euclides in duodecimo docuit manifeſtant. </
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>Abſciſſione
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igitur facta fruſti AD, & cylindri, vel portionis cylindricæ
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CG, abſciſſa ſimul erunt fruſtum pyramidis inſcriptum
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fruſto AD, & priſma inſcriptum cylindro, vel portioni cy
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lindricæ CG, eiuſdem altitudinis inter ſe, & duobus præ
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dictis ſolidis AD, CG, deficien
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tia vnum à fruſto, alterum à cy
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lindro, vel portione cylindrica
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multo minori ſpacio magnitudine
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propoſita: ſectiones autem priſma
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tis, & pyramidis erunt polygona
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circulis, vel ellipſibus ipſi CD op
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poſitis & ſimilibus inſcripta in
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ter ſe ſimilia, vt multi oſtendunt.
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>erunt etiam ſimilium polygono
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rum circulis, vel ellipſibus ſimili
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bus, quæ ſunt baſes oppoſitæ fru
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ſti AD, inſcriptorum diametri eædem AB, CD. </
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>Quo
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niam igitur ſimilium polygonorum circulis, & ſimilibus
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ellipſibus inſcriptorum latera homologa inter ſe ſunt vt
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diametri dictorum circulorum, vel ellipſium, eadem erit
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proportio inter duas diametros AB, CD, hoc eſt FC,
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CD, quæ inter duo quælibet latera homologa polyga
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norum circulis, vel ellipſibus ſimilibus AB, CD in
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ſcriptorum. </
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<
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>Sed pyramidis fruſtum fruſto CB inſcri
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ptum ad priſma, cuius baſis eſt maior baſis fruſti pyrami
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dis, & eadem altitudo, ſolido CG inſcriptum, eſt vt re-</
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