Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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[Figure 191]
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>Manifeſta item ſunt hæc omnia, ex ijs, quæ in eodem li
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bro de ſphæroidibus, & conoidibus demonſtrat Archi
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medes. </
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PROPOSITIO IX.
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<
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>Omnis fruſti pyramidis triangulam baſim ha
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bentis ad priſtina, cuius baſis eſt maior baſis fru
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ſti, & eadem altitudo, cam habet proportionem,
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quàm rectangulum contentum duobus lateribus
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homologis baſium oppoſitarum, vnà cum tertia
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parte quadrati differentiæ dictorum laterum, ad
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maioris lateris quadratum. </
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<
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>Ad pyramidem autem,
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cuius baſis eſt maior baſis fruſti, & eadem altitu
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do, vt prædictum rectangulum, vna cum prædicti
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quadrati tertia parte, ad tertiam partem quadrati
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maioris lateris. </
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<
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>Sit pyramidis triangulam baſim habentis fruſtum AB
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CD EF: laterum autem homo
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logorum AB, DE, triangulorum
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ſimilium oppoſitorum ABC, D
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EF, ſit differentia DG: & eiuſ
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dem altitudinis fruſto ſit priſma
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DEFCHK: & pyramis intelli
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gatur ADEF. </
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<
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>Dico fruſtum
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BDF ad priſma HKF, eſſe vt
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rectangulum DEG vna cum ter
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tia parte quadrati DG. </
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<
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>Ad qua
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dratum DE: ad pyramidem au
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tem ADEF, vt
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prædictũ
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rectan
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id
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xlink:href
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number
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142
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gulum DEG, vnà cum tertia parte quadrati DG, ad ter</
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