Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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pyramidem, uel conum, uel coni portionem eandem pro
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portionem habet, quam baſes ab, cd unà cum ef ad ba
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ſim ab. </
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6. 11. duo
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decimi</
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<
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">Fruſtum uero ad æquale eſſe pyramidi, uel co
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no, uel coni portioni, cuius baſis conſtat ex baſi
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bus ab, cd, ef, & altitudo fruſti altitudini eſt æ
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qualis, hoc modo oſtendemus.</
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<
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">Sit fruſtum pyramidis abcdef, cuius maior baſis trian
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gulum abc; minor def: & ſecetur plano baſibus æquidi
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ſtante, quod ſectionem faciat triangulum ghk inter trian
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gula abc, def proportionale. </
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<
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">Iam ex iis, quæ demonſtrata
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ſunt in 23. huius, patet fruſtum abcdef diuidi in tres pyra
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mides proportionales; & earum maiorem eſſe
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abcd
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uero defb. </
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">ergo pyramis à triangulo ghk
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conſtituta, quæ altitudinem habeat fruſti altitudini æqua
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lem, proportionalis eſt inter pyramides abcd, defb: &
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idcirco fruſtum abcdef tribus dictis pyramidibus æqua
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le erit. </
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">Itaque ſi intelligatur alia pyra
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mis æque alta, quæ baſim habeat ex tri
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bus baſibus abc, def, ghk conſtan
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tem; perſpicuum eſt ipſam eiſdem py
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ramidibus, & propterea ipſi fruſto æ
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qualem eſſe.</
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">Rurſus ſit fruſtum pyramidis ag, cu
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ius maior baſis quadrilaterum abcd,
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minor efgh: & ſecetur plano baſi
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bus æquidiſtante, ita ut fiat ſectio qua
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drilaterum Klmn, quod ſit proportio
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nale inter quadrilatera abcd, efgh. </
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">Dico pyramidem,
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cuius baſis ſit æqualis tribus quadrilateris abcd, klmn,
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efgh, & altitudo æqualis altitudini fruſti, ipſi fruſto ag
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æqualem eſſe. </
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