Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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proportionem habet, quam baſis abcd ad baſim ghkl:
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ſi enim intelligantur duæ pyramides abcde, ghklm, ha
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bebunt hæ inter ſe proportionem eandem, quam ipſarum
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baſes ex ſexta duodecimi elementorum. </
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<
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">Sed ut baſis abcd
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ad ghKl baſim, ita linea o ad lineam p; hoc eſt ad lineam q
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ei æqualem. </
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<
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id
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">ergo priſma ae ad priſma gm eſt, ut linea o
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ad lineam q.</
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<
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id
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"> proportio autem o ad q copoſita eſt ex pro
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portione o ad p, & ex proportione p ad q.</
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id
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"> quare priſma
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ae ad priſma gm, & idcirco pyramis abcde, ad pyrami
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dem ghKlm proportionem habet ex eiſdem proportio
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nibus compoſitam, uidelicet ex proportione baſis abcd
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ad baſim ghKl, & ex proportione altitudinis ef ad mn al
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titudinem. </
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<
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id
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">Quòd ſi lineæ ef, mn inæquales ponantur, ſit
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ef minor: & ut ef ad mn, ita fiat linea p ad lineam u: de
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inde ab ipſa mn abſcindatur rn æqualis ef: & per r duca
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tur planum, quod oppoſitis planis æquidiſtans faciat ſe
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ctionem st. </
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<
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id
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">erit priſma ae, ad priſma gt, ut baſis abcd
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ad baſim ghkl; hoc eſt ut o ad p: ut autem priſma gt ad
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priſma gm, ita altitudo rn; hoc eſt ef ad altitudine mn;
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uidelicet linea p ad lineam u. </
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<
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id
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">ergo ex æquali priſma ae ad
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priſma gm eſt, ut linea o ad ipſam u. </
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<
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id
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">Sed proportio o ad
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u
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eſt ex proportione o ad p, quæ eſt baſis abcd
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ad baſim ghkl; & ex proportione p ad u, quæ eſt altitudi
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nis ef ad altitudinem mn. </
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<
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">priſma igitur ae ad priſma gm </
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