Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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ad triangulum FBG, hoc eſt vt AF ad FG, ita eſt
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triangulum AFC ad triangulum FCG; triangulum er
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go FBG triangulo FCG æquale erit, & baſis BG ba
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ſi GC æqualis. </
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>Quoniam igitur & AE eſt æqualis
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EC, ſimiliter vt ante, oſtenderemus, triangulum BCF,
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triangulo ACF, eademque ratione triangulum ABF,
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triangulo BCF æquale eſſe: igitur vnumquodque trian
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gulorum ABF, ACF, BCF, tertia pars eſt trianguli
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ABC: ſed vt triangulum ABC, ad triangulum BCF,
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ita eſt AG, ad GF; tripla igitur eſt AG ipſius GF,
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ac proinde AF, ipſius FG dupla. </
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>Eadem ratione
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BE, ipſius FE, & CF, ipſius FD, dupla concludetur. </
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>Sed ſint ſi fieri poteſt, trianguli ABC duo centra qua
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lia diximus D, E: & ab ipſis ad ſingulos angulos du
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cantur binæ rectæ lineæ:
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& eadat D in aliquo trian
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gulo BEC. </
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<
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>Quoniam
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igitur D eſt centrum trian
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guli ABC erit triangu
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lum BDC tertia pars
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trianguli ABC. </
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<
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>Eadem
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ratione triangulum BEC
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tertia pars erit trianguli
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ABC; triangulum ergo
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DBC æquale erit trian
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gulo BEC pars toti, quod
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fieri non poteſt, atqui
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abſurdum ſequitur, ſi punctum D cadat in aliquo latere
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triangulorum, quorum vertex E; Manifeſtum eſt igitur
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propoſitum. </
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