Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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grauitatis trianguli ABC, erit aliud à puncto G: pun
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ctum igitur G, erit centrum grauitatis trianguli ABC.
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<
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>Quod demonſtrandum erat. </
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<
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>Quod autem ex huius theorematis demonſtratione li
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quet centrum grauitatis trianguli eſse in ea recta linea,
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quæ ab angulo ad bipartiti lateris ſectionem pertinet,
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Archimedes per inſcriptionem figuræ ex parallelogram
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mis demonſtrauit, aliter autem per diuiſionem trianguli
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in triangula nequaquam: qua enim ratione hoc ille tentat,
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ea ex nono theoremate eiuſdem prioris libri de æquipon
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derantibus neceſsario pendet. </
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<
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>Cum igitur in illo ante ceden
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ti ſit fallacia accipientis latenter ſpeciem trianguli; ſcale
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num ſcilicet pro genere triangulo, neque conſequens erit
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demonſtratum. </
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<
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>Quod autem dico manifeſtum eſt: Datis
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enim duobus triangulis ſimilibus, & in altero eorum dato
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puncto, quod ſit trianguli centrum grauitatis, punctum in
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altero triangulo modo ſimiliter poſitum ſit prædicto pun
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cto, nititur demonſtrare eſse alterius trianguli centrum
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grauitatis: cum autem nondum conſtet centrum graui
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tatis trianguli eſse in recta, quæ ab angulo latus oppoſi
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tum bifariam ſecat, ſed ex nono theoremate ſit demonſtran
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dum medio decimo, non poteſt illud accipi in nono theo
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remate, quod ad demonſtrationem eſset neceſsarium. </
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<
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>per
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mittitur igitur aduerſario ponere centrum grauitatis trian
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guli, vbicumque vult intra illius limites. </
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<
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>atqui cum datis
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duobus triangulis iſoſceliis ſimilibus, & in altero eorum
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dato puncto, quod non ſit in prædicta recta linea, poſsint
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in altero duo puncta prædicto ſimiliter poſita inueniri, quo
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rum vnum duntaxat concedet aduerſarius eſse alterius
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trianguli centrum grauitatis, non autem non ſimiliter po
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ſitum, ex quo abſurdum infertur partem anguli æqualem
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eſse toti: quid quod datis duobus triangulis æquilateris, &
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in altero eorum dato puncto, quod non ſit centrum trian-</
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