Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/047.jpg" pagenum="39"/>
              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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              </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="main">
              <s>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. </s>
              <s>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. </s>
              <s>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. </s>
              <s>per­
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              mittitur igitur aduerſario ponere centrum grauitatis trian­
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              guli, vbicumque vult intra illius limites. </s>
              <s>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-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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