Valerio, Luca, De centro gravitatis solidorum, 1604

List of thumbnails

< >
41
41 		42
42
43
43 		44
44
45
45 		46
46
47
47 		48
48
49
49 		50
50
< >
page |< < of 283 > >|
    <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
                <lb/>
              ctum igitur G, erit centrum grauitatis trianguli ABC.
                <lb/>
              </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="main">
              <s>Quod autem ex huius theorematis demonſtratione li­
                <lb/>
              quet centrum grauitatis trianguli eſse in ea recta linea,
                <lb/>
              quæ ab angulo ad bipartiti lateris ſectionem pertinet,
                <lb/>
              Archimedes per inſcriptionem figuræ ex parallelogram­
                <lb/>
              mis demonſtrauit, aliter autem per diuiſionem trianguli
                <lb/>
              in triangula nequaquam: qua enim ratione hoc ille tentat,
                <lb/>
              ea ex nono theoremate eiuſdem prioris libri de æquipon­
                <lb/>
              derantibus neceſsario pendet. </s>
              <s>Cum igitur in illo ante ceden
                <lb/>
              ti ſit fallacia accipientis latenter ſpeciem trianguli; ſcale­
                <lb/>
              num ſcilicet pro genere triangulo, neque conſequens erit
                <lb/>
              demonſtratum. </s>
              <s>Quod autem dico manifeſtum eſt: Datis
                <lb/>
              enim duobus triangulis ſimilibus, & in altero eorum dato
                <lb/>
              puncto, quod ſit trianguli centrum grauitatis, punctum in
                <lb/>
              altero triangulo modo ſimiliter poſitum ſit prædicto pun­
                <lb/>
              cto, nititur demonſtrare eſse alterius trianguli centrum
                <lb/>
              grauitatis: cum autem nondum conſtet centrum graui­
                <lb/>
              tatis trianguli eſse in recta, quæ ab angulo latus oppoſi­
                <lb/>
              tum bifariam ſecat, ſed ex nono theoremate ſit demonſtran
                <lb/>
              dum medio decimo, non poteſt illud accipi in nono theo­
                <lb/>
              remate, quod ad demonſtrationem eſset neceſsarium. </s>
              <s>per­
                <lb/>
              mittitur igitur aduerſario ponere centrum grauitatis trian­
                <lb/>
              guli, vbicumque vult intra illius limites. </s>
              <s>atqui cum datis
                <lb/>
              duobus triangulis iſoſceliis ſimilibus, & in altero eorum
                <lb/>
              dato puncto, quod non ſit in prædicta recta linea, poſsint
                <lb/>
              in altero duo puncta prædicto ſimiliter poſita inueniri, quo­
                <lb/>
              rum vnum duntaxat concedet aduerſarius eſse alterius
                <lb/>
              trianguli centrum grauitatis, non autem non ſimiliter po­
                <lb/>
              ſitum, ex quo abſurdum infertur partem anguli æqualem
                <lb/>
              eſse toti: quid quod datis duobus triangulis æquilateris, &
                <lb/>
              in altero eorum dato puncto, quod non ſit centrum trian-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum