Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000676">
                <pb pagenum="34" xlink:href="009/01/034.jpg"/>
              medis eſt propoſitio prima acutiſſimi libelli de Dimenſione circuli; eſt au­
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              tem huiuſmodi. </s>
              <s id="s.000677">Quilibet circulus æqualis eſt triangulo rectangulo, cuius
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              quidem ſemidiameter vni laterum, quæ circa rectum angulum ſunt, ambi­
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              tus verò baſi eius eſt æqualis.</s>
            </p>
            <figure id="id.009.01.034.1.jpg" place="text" xlink:href="009/01/034/1.jpg" number="1"/>
            <p type="main">
              <s id="s.000678">Sit, v.g. datus circulus, cuius ſemidiameter A B; & fit triangulum rectangu­
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              lum A B C, cuius angulus B, ſit rectus, & latus B A,
                <expan abbr="conſtituẽs">conſtituens</expan>
              angulum re­
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              ctum B, cum baſi B C, ſit æquale ſemidiametro A B; baſis verò B C, ſit æqua­
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              lis peripheriæ eiuſdem circuli dati. </s>
              <s id="s.000679">demonſtrat iam ibi Archimedes acuta
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              æquè, ac euidenti demonſtratione triangulum iſtud æquale eſſe circulo illi.
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              </s>
              <s id="s.000680">quod perinde eſt, ac ſi oſtendiſſet cuinam quadrato ſit æqualis, cum per vl­
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              timam 2. Eucl. poſſimus triangulo huic quadratum æquale conſtruere, quod
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              conſequenter dato circulo æquale erit. </s>
              <s id="s.000681">Quod ſi in modum Problematis ita
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              proponatur: Dato circulo æquale quadratum conſtruere, nondum inuenta
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              eſt ratio, quæ demonſtratione confirmetur, qua id geometricè penitus, hoc
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              eſt ad æqualitatem mathematicam, ſeu exactiſſimam effici poſſit,
                <expan abbr="totaq́">totaque</expan>
              ; dif­
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              ficultas poſita eſſe videtur in inueſtigando, quonam modo exhibeamus li­
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              neam rectam B C, æqualem peripheriæ circuli dati. </s>
              <s id="s.000682">quam nullus hactenus
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              geometricè illi æqualem potuit exhibere,
                <expan abbr="atq;">atque</expan>
              exhibita
                <expan abbr="euidẽti">euidenti</expan>
              demonſtra­
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              tione comprobare; Quamuis Archimedes acumine ſanè mirabili in lib. de
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              lineis ſpiralibus, eam
                <expan abbr="quoq;">quoque</expan>
              theorematicè, non tamen problematicè inue­
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              ſtigauit. </s>
              <s id="s.000683">nam propoſitione 18. illius
                <expan abbr="admirãdi">admirandi</expan>
              operis inuenit lineam rectam
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              æqualem circumferentiæ primi circuli ſpiralis lineæ; propoſ verò 19. repe­
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              rit aliam rectam æqualem circumferentiæ ſecundi circuli. </s>
              <s id="s.000684">tu ipſum conſule,
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              ſi admirandarum rerum contemplatione delectaris. </s>
              <s id="s.000685">Multa hac de re Pap­
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              pus Alexandrinus lib. 4. Math. coll. </s>
              <s id="s.000686">& Ioannes Buteo vnico volumine om­
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              nes quadraturas tain priſcorum, quam recentiorum
                <expan abbr="cõprehenſus">comprehenſus</expan>
              eſt. </s>
              <s id="s.000687">Qua­
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              re qui plura cupit, eos adeat; nos tamen infra ſuis locis explicabimus tres
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              illas celebres antiquorum Antiphontis, Briſſonis, & Hippocratis quadra­
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              turas, quamuis falſas,
                <expan abbr="quarũ">quarum</expan>
              ſæpe meminit Ariſt. & alij. </s>
              <s id="s.000688">ſolet autem à non­
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              nullis diſputari, vtrum quadratura iſta problematica ſit poſſibilis, nec ne,
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              cum videant eam à nemine, quamuis diu magno labore perquiſitam, hacte­
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              nus adinuentam eſſe. </s>
              <s id="s.000689">ego quidem eſſe poſſibilem exiſtimo, quis enim dubi­
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              tare poteſt, poſſe exiſtere quadratum æquale circulo propoſito? </s>
              <s id="s.000690">Quod ſi po­
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              teſt fieri, quare non etiam demonſtrari? </s>
              <s id="s.000691">pręfertim cum videamus ab Archi­
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              mede iam inuentam eſſe, quatenus Theorema eſt. </s>
              <s id="s.000692">& præterea conſtet, Hip­
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              pocratem quadraſſe lunulam, vt ſuo loco dicemus, & Archimedem in </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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