Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.003490">
                <pb pagenum="208" xlink:href="009/01/208.jpg"/>
                <emph type="italics"/>
              trumqué mediam æquat: quare non erit minima. </s>
              <s id="s.003491">neque duplum erit ſpatium à diame­
                <lb/>
              tro conſurgens illius, quod ab indiuidua procreatur: nans æquali ablato, reliquum
                <lb/>
              erit minus indiuidua, nam ſi æqualis, diameter quadruplum deſcriberet, &c.)
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.009.01.208.1.jpg" place="text" xlink:href="009/01/208/1.jpg" number="132"/>
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              ideſt ſi per 46 primi quadratum. </s>
              <s id="s.003492">v.g. A B C D, ex qua­
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              tuor inſecabilibus componatur, cuius diametro B C,
                <lb/>
              perpendicularis A E, inſiſtat, erit per 47. primi qua­
                <lb/>
              dratum lineæ A B, æquale quadratis
                <expan abbr="linearũ">linearum</expan>
              A E, E B,
                <lb/>
              quare tam E B, quàm A E, minores erunt ipſa A B;
                <lb/>
              quare ipſa non erit minima cum ſit indiuidua, quod eſt
                <lb/>
              abſurdum. </s>
              <s id="s.003493">Præterea ex ſcholio 47. primi, quadratum
                <lb/>
              C B F G, diametri C B, duplum eſt quadrati A B C D,
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              ergò diameter C B, maior quàm A B. </s>
              <s id="s.003494">Auferatur igitur ab ipſa, C B, æqua­
                <lb/>
              lis ipſi A B, quæ igitur reliqua erit, vel erit æqualis ipſi A B, vel minor. </s>
              <s id="s.003495">non
                <lb/>
              æqualis, quia tunc diameter dupla eſſet lateris A B, & quadratum diametri
                <lb/>
              quadruplum foret quadrati lateris A B. ex ſcholio 4. ſecundi, quod abſur­
                <lb/>
              dum eſt, repugnat enim 47. primi. </s>
              <s id="s.003496">nec minor, quia hoc modo exiſteret linea
                <lb/>
              quædam minor minima, ſcilicet atoma, quod pariter eſt inconueniens.</s>
            </p>
            <p type="main">
              <s id="s.003497">
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            <p type="margin">
              <s id="s.003498">
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              288</s>
            </p>
            <p type="main">
              <s id="s.003499">Duodecimus locus
                <emph type="italics"/>
              (Amplius ſi quæuis linea præter inſectilem in partes diui­
                <lb/>
              di poteſt, tùm æquales, tùm inæquales, ſeindatur linea in tria fruſta, quæ non con­
                <lb/>
              ſtet ex tribus atomis, ſed vniuerſaliter ex imparibus numero atomis, ſic diuiſa erit
                <lb/>
              linea indiuidua. </s>
              <s id="s.003500">ſimiliter autem ſi in duo diuidatur linea, quæ ex imparibus
                <expan abbr="cõſtat">conſtat</expan>
              )
                <emph.end type="italics"/>
                <lb/>
              hoc eſt detur linea quæpiam ab aduerſario ex lineis indiuiduis numerò im­
                <lb/>
              paribus, conſtans. </s>
              <s id="s.003501">v. g. ex quinque; hæc diuidi poteſt in tres æquas partes
                <lb/>
              per 10.6. Si igitur diuidatur in tria æqualia, neceſſariò tres ex atomis illam
                <lb/>
              integrantibus erunt diſſectæ, nam tertia quælibet pars continebit indiui­
                <lb/>
              duam vnam cum duabus tertijs alterius partibus. </s>
              <s id="s.003502">idem accidet ſi bifariam
                <lb/>
              per 10. primi, ſecetur quæuis ex imparibus numero atomis conflata.</s>
            </p>
            <p type="main">
              <s id="s.003503">
                <arrow.to.target n="marg279"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003504">
                <margin.target id="marg279"/>
              289</s>
            </p>
            <p type="main">
              <s id="s.003505">Decimustertius locus
                <emph type="italics"/>
              (Quod ſi bifariam quidem non omnis linea finditur, ſed
                <lb/>
              quæ ſolum ex paribus conflata ſit. </s>
              <s id="s.003506">ſi iam in duas partes diuiſa, in
                <expan abbr="quæcunq;">quæcunque</expan>
              diuidi
                <lb/>
              poteſt diuideretur, ſic
                <expan abbr="quoq;">quoque</expan>
              inſectilis linea diuideretur, quando ex paribus compo­
                <lb/>
              ſita, per inæqualia ſcinderetur)
                <emph.end type="italics"/>
              ideſt, quod ſi dixerit aduerſarius, non omnem
                <lb/>
              lineam bifariam diuidi poſſe, ſed eam ſolùm, quæ ex numero paribus atomis
                <lb/>
              conſtiterit: ea igitur diuidatur primo bifariam. </s>
              <s id="s.003507">deinde iterum diuidatur
                <lb/>
              quomodocunque, ideſt & bifariam, & non bifariam, nam hoc etiam pacto
                <lb/>
              indiuidua diuidetur, quod eſt inconueniens.</s>
            </p>
            <p type="main">
              <s id="s.003508">
                <arrow.to.target n="marg280"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003509">
                <margin.target id="marg280"/>
              290</s>
            </p>
            <p type="main">
              <s id="s.003510">Decimusquartus locus
                <emph type="italics"/>
              (Amplius non eſſet cuiuſuis lineæ quadratum: habe­
                <lb/>
              ret enim longitudinem, & latitudinem;
                <expan abbr="atq;">atque</expan>
              idcircò diuiſibile erit, cum illa quidem
                <lb/>
              aliquid, hæc autem aliquid aliud; quod ſi quadratum diuiduum eſt, & linea, vnde
                <lb/>
              procreatur, diuidua erit)
                <emph.end type="italics"/>
              poſſe ſuper quamuis datam lineam quadratum de­
                <lb/>
              ſcribi patet ex 46. primi, quadratum igitur deſcriptum ab indiuidua, cum
                <lb/>
              ſit ſuperficies, latitudinem, ac longitudinem habebit, quæ diuerſæ ſunt di­
                <lb/>
              menſiones. </s>
              <s id="s.003511">poterit ergò ſecundum
                <expan abbr="vtramq;">vtramque</expan>
              diuidi; ex qua diuiſione neceſ­
                <lb/>
              ſariò latera ipſius, hoc eſt lineæ, quas indiuiduas illi ponunt diuidentur,
                <lb/>
              quod eſt inconueniens, non igitur indiuiduæ erunt.</s>
            </p>
            <p type="main">
              <s id="s.003512">
                <arrow.to.target n="marg281"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003513">
                <margin.target id="marg281"/>
              291</s>
            </p>
            <p type="main">
              <s id="s.003514">Decimusquintus locus
                <emph type="italics"/>
              (Adhuc etiam, vt linea ſic, & ſuperficies, & corpus
                <lb/>
              erit impartibile: vno quippe indiuiduo exiſtente, cætera
                <expan abbr="quoq;">quoque</expan>
              conſequentur, quia
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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