Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.001421">
                <pb pagenum="77" xlink:href="009/01/077.jpg"/>
              non potuerunt tamen deſcribi, niſi finitæ; appoſitæ idcircò ſunt ad partes
                <lb/>
              illas, ad quas deberent eſſe infinitæ lineolæ quædam infinitatem indicantes.
                <lb/>
              </s>
              <s id="s.001422">debemus poſtea, vt mentem Ariſt. percipiamus concipere lineam A G E,
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              moueri circulariter facto centro in G. quæ quia infinita ſupponitur ad par­
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              tem E, ſecabit neceſſariò alteram
                <expan abbr="vtrinq;">vtrinque</expan>
              infinitam
                <foreign lang="grc">β</foreign>
              B,
                <expan abbr="illamq́">illamque</expan>
              ; neceſſariò
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              finito tempore percurret, finito enim tempore tota mundi circulatio per­
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              agitur, ſpatio videlicet viginti quatuor horarum. </s>
              <s id="s.001423">ex quo Ariſt. infert mun­
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              dum non poſſe eſſe infinitæ magnitudinis; quia ſi mundus eſſet infinitus; &.
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              </s>
              <s id="s.001424">duæ lineæ infinitæ, quales ſunt prædictæ in ipſo,
                <expan abbr="atq;">atque</expan>
              cum ipſo moueri alte­
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              ra earum A E, intelligatur, alteram
                <foreign lang="grc">β</foreign>
              B, manentem in tempore finito, ideſt,
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              in diurna conuerſione pertranſibit: fieri autem nequit, vt infinita magni­
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              tudo finito tempore percurratur; quare dicendum eſt, mundum eſſe finita
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              magnitudine præditum.</s>
            </p>
            <p type="main">
              <s id="s.001425">
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            <p type="margin">
              <s id="s.001426">
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              102</s>
            </p>
            <p type="main">
              <s id="s.001427">Tex. 48.
                <emph type="italics"/>
              (Nihil autem refert grauitates, commenſurabiles ſint, an incommen­
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              ſurabiles)
                <emph.end type="italics"/>
              quidnam ſit commenſurabilitas, & incommenſurabilitas, expli­
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              catum eſt lib. 1. Priorum, ſecto 1. cap. 23.</s>
            </p>
            <p type="main">
              <s id="s.001428">
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              </s>
            </p>
            <p type="margin">
              <s id="s.001429">
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              103</s>
            </p>
            <p type="main">
              <s id="s.001430">Tex. 119.
                <emph type="italics"/>
              (Est autem impoſſibile, & poſſibile; falſum, & verum, ex ſuppoſitio­
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              ne quidem, dico autem, vt triangulum impoſſibile eſt duos rectos habere, ſi hæc)
                <emph.end type="italics"/>
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              ideſt, ſi ſupponantur falſa quædam, quæ ſupponi poſſunt, ſequetur impoſſi­
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              bile eſſe triangulum habere tres angulos æquales duobus rectis angulis, vi­
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              de, quæ ſcripſi lib. 1. Priorum, ſecto 3. cap. 1. de hoc, quod eſt, habere tres
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              angulos æquales duobus rectis. </s>
              <s id="s.001431">v. g. ſi in triangulo pag. </s>
              <s id="s.001432">73. producto late­
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              re A C, in D. ſi ſupponatur externus angulus B C D, non eſſe æqualis duobus
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              internis, & oppoſitis A, & B, nunquam poterimus eo modo, quo Euclides,
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              demonſtrare paſſionem prædictam de triangulo A B C. huiuſmodi impoſſi­
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              bile, cuius oppoſitum non ſolum poſſibile, ſed etiam neceſſarium eſt, vocat
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              Ariſt. impoſſibile ex ſuppoſitione, quia ſcilicet impoſſibile euadit ex quo­
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              dam falſo ſuo ſuppoſito, vt in allato exemplo, triangulum habere tres an­
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              gulos æquales duobus rectis, quamuis neceſſarium ſit, tamen ex falſa ſup­
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              poſitione, impoſſibile euaſit.</s>
            </p>
            <p type="main">
              <s id="s.001433">
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              </s>
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            <p type="margin">
              <s id="s.001434">
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              104</s>
            </p>
            <p type="main">
              <s id="s.001435">Ibidem
                <emph type="italics"/>
              (Et diameter commenſurabilis est coſtæ, ſi hæc)
                <emph.end type="italics"/>
              vide primo Priorum,
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              ſecto 3. cap. 23. hoc ſolum nunc addendum
                <emph type="italics"/>
              (Si hæc)
                <emph.end type="italics"/>
              v. g. ſi ſupponamus li­
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              neas eſſe compoſitas ex indiuiſibilibus, conſectarium erit diametrum eſſe
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              commenſurabilem coſtæ, quia indiuiſibile illud, ex quo vtraque linea con­
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              ſtat, erit
                <expan abbr="vtriuſq;">vtriuſque</expan>
              menſura communis.</s>
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          </chap>
          <chap>
            <p type="head">
              <s id="s.001436">
                <emph type="italics"/>
              Ex Secundo de Cælo.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.001437">
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              </s>
            </p>
            <p type="margin">
              <s id="s.001438">
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              105</s>
            </p>
            <p type="main">
              <s id="s.001439">Tex. 24.
                <emph type="italics"/>
              (Amplius qui ſolida diuidunt in plana,
                <expan abbr="atq;">atque</expan>
              ex planis corpora
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              generant, his teſtes fuiſſe videntur: ſolam enim figurarum ſolidarum
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              ſphæram non diuidunt, vt non plures ſuperficies. </s>
              <s id="s.001440">quam vnam
                <expan abbr="habẽum">habentem</expan>
              .
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              </s>
              <s id="s.001441">diuiſio enim in plana non perinde efficitur, vt quiſpiam
                <expan abbr="diuidẽs">diuidens</expan>
              in par­
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              tes diuidat totum, ſed vt in ſpecie diuerſa: patet igitur ſphæram eſſe ſolidarum
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              primam)
                <emph.end type="italics"/>
              qui ſolida diuidunt in plana, ea diuidunt
                <expan abbr="ſecũdum">ſecundum</expan>
              numerum ſuper­
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              ficierum, quibus ambiuntur, v. g. diuidunt cubum in ſex ſuperficies, quia
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              cubus ſex quadratis planis ſuperficiebus continetur: qua ratione nequeunt </s>
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          </chap>
        </body>
      </text>
    </archimedes>
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