Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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    <archimedes>
      <text>
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          <chap>
            <pb pagenum="207" xlink:href="009/01/207.jpg"/>
            <p type="main">
              <s id="s.003472">Pergit adhuc nouis rationibus aduerſarios refellere, dicens, ſi extarent
                <lb/>
              huiuſmodi indiuiduæ lineæ, ſequeretur omnes omninò lineas eſſe commen­
                <lb/>
              ſurabiles, quod eſt contra demonſtrata in 10. Elem. quia cum omnes lineæ
                <lb/>
                <expan abbr="conſtẽt">conſtent</expan>
              per ipſos ex lineis atomis, iſtæ atomæ eſſent omnium linearum com­
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              munes menſuræ, vnde & illæ, quæ dicuntur potentia tantum commenſura­
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              biles, vt ſupra explicaui, erunt etiam commenſurabiles longitudine. </s>
              <s id="s.003473">indiui­
                <lb/>
              duæ verò ipſæ, cum ſint inuicem æquales, erunt ipſæ
                <expan abbr="quoq;">quoque</expan>
              commenſurabi­
                <lb/>
              les longitudine, quare & potentia, omnes enim longitudine commenſura­
                <lb/>
              biles, ſunt etiam potentia commenſurabiles, ex 9. 10. vnde ſequitur qua­
                <lb/>
              drata earum omnia eſſe
                <expan abbr="quoq;">quoque</expan>
              commenſurabilia:
                <expan abbr="atq;">atque</expan>
              hinc conſequitur, in­
                <lb/>
              quit, ea eſſe
                <expan abbr="quoq;">quoque</expan>
              diuidua (quam conſecutionem probat infra num. </s>
              <s id="s.003474">290.)
                <lb/>
              vnde ſequeretur ipſam
                <expan abbr="quoq;">quoque</expan>
              lineam latus quadrati poſſe diuidi, non igitur
                <lb/>
              ponenda erat indiuidua.</s>
            </p>
            <p type="main">
              <s id="s.003475">
                <arrow.to.target n="marg275"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003476">
                <margin.target id="marg275"/>
              285</s>
            </p>
            <p type="main">
              <s id="s.003477">Nonus Iocus, cuius latinam interpretationem, cum admodum eſſet de­
                <lb/>
              prauata ex græco textu, in hunc modum correxi
                <emph type="italics"/>
              (Præterea cùm circa maio­
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              rem latitudinem facit applicata, æquale ei, quod ab indiuidua, & pedali copulatis
                <lb/>
              circa bipedalem, minorem faciet latitudinem, quàm ſit indiuidua: erit minus, quod
                <lb/>
              circa indiuiduam)
                <emph.end type="italics"/>
              ideſt cùm minor linea applicata cum maiore, latitudinem
                <lb/>
                <figure id="id.009.01.207.1.jpg" place="text" xlink:href="009/01/207/1.jpg" number="129"/>
                <lb/>
              faciat. </s>
              <s id="s.003478">v. g. linea minor A B, applicata cum ma­
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              iori B C, vt in figura, ita vt contineant figuram
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              A B C D. </s>
              <s id="s.003479">Minor A B, facit latitudinem figuræ,
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              maior verò B C, facit longitudinem. </s>
              <s id="s.003480">Iam cum
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              aduerſarij velint extare huiuſmodi lineas ato­
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              mas, conſtituatur figura ſub vna ex illis, quæ ſit v. g. A B, & altera maiori,
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              quæ ſit pedalis, v. g. B C, vt in præcedenti figura, ſumatur deinde linea bi­
                <lb/>
                <figure id="id.009.01.207.2.jpg" place="text" xlink:href="009/01/207/2.jpg" number="130"/>
                <lb/>
              pedalis E F, cui per 45. primi ap­
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              plicetur ſpatium E F G H, æquale
                <lb/>
              ſpatio ſuperiori A B C D, neceſſa­
                <lb/>
              riò latitudo E H, huius ſecundæ fi­
                <lb/>
              guræ minor erit quàm latitudo il­
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              lius, hoc eſt minor, quàm ſit indiuidua A B, quod eſt abſurdum. </s>
              <s id="s.003481">vel dicere
                <lb/>
              oportet
                <expan abbr="ſpatiũ">ſpatium</expan>
              circa indiuiduam A B, eſſe minus quàm iſtud poſterius, quod
                <lb/>
              eſt contra conſtructionem, & propterea pariter inconueniens, non igitur
                <lb/>
              huiuſmodi lineæ ſunt ponendæ.</s>
            </p>
            <p type="main">
              <s id="s.003482">
                <arrow.to.target n="marg276"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003483">
                <margin.target id="marg276"/>
              286</s>
            </p>
            <p type="main">
              <s id="s.003484">Decimus locus
                <emph type="italics"/>
              (Cum ex tribus datis lineis triangulus componatur, ex tribus
                <lb/>
                <expan abbr="quoq;">quoque</expan>
              indiuiduis lineis componi poterit. </s>
              <s id="s.003485">in omni autem æquilatero perpendicularis
                <lb/>
              in mediam baſim incidit, quare, & in medium indiuiduæ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.003486">Ex 22. primi Elem. ex tribus datis lineis, quarum quælibet duæ ſint, re­
                <lb/>
              liqua maiores poteſt conſtitui triangulum: poterit igitur ex tribus indiui­
                <lb/>
                <figure id="id.009.01.207.3.jpg" place="text" xlink:href="009/01/207/3.jpg" number="131"/>
                <lb/>
              duis conſtitui
                <expan abbr="triãgulum">triangulum</expan>
              ,
                <expan abbr="illudq́">illudque</expan>
              ; æquilaterum, cum omnes in­
                <lb/>
              diuiduæ lineæ ſint æquales. </s>
              <s id="s.003487">ſit igitur ex eis triangulum A B C,
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              ſi igitur ab angulo A, ducatur perpendicularis A D, ad baſim
                <lb/>
              B C, eam bifariam ſecabit ex ſcholio 26. primi, erit igitur li­
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              nea B C, ſecabilis, contra quam aduerſarij opinantur.</s>
            </p>
            <p type="main">
              <s id="s.003488">
                <arrow.to.target n="marg277"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003489">
                <margin.target id="marg277"/>
              287</s>
            </p>
            <p type="main">
              <s id="s.003490">Vndecimus locus
                <emph type="italics"/>
              (Si quadratum ex quatuor indiuiduis conſtituatur diametro
                <lb/>
              protracta, & perpendiculari ducta, quadrati coſta potentia
                <expan abbr="perpẽdicularem">perpendicularem</expan>
              , diame-
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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