Biancani, Giuseppe, Aristotelis loca mathematica, 1615

List of thumbnails

< >
51
51 		52
52
53
53 		54
54
55
55 		56
56
57
57 		58
58
59
59 		60
60
< >
page |< < of 355 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000984">
                <pb pagenum="54" xlink:href="009/01/054.jpg"/>
                <figure id="id.009.01.054.1.jpg" place="text" xlink:href="009/01/054/1.jpg" number="25"/>
                <lb/>
              proportionem, quam 2. ad 1.
                <lb/>
              ſiue duplam, ergo etiam ſo­
                <lb/>
              nus totius chordæ A B, ad
                <expan abbr="ſo-nũ">ſo­
                  <lb/>
                num</expan>
              chordæ dimidiæ A C, ha­
                <lb/>
              bebit eandem rationem,
                <expan abbr="nimirũ">nimirum</expan>
              quam 2. ad 1. ſiue duplam. </s>
              <s id="s.000985">ſed ſonus chor­
                <lb/>
              dæ A B, ad ſonum chordæ A C, conſonat diapaſon, ſeu octauam, ergo in
                <lb/>
              data chorda collocata eſt conſonantia diapaſon, quod oportebat. </s>
              <s id="s.000986">vides me­
                <lb/>
              dium eſſe arithmeticam, concluſionem verò harmonicam. </s>
              <s id="s.000987">Aliud exemplum
                <lb/>
              Tonus, quod eſt
                <expan abbr="interuallũ">interuallum</expan>
              primæ vocis, Vt, ad ſecundam, Rè, in duo æqua­
                <lb/>
              lia ſemitonia diuidi nequit, ratio eſt Arithmetica, quia proportio ſuper­
                <lb/>
              particularis in duo æqualia arithmeticè ſecari nequit; at Tonus conſiſtit in
                <lb/>
              ratione ſuperparticulari, nempè in ſeſquioctaua, ergo Tonus bifariam diui­
                <lb/>
              di nequit. </s>
              <s id="s.000988">deſumptum eſt ex Boetio.</s>
            </p>
            <p type="main">
              <s id="s.000989">
                <arrow.to.target n="marg35"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000990">
                <margin.target id="marg35"/>
              35</s>
            </p>
            <p type="main">
              <s id="s.000991">Tex. 23.
                <emph type="italics"/>
              (Est autem ſic monſtrare, quemadmodum Bryſo quadraturam, ſecun­
                <lb/>
              dum enim commune monſtrant tales rationes)
                <emph.end type="italics"/>
              cum velit oſtendere veram de­
                <lb/>
              monſtrationem conſtare debere ex proprijs, non autem ex communibus;
                <lb/>
              primum affert exemplum demonſtrationis cuiuſdam Bryſonis, quæ ex com­
                <lb/>
              munibus procedat, vt autem benè intelligamus, qualeſnam ſint huiuſmodi
                <lb/>
              demonſtrationes, quæ per communia oſtendunt, legenda prius ea ſunt, quæ
                <lb/>
              ſcripſimus de quadratura circuli in prędicamento relationis. </s>
              <s id="s.000992">Bryſo itaque,
                <lb/>
              vt tradit Alexander, in hunc modum conabatur quadrare
                <expan abbr="circulũ">circulum</expan>
              . </s>
              <s id="s.000993">ſit qua­
                <lb/>
              drandus circulus A B C D, cui circumſcribatur quadratum E F G H. per
                <lb/>
              7 quarti, & alterum quadratum I L M N, eidem inſcribatur per 6. quarti,
                <lb/>
              quid autem ſit circumſcribere, & inſcribere figuram circulo, ex definitione
                <lb/>
                <figure id="id.009.01.054.2.jpg" place="text" xlink:href="009/01/054/2.jpg" number="26"/>
                <lb/>
              3. & 4. eiuſdem libri petatur, quamuis
                <lb/>
              ex inſpectione figuræ
                <expan abbr="pręsẽtis">pręsentis</expan>
              ſatis per­
                <lb/>
              cipi poſſit; deinde aliud
                <expan abbr="quadratũ">quadratum</expan>
              me­
                <lb/>
              dium inter prædicta duo conſtituatur,
                <lb/>
                <expan abbr="ſitq́">ſitque</expan>
              ; O P Q R. </s>
              <s id="s.000994">Iam ſic oſtendebat iſtud
                <lb/>
              medium quadratum eſſe æquale circu­
                <lb/>
              lo propoſito. </s>
              <s id="s.000995">
                <expan abbr="Quæcunq;">Quæcunque</expan>
              ſunt, ſimul ma­
                <lb/>
              iora eodem, & minora eodem, ſunt in­
                <lb/>
              uicem æqualia, ſed circulus, & quadra­
                <lb/>
              tum medium, ſunt ambo maiora qua­
                <lb/>
              drato inſcripto, & ambo minora qua­
                <lb/>
              drato circumſcripto, ergo circulus, &
                <lb/>
              quadratum medium, ſunt æqualia. </s>
              <s id="s.000996">vte­
                <lb/>
              batur, inquit Ariſt prędicto principio,
                <lb/>
              etiam numeris, lineis, temporibus, &
                <lb/>
              qualitatibus communi,
                <expan abbr="neq;">neque</expan>
              deducto ex natura circuli, aut quadrati, de qui­
                <lb/>
              bus erat demonſtratio. </s>
              <s id="s.000997">præterea aduertendum eſt, illud eſſe falſum, nam ſex,
                <lb/>
              & quinque, ambo ſunt maiores, quam quatuor, & minores, quam ſeptem,
                <lb/>
              & tamen non ſunt æquales.</s>
            </p>
            <p type="main">
              <s id="s.000998">
                <arrow.to.target n="marg36"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000999">
                <margin.target id="marg36"/>
              36</s>
            </p>
            <p type="main">
              <s id="s.001000">In codem textu
                <emph type="italics"/>
              (
                <expan abbr="Vnumquodq;">Vnumquodque</expan>
              autem ſcimus, non ſecundum accidens, quando
                <lb/>
              ſecundum illud cognoſcamus, ſecundum quod ineſt ex principijs illius, ſecundam
                <lb/>
              quod illud; vt duobus rectis æquales, habere, cui ineſt per ſe, quod dictum eſt ex
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum