Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <p>
            <s xml:id="echoid-s4626" xml:space="preserve">Nam quadratum AF æquatur rectangulo ſub FB, & </s>
            <s xml:id="echoid-s4627" xml:space="preserve">recto latere,
              <note symbol="a" position="left" xlink:label="note-0162-01" xlink:href="note-0162-01a" xml:space="preserve">Coroll.
                <lb/>
              1. h.</note>
            ſub dupla FB, ſiue ſub EF, & </s>
            <s xml:id="echoid-s4628" xml:space="preserve">dimidio recti, ſed idem quadratum A F æ- quatur rectangulo ſub eadem EF, & </s>
            <s xml:id="echoid-s4629" xml:space="preserve">ſub FD; </s>
            <s xml:id="echoid-s4630" xml:space="preserve">quare FD erit dimidium recti.
              <lb/>
            </s>
            <s xml:id="echoid-s4631" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-0162-02" xlink:href="note-0162-02a" xml:space="preserve">35. pri-
                <lb/>
              mi conic.</note>
            Quod primò, &</s>
            <s xml:id="echoid-s4632" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4633" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4634" xml:space="preserve">Amplius in Hyperbola ſecundæ figuræ, dico interceptam portionem FD
              <lb/>
            eſſe pluſquam dimidium recti lateris.</s>
            <s xml:id="echoid-s4635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4636" xml:space="preserve">Nam reperto eius centro G, erit rectangulum GFE ad quadratum AF,
              <lb/>
            vel ad rectangulum DFE, vt tranſuerſum latus ad rectum, ſed
              <note symbol="c" position="left" xlink:label="note-0162-03" xlink:href="note-0162-03a" xml:space="preserve">37. pri-
                <lb/>
              mi conic.</note>
            GFE ad DFE, eſt vt linea GF ad FD, ergo GF ad FD eſt vt tranſuerſum la-
              <lb/>
            tus ad rectum, vel vt ſemi-tranſuerſum GB ad ſemi-rectum, & </s>
            <s xml:id="echoid-s4637" xml:space="preserve">permutando
              <lb/>
            GF ad GB, erit vt FD ad ſemirectum, ſed eſt GF maior GB, ergo FD erit
              <lb/>
            maior ſemi-recto latere. </s>
            <s xml:id="echoid-s4638" xml:space="preserve">Quod ſecundò erat, &</s>
            <s xml:id="echoid-s4639" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4640" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4641" xml:space="preserve">Tandem in Ellipſi
              <lb/>
              <figure xlink:label="fig-0162-01" xlink:href="fig-0162-01a" number="128">
                <image file="0162-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0162-01"/>
              </figure>
            tertiæ figuræ, in qua
              <lb/>
            intercepta axis portio
              <lb/>
            DF eſt de maiori axe,
              <lb/>
            vel in quarta figura, in
              <lb/>
            qua prædicta portio
              <lb/>
            DF eſt de minori axe,
              <lb/>
            dico item ipſam DF
              <lb/>
            minorem eſſe dimidio
              <lb/>
            recti lateris eius axis,
              <lb/>
            cui ductæ perpendicu-
              <lb/>
            lares occurrunt.</s>
            <s xml:id="echoid-s4642" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4643" xml:space="preserve">Sumpto enim Elli-
              <lb/>
            pſis centro G, eſt re-
              <lb/>
            ctangulũ EFG ad qua-
              <lb/>
            dratum AF, vel ad re-
              <lb/>
            ctangulum E F D,
              <note symbol="d" position="left" xlink:label="note-0162-04" xlink:href="note-0162-04a" xml:space="preserve">ibidem.</note>
            tranſuerſum latus ad
              <lb/>
            rectum, ſed idem rectangulum EFG ad EFD eſt vt linea GF ad FD quare
              <lb/>
            GF ad FD eſt vt tranſuerſum ad rectum, vel vt GB dimidium tranſuerſi ad
              <lb/>
            dimidium recti, & </s>
            <s xml:id="echoid-s4644" xml:space="preserve">permutando GF ad GB, vt FD ad dimidium recti, ſed eſt
              <lb/>
            GF minor GB, ergo & </s>
            <s xml:id="echoid-s4645" xml:space="preserve">FD erit minor quàm dimidium recti. </s>
            <s xml:id="echoid-s4646" xml:space="preserve">Quod vlti-
              <lb/>
            mò, &</s>
            <s xml:id="echoid-s4647" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4648" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div460" type="section" level="1" n="188">
          <head xml:id="echoid-head193" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s4649" xml:space="preserve">HInc patet in Parabola, & </s>
            <s xml:id="echoid-s4650" xml:space="preserve">Hyperbola contingenti perpendicularem in-
              <lb/>
            ter contactum, & </s>
            <s xml:id="echoid-s4651" xml:space="preserve">axem, ſemper eſſe pluſquam dimidium recti lateris
              <lb/>
            ſectionis. </s>
            <s xml:id="echoid-s4652" xml:space="preserve">Nam in triangulo AFD recta AD recto angulo oppoſita maior eſt
              <lb/>
            latere DF, ſed DF, vel æqualis eſt (in Parabola) vel maior (in Hyperbola)
              <lb/>
            prædicto dimidio, quare perpẽdicularis AD erit omninò maior ipſo dimidio.</s>
            <s xml:id="echoid-s4653" xml:space="preserve"/>
          </p>
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