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

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        <div xml:id="echoid-div598" type="section" level="1" n="242">
          <head xml:id="echoid-head250" xml:space="preserve">THEOR. XV. PROP. XXI.</head>
          <p>
            <s xml:id="echoid-s5767" xml:space="preserve">Semita MINIMARVM linearum, ducibilium à puncto com-
              <lb/>
            munis axis infinitarum Parabolarum, per eundem verticem ſi-
              <lb/>
            mul adſcriptarum, ad earundem ſectionum peripherias, eſt cir-
              <lb/>
            cumferentia Ellipſis, cuius tranſuerſum latus ſit ipſum axis ſe-
              <lb/>
            gmentum, inter aſſumptum punctum, & </s>
            <s xml:id="echoid-s5768" xml:space="preserve">vertieem interceptum:
              <lb/>
            </s>
            <s xml:id="echoid-s5769" xml:space="preserve">rectum verò eiuſdem tranſuerſi ſit duplum.</s>
            <s xml:id="echoid-s5770" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5771" xml:space="preserve">ESto Parabole A B C, cuius axis B D, in quo ſumptum ſit punctum D
              <lb/>
            à vertice B diſtans per interuallum æquale dimidio ſui recti B E: </s>
            <s xml:id="echoid-s5772" xml:space="preserve">pa-
              <lb/>
            tet ipſam D B eſſe _MINIMAM_ ad peripheriam A B C; </s>
            <s xml:id="echoid-s5773" xml:space="preserve">& </s>
            <s xml:id="echoid-s5774" xml:space="preserve">ſi aliæ
              <note symbol="a" position="right" xlink:label="note-0207-01" xlink:href="note-0207-01a" xml:space="preserve">9. huius
                <lb/>
              ad nu. 1.</note>
            bolæ concipiantur per B adſcriptæ, quarum recta latera excedant B E,
              <lb/>
            conſtat ipſas cadere extra, qualis eſt M B N, & </s>
            <s xml:id="echoid-s5775" xml:space="preserve">eandem D B (quæ
              <note symbol="b" position="right" xlink:label="note-0207-02" xlink:href="note-0207-02a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19.
                <lb/>
              pr. huius.</note>
            nino erit minor dimidio ipſius rectilateris) ad eius peripheriam eſſe _MI-_ _NIMAM_. </s>
            <s xml:id="echoid-s5776" xml:space="preserve">At ſi Parabolæ fuerint ipſi A B C per B verticem inſcriptæ,
              <lb/>
              <note symbol="c" position="right" xlink:label="note-0207-03" xlink:href="note-0207-03a" xml:space="preserve">9. huius
                <lb/>
              ad nu. 1.</note>
              <figure xlink:label="fig-0207-01" xlink:href="fig-0207-01a" number="168">
                <image file="0207-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0207-01"/>
              </figure>
            patet etiam ipſarum latera minora eſſe recto B E, ac ideo D E
              <note symbol="d" position="right" xlink:label="note-0207-04" xlink:href="note-0207-04a" xml:space="preserve">ex 2. Co
                <lb/>
              roll. 19.
                <lb/>
              pr. huius.</note>
            libet ipſorum laterum dimidium excedere, & </s>
            <s xml:id="echoid-s5777" xml:space="preserve">_MINIMAS_ ducibiles ex D,
              <lb/>
            ad harum Parabolarum peripherias pertingere, præter ad verticem B. </s>
            <s xml:id="echoid-s5778" xml:space="preserve">Si
              <lb/>
            ergo quæratur, quàm delineent ſemitam harum _MINIMARV M_ extrema
              <lb/>
            puncta. </s>
            <s xml:id="echoid-s5779" xml:space="preserve">Deſcribatur circa ſegmentum axis B D, tanquam circa tranſuer-
              <lb/>
            ſum latus, Ellipſis B F D G, cuius rectum ſit ipſum B E. </s>
            <s xml:id="echoid-s5780" xml:space="preserve">Conſtat hanc
              <lb/>
            eſſe _MAXIMAM_ Parabolæ A B C per B verticem inſcriptibilem. </s>
            <s xml:id="echoid-s5781" xml:space="preserve">
              <note symbol="e" position="right" xlink:label="note-0207-05" xlink:href="note-0207-05a" xml:space="preserve">ex 20.
                <lb/>
              pr. huius.</note>
            huius peripheriam B F D G prædictarum _MINIMARV M_ eſſe tramitem.</s>
            <s xml:id="echoid-s5782" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5783" xml:space="preserve">Iungatur Ellipſis regula D E: </s>
            <s xml:id="echoid-s5784" xml:space="preserve">& </s>
            <s xml:id="echoid-s5785" xml:space="preserve">Parabolę A B C inſcribatur quælibet
              <lb/>
            alia F B G, quæ Ellipſis peripheriam ad vtranq; </s>
            <s xml:id="echoid-s5786" xml:space="preserve">partem omnino ſecabit, </s>
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