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

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        <div xml:id="echoid-div342" type="section" level="1" n="147">
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        <div xml:id="echoid-div345" type="section" level="1" n="148">
          <head xml:id="echoid-head153" xml:space="preserve">THEOR. XXXIV. PROP. LXIII.</head>
          <p>
            <s xml:id="echoid-s3598" xml:space="preserve">In quacunque coni-ſectione, etiam in triangulo, MAXIMA
              <lb/>
            diametro æquidiſtantium inter ſectionem, & </s>
            <s xml:id="echoid-s3599" xml:space="preserve">quamcunque ordina-
              <lb/>
            tim applicatam interceptarum, eſt ipſa diameter; </s>
            <s xml:id="echoid-s3600" xml:space="preserve">aliarum verò
              <lb/>
            ea, quæ propinquior eſt diametro, maior eſt remotiori.</s>
            <s xml:id="echoid-s3601" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3602" xml:space="preserve">ESto triangulum, vt in prima figura, vel circuli, aut Ellipſis, vel Parabo-
              <lb/>
            læ, vel tandem Hyperbolæ portio ABC, vt in ſecunda, quarum dia-
              <lb/>
            meter ſit BD, & </s>
            <s xml:id="echoid-s3603" xml:space="preserve">ordinatim applicata ſit AC, ductiſque quotcunque EF,
              <lb/>
            GH, &</s>
            <s xml:id="echoid-s3604" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3605" xml:space="preserve">parallelis ad BD. </s>
            <s xml:id="echoid-s3606" xml:space="preserve">Dico BD eſſe _MAXIMAM_, diametro reliqua-
              <lb/>
            rum verò, propinquiorem EF, maiorem eſſe remotiori.</s>
            <s xml:id="echoid-s3607" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3608" xml:space="preserve">Nam ſi concipiatur ex B duci
              <lb/>
              <figure xlink:label="fig-0131-01" xlink:href="fig-0131-01a" number="96">
                <image file="0131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0131-01"/>
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            quædam linea ordinatim appli-
              <lb/>
            catæ AC æquidiſtans quæ
              <note symbol="a" position="right" xlink:label="note-0131-01" xlink:href="note-0131-01a" xml:space="preserve">17. pri-
                <lb/>
              mi conic.</note>
            cadet extra ſectionem, iungique
              <lb/>
            recta linea puncta E, B quæ
              <note symbol="b" position="right" xlink:label="note-0131-02" xlink:href="note-0131-02a" xml:space="preserve">10. pri.
                <lb/>
              conic. &
                <lb/>
              32. eiuſd.</note>
            cadet intra, patet ipſam EB ad al-
              <lb/>
            teram partem productam (cum
              <lb/>
            ſecet in B eam, quæ ducta ſit ex
              <lb/>
            B parallela ad AC) conuenire
              <lb/>
            quoque cum CA ad partes A, & </s>
            <s xml:id="echoid-s3609" xml:space="preserve">ſic BD maiorem eſſe recta EF, ſiue omnium
              <lb/>
            _MAXIMAM_. </s>
            <s xml:id="echoid-s3610" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s3611" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3612" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3613" xml:space="preserve">Item ſi puncta G, E, iungantur recta linea ipſa omnino cum
              <note symbol="c" position="right" xlink:label="note-0131-03" xlink:href="note-0131-03a" xml:space="preserve">22. pri.
                <lb/>
              conic. &
                <lb/>
              23. eiuſd.</note>
            extra ſectionem conueniet, ac propterea ſecabit priùs eam, quæ ex B ducta
              <lb/>
            ſit ipſi A C ęquidiſtans; </s>
            <s xml:id="echoid-s3614" xml:space="preserve">cum ergo GE ſecet vnam parallelarum, ſecabit quo-
              <lb/>
            que, ſi producatur, alteram CA ad partes A, & </s>
            <s xml:id="echoid-s3615" xml:space="preserve">ſic EF erit maior ipſa GH.
              <lb/>
            </s>
            <s xml:id="echoid-s3616" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s3617" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3618" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div348" type="section" level="1" n="149">
          <head xml:id="echoid-head154" xml:space="preserve">THEOR. XXXV. PROP. LXIV.</head>
          <p>
            <s xml:id="echoid-s3619" xml:space="preserve">Ellipſium æqualium diametrorum, eidem angulo, vel Parabo-
              <lb/>
            læ, vel Hyperbolæ, aut portioni Ellipticæ, vel circulari, quæ non
              <lb/>
            ſit maior Ellipſis, vel circuli dimidio, inſcriptarum, ſe mutuò, ac
              <lb/>
            ſectionem contingentium, quæ propior eſt vertici, minor eſt re-
              <lb/>
            motiori.</s>
            <s xml:id="echoid-s3620" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3621" xml:space="preserve">ESto ABC, vel angulus rectilineus, vel Parabole, vel Hyperbole, aut por-
              <lb/>
            tio non maior dimidio ſemi-Ellipſis, vel ſemi-circuli, cuius vertex B,
              <lb/>
            diameter BD, & </s>
            <s xml:id="echoid-s3622" xml:space="preserve">circa æqualia ipſius ſegmenta DE, EF adſcriptæ ſint dato
              <lb/>
            angulo, vel ſectioni Ellipſes DVE, ETF, ope diagonalium AG, IL, & </s>
            <s xml:id="echoid-s3623" xml:space="preserve">ap-
              <lb/>
            plicatarum KHV, NMT, vt in præcedenti Scholio monuimus, quæ anguli
              <lb/>
            latera, vel ſectionem contingent in K, V, N, T, eique erunt inſcriptæ, & </s>
            <s xml:id="echoid-s3624" xml:space="preserve">ſe
              <lb/>
            mutuò contingent in E (cum applicata LEG vtranque ſectionem contingat.)</s>
            <s xml:id="echoid-s3625" xml:space="preserve"/>
          </p>
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