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

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        <div xml:id="echoid-div731" type="section" level="1" n="292">
          <pb o="69" file="0253" n="253" rhead=""/>
          <p>
            <s xml:id="echoid-s6997" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6998" xml:space="preserve">INter baſes æqualiũ portionum eiuſdem anguli, vel coni-ſectionis _MINIMA_
              <lb/>
            eſt ea illius portionis, cuius diameter ſit ſegmentum maioris axis, reſpectiuè
              <lb/>
            ad Ellipſim: </s>
            <s xml:id="echoid-s6999" xml:space="preserve">& </s>
            <s xml:id="echoid-s7000" xml:space="preserve">_MAXIMA_ eius, cuius diameter ſit ſegmentum minoris.</s>
            <s xml:id="echoid-s7001" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7002" xml:space="preserve">In qualibet enim ſigura, baſis A C portionis A B C, circa maiorem axim,
              <lb/>
            _MINIMA_ eſt baſium, aliarum æqualium portionum; </s>
            <s xml:id="echoid-s7003" xml:space="preserve">& </s>
            <s xml:id="echoid-s7004" xml:space="preserve">in Ellipſi baſis V
              <note symbol="a" position="right" xlink:label="note-0253-01" xlink:href="note-0253-01a" xml:space="preserve">47. h.</note>
            portionis V L T circa minorem, _MAXIMA_ eſt baſium, reliquarum æqualium
              <lb/>
            portionum, vel ipſæ ſimul ſint ſemi-Ellipſi minores, vel ſimul maiores, &</s>
            <s xml:id="echoid-s7005" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7006" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7007" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7008" xml:space="preserve">INter altitudines æqualium portionum de eodem angulo, vel coni-ſectione
              <lb/>
            _MAXIMA_ eſt ea illius portionis, cuius diameter ſit ſegmentum maioris axis
              <lb/>
            reſpectiuè ad Ellipſim, & </s>
            <s xml:id="echoid-s7009" xml:space="preserve">_MINIMA_ eius, cuius diameter ſit ſegmétum minoris.</s>
            <s xml:id="echoid-s7010" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7011" xml:space="preserve">Id autem in ſuperiori propoſitione oſtenſum fuit: </s>
            <s xml:id="echoid-s7012" xml:space="preserve">nempe B D, quæ eſt alti-
              <lb/>
            tudo portionis A B C, circa maiorem axim, maiorem eſſe O P altitudine ęqua-
              <lb/>
            lis portionis H O I, atque ampliùs, in Ellipſi, altitudinem M K portionis T M
              <lb/>
            V circa minorẽ axim, minorem eſſe altitudine X Z æqualis portionis HXI, &</s>
            <s xml:id="echoid-s7013" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7014" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7015" xml:space="preserve">E´ prima itaque harum concluſionum, elicitur veritas prop. </s>
            <s xml:id="echoid-s7016" xml:space="preserve">48. </s>
            <s xml:id="echoid-s7017" xml:space="preserve">& </s>
            <s xml:id="echoid-s7018" xml:space="preserve">49. </s>
            <s xml:id="echoid-s7019" xml:space="preserve">h. </s>
            <s xml:id="echoid-s7020" xml:space="preserve">ex
              <lb/>
            altera verò prop. </s>
            <s xml:id="echoid-s7021" xml:space="preserve">50. </s>
            <s xml:id="echoid-s7022" xml:space="preserve">è tertia denique prop. </s>
            <s xml:id="echoid-s7023" xml:space="preserve">51. </s>
            <s xml:id="echoid-s7024" xml:space="preserve">quæ omnia per ſe ſatis patent.</s>
            <s xml:id="echoid-s7025" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7026" xml:space="preserve">Sed hæc de planis, pro hac vice, dixiſſe ſufſiciat. </s>
            <s xml:id="echoid-s7027" xml:space="preserve">Nonnulla ſequuntur quæ
              <lb/>
            iam diù pariter circa ſolida à coni-ſectionibus genita excogitauimus. </s>
            <s xml:id="echoid-s7028" xml:space="preserve">Noua
              <lb/>
            omnia, ni fallor, omnia ſaltem geometrica: </s>
            <s xml:id="echoid-s7029" xml:space="preserve">quæ ſi apertæ iucunditatis referta
              <lb/>
            comperies amice Lector, reconditæ vtilitatis haud expertia eße aliquando te
              <lb/>
            certiorem factum non dubito.</s>
            <s xml:id="echoid-s7030" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div734" type="section" level="1" n="293">
          <head xml:id="echoid-head302" xml:space="preserve">THEOR. XXXIII. PROP. LII.</head>
          <p>
            <s xml:id="echoid-s7031" xml:space="preserve">Recta linea, quę à puncto extra planũ dato ſit ipſi plano perpẽdicu-
              <lb/>
            laris, MINIMA eſt rectarũ ab eodem pũcto ad idem planũ ducibiliũ.</s>
            <s xml:id="echoid-s7032" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7033" xml:space="preserve">SIt extra planum A B, punctum C, à quo ducta ſit ipſi
              <lb/>
              <figure xlink:label="fig-0253-01" xlink:href="fig-0253-01a" number="209">
                <image file="0253-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0253-01"/>
              </figure>
            plano perpendicularis C D. </s>
            <s xml:id="echoid-s7034" xml:space="preserve">Dico hanc eſſe _MINI_-
              <lb/>
            _MAM_ ducibilium ex C ad alia puncta plani A B.</s>
            <s xml:id="echoid-s7035" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7036" xml:space="preserve">Sumatur vbicunque in dato plano aliud punctum E,
              <lb/>
            iunganturque D E, C E. </s>
            <s xml:id="echoid-s7037" xml:space="preserve">Et cum C D recta ſit ad pla-
              <lb/>
            num A B, erit angulus C D E rectus, ideoque C E
              <note symbol="b" position="right" xlink:label="note-0253-02" xlink:href="note-0253-02a" xml:space="preserve">3. deſ.
                <lb/>
              vnd. Ele.</note>
            acutus, ſiue minor C D E: </s>
            <s xml:id="echoid-s7038" xml:space="preserve">quare C D minor erit C E,
              <lb/>
            & </s>
            <s xml:id="echoid-s7039" xml:space="preserve">hoc ſemper. </s>
            <s xml:id="echoid-s7040" xml:space="preserve">Vnde C D eſt _MINIMA_, &</s>
            <s xml:id="echoid-s7041" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7042" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s7043" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7044" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div737" type="section" level="1" n="294">
          <head xml:id="echoid-head303" xml:space="preserve">THEOR. XXXIV. PROP. LIII.</head>
          <p>
            <s xml:id="echoid-s7045" xml:space="preserve">Si in Cono, vel Cylindro recto planum ductum per vnum laterum
              <lb/>
            trianguli, vel rectanguli per axem eidem triangulo, vel rectangulo
              <lb/>
            rectum fuerit, idem planum in ipſo tantùm latere conicam, vel cy-
              <lb/>
            lindricam ſuperficiem continget, quæ tota cadet ad alteram partem
              <lb/>
            plani contingentis.</s>
            <s xml:id="echoid-s7046" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7047" xml:space="preserve">ESto in figura, (que & </s>
            <s xml:id="echoid-s7048" xml:space="preserve">Conum, & </s>
            <s xml:id="echoid-s7049" xml:space="preserve">Cylindrum rectum exhibeat) planum per
              <lb/>
            axẽ A B C, cui rectũ ſit aliud planũ G D K H tranſiens per latus A B, </s>
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