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

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          <p>
            <s xml:id="echoid-s5471" xml:space="preserve">
              <pb o="13" file="0195" n="195" rhead=""/>
            bita tamen ratione proportionis inter minorem axim, & </s>
            <s xml:id="echoid-s5472" xml:space="preserve">maiorem, quæ
              <lb/>
            proportio, quò minor fuerit, eò magis E, terminus ſemi - recti lateris,
              <lb/>
            remouebitur à centro H, vt vel modicè introſpicienti ſatit conſtat.</s>
            <s xml:id="echoid-s5473" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div565" type="section" level="1" n="229">
          <head xml:id="echoid-head237" xml:space="preserve">THEOR. VI. PROP. X.</head>
          <p>
            <s xml:id="echoid-s5474" xml:space="preserve">Si quamcunque coni - fectionem recta linea contingat, cui à
              <lb/>
            tactu extra ſectionem perpendicularis erigatur, in qua ſumptum
              <lb/>
            ſit quodlibet punctum. </s>
            <s xml:id="echoid-s5475" xml:space="preserve">Linea intercepta inter aſſumptum pun-
              <lb/>
            ctum, & </s>
            <s xml:id="echoid-s5476" xml:space="preserve">contactum, erit MINIMA ducibilium ab eodem pun-
              <lb/>
            cto, ad conuexam coni-ſectionis peripheriam.</s>
            <s xml:id="echoid-s5477" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5478" xml:space="preserve">ESto coni-ſectio A B C, quam contingat recta D E in B, à quo ipſi
              <lb/>
            erecta ſit perpendicularis B F ad partes conuexæ peripheriæ ABC,
              <lb/>
            ſitque in ea aſſumptum quodlibet punctum F. </s>
            <s xml:id="echoid-s5479" xml:space="preserve">Dico rectam F B eſſe _MI-_
              <lb/>
            _NIMAM_ rectarum ducibilium ab F ad conuexam peripheriam A B C.</s>
            <s xml:id="echoid-s5480" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5481" xml:space="preserve">Hoc enim per ſe ſatis patet: </s>
            <s xml:id="echoid-s5482" xml:space="preserve">nam cum
              <lb/>
              <figure xlink:label="fig-0195-01" xlink:href="fig-0195-01a" number="155">
                <image file="0195-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0195-01"/>
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            F B ſit perpendicularis rectæ D E, erit
              <lb/>
            quoque _MINIMA_ ducibilium ad
              <note symbol="a" position="right" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">ex ele-
                <lb/>
              mentis.</note>
            D E, quare F B eò magis erit _MINIMA_
              <lb/>
            ducibilium ad conuexam A B C, quę ca-
              <lb/>
            dit infra D E. </s>
            <s xml:id="echoid-s5483" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s5484" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5485" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5486" xml:space="preserve">Quod autem de coni - ſectione hoc
              <lb/>
            loco oſtenditur, de quacunque etiam
              <lb/>
            curua linea verificari ex ipſa figura ſatis
              <lb/>
            patet, dummodo curua A B C ſit tota ad
              <lb/>
            alteram partem contingentis D E, per-
              <lb/>
            pendicularis verò B F ad aliam.</s>
            <s xml:id="echoid-s5487" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div567" type="section" level="1" n="230">
          <head xml:id="echoid-head238" xml:space="preserve">THEOR. VII. PROP. XI.</head>
          <p>
            <s xml:id="echoid-s5488" xml:space="preserve">Si quamcunq, coni-ſectionem recta linea, pręter ad axis ver-
              <lb/>
            ticem contingat, cui à tactu intra ſectionem erigatur perpendi-
              <lb/>
            cularis, in qua ſumptum ſit punctum quodlibet, non tamen, quò
              <lb/>
            ad Ellipſim, vltra maiorem axim; </s>
            <s xml:id="echoid-s5489" xml:space="preserve">linea intercepta inter aſſum-
              <lb/>
            ptum punctum, & </s>
            <s xml:id="echoid-s5490" xml:space="preserve">contactum erit MINIMA ducibilium ex eo-
              <lb/>
            dem puncto, ad coni- ſectionis peripheriam.</s>
            <s xml:id="echoid-s5491" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5492" xml:space="preserve">Si verò in Ellipſi aſſumptum punctum in perpendiculari fue-
              <lb/>
            rit, vel in ipſo minori axe, vel vltra: </s>
            <s xml:id="echoid-s5493" xml:space="preserve">linea inter punctum, & </s>
            <s xml:id="echoid-s5494" xml:space="preserve">
              <lb/>
            contactum intercepta erit MAXIMA ducibilium ex ipſomet pun-
              <lb/>
            cto ad Ellipſis peripheriam.</s>
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          </p>
          <p>
            <s xml:id="echoid-s5496" xml:space="preserve">ESto A B C Parabole, vel Hyperbole, vt in prima figura, vel Ellipſis,
              <lb/>
            vt in ſecunda, circa maiorem axim B D, quas in puncto A </s>
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