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

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        <div xml:id="echoid-div626" type="section" level="1" n="247">
          <head xml:id="echoid-head255" xml:space="preserve">THEOR. XVII. PROP. XXV.</head>
          <p>
            <s xml:id="echoid-s6072" xml:space="preserve">Rectorum laterum in Parabola, MINIMVM eſt rectum axis.</s>
            <s xml:id="echoid-s6073" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6074" xml:space="preserve">ESto Parabole A B C, cuius axis B D, rectum B E. </s>
            <s xml:id="echoid-s6075" xml:space="preserve">Dico ipſum B E
              <lb/>
            reliquorum rectorum eſſe _MINIMVM_. </s>
            <s xml:id="echoid-s6076" xml:space="preserve">Sit quælibet alia diameter
              <lb/>
            A F, quæ axi B D æquidiſtabit, ſitque ad A contingens A G, & </s>
            <s xml:id="echoid-s6077" xml:space="preserve">B
              <note symbol="a" position="right" xlink:label="note-0217-01" xlink:href="note-0217-01a" xml:space="preserve">ex 46.
                <lb/>
              pr. conic.</note>
            ipſi A G æquidiſtans, quæ diametro A F erit ordinatim applicata; </s>
            <s xml:id="echoid-s6078" xml:space="preserve">tan-
              <lb/>
            dem axi applicetur A H, ſumaturque A I æqualis recto diametri A F.</s>
            <s xml:id="echoid-s6079" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6080" xml:space="preserve">Iam, ob contingentem A G, cum ſit
              <lb/>
            H B æqualis B G, & </s>
            <s xml:id="echoid-s6081" xml:space="preserve">F A eidem B G ę-
              <lb/>
              <figure xlink:label="fig-0217-01" xlink:href="fig-0217-01a" number="178">
                <image file="0217-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0217-01"/>
              </figure>
            qualis, erit H B ęqualis F A: </s>
            <s xml:id="echoid-s6082" xml:space="preserve">rectan-
              <lb/>
            gulum ergo H B E ad F A I, vel qua-
              <lb/>
            dratum H A, ad quadratum B
              <note symbol="b" position="right" xlink:label="note-0217-02" xlink:href="note-0217-02a" xml:space="preserve">Coroll.
                <lb/>
              primæ 1.
                <lb/>
              huius.</note>
            vel ad quadratum G A, erit vt B E
              <lb/>
            ad A I, ſed eſt quadratum A H minus
              <lb/>
            quadrato A G, ſiue recta A H minor
              <lb/>
            recta A G, cum acutus angulus A G B
              <lb/>
            minor ſit recto A H G, quare B E
              <lb/>
            rectum, minus erit recto A I: </s>
            <s xml:id="echoid-s6083" xml:space="preserve">eadem-
              <lb/>
            que ratione demonſtrabitur B E quo-
              <lb/>
            cunque alio recto minus eſſe: </s>
            <s xml:id="echoid-s6084" xml:space="preserve">quare
              <lb/>
            B E rectum axis, eſt _MINIMVM._
              <lb/>
            </s>
            <s xml:id="echoid-s6085" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s6086" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div629" type="section" level="1" n="248">
          <head xml:id="echoid-head256" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s6087" xml:space="preserve">HInc patet, data quacunque Parabolæ diametro, ſi quæratur ratio
              <lb/>
            inter eius rectum, rectumque axis, hanc ipſam reperiri inter qua-
              <lb/>
            dratum contingentis interceptæ, à vertice datæ diametri vſque ad axim,
              <lb/>
            & </s>
            <s xml:id="echoid-s6088" xml:space="preserve">quadratum axi ſemi-applicatæ ab eodem vertice.</s>
            <s xml:id="echoid-s6089" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6090" xml:space="preserve">Verùm ſi omnium rectorum continuam proportionem, in lineis, & </s>
            <s xml:id="echoid-s6091" xml:space="preserve">
              <lb/>
            veluti ipſorum quandam propagationem ante oculos ponere expetemus, id
              <lb/>
            à proximo Theoremate addiſcere liceat.</s>
            <s xml:id="echoid-s6092" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div630" type="section" level="1" n="249">
          <head xml:id="echoid-head257" xml:space="preserve">THEOR. XIIX. PROP. XXVI.</head>
          <p>
            <s xml:id="echoid-s6093" xml:space="preserve">Recta latera diametrorum in Parabola, ſunt inter ſe in ratio-
              <lb/>
            ne linearum ex puncto axis remoto à vertice per quadrantem
              <lb/>
            ſui recti, ad ipſarum diametrorum vertices eductarum.</s>
            <s xml:id="echoid-s6094" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6095" xml:space="preserve">ESto Parabole A B C, cuius axis B D rectum B I, ac eius quarta pars
              <lb/>
            ſit B D, & </s>
            <s xml:id="echoid-s6096" xml:space="preserve">quælibet aliæ diametri ſint A E, F G, &</s>
            <s xml:id="echoid-s6097" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6098" xml:space="preserve">quarum ver-
              <lb/>
            tices iungantur rectis D B, D A, D F, &</s>
            <s xml:id="echoid-s6099" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6100" xml:space="preserve">Dico, tùm axis, tùm prædi-
              <lb/>
            ctorum diametrorum latera eſſe inter ſe, vt ſunt ipſæ eductæ D B, D A,
              <lb/>
            D F, &</s>
            <s xml:id="echoid-s6101" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6102" xml:space="preserve"/>
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