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

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        <div xml:id="echoid-div461" type="section" level="1" n="189">
          <head xml:id="echoid-head194" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s4654" xml:space="preserve">PAtet quoque in Parabola, & </s>
            <s xml:id="echoid-s4655" xml:space="preserve">Hyperbola interceptam axis portionem in-
              <lb/>
            ter verticem, & </s>
            <s xml:id="echoid-s4656" xml:space="preserve">contingenti perpendicularem ſemper item eſſe pluſ-
              <lb/>
            quam dimidium recti lateris propriæ ſectionis. </s>
            <s xml:id="echoid-s4657" xml:space="preserve">Quoniam cum demonſtra-
              <lb/>
            tum ſit DB maiorem eſſe DA, & </s>
            <s xml:id="echoid-s4658" xml:space="preserve">DA in præcedenti Corollario ſit maior
              <note symbol="a" position="right" xlink:label="note-0163-01" xlink:href="note-0163-01a" xml:space="preserve">88. h.</note>
            midio rectilateris, eò magis DB erit maior prædicto dimidio.</s>
            <s xml:id="echoid-s4659" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div463" type="section" level="1" n="190">
          <head xml:id="echoid-head195" xml:space="preserve">COROLL. III.</head>
          <p>
            <s xml:id="echoid-s4660" xml:space="preserve">MAnifeſtum eſt etiam in Hyperbola, & </s>
            <s xml:id="echoid-s4661" xml:space="preserve">Ellipſi ſemper eam axis portio-
              <lb/>
            nem, quæ eſt inter centrum ſectionis, & </s>
            <s xml:id="echoid-s4662" xml:space="preserve">ordinatim ductam ex con-
              <lb/>
            tactu, ad portionem eiuſdem axis inter ipſam ordinatam, & </s>
            <s xml:id="echoid-s4663" xml:space="preserve">contingenti
              <lb/>
            perpendicularem, eſſe vt ſemi-tranſuerſum ſectionis ad ſemi-rectum, vel vt
              <lb/>
            tranſuerſum ad rectum. </s>
            <s xml:id="echoid-s4664" xml:space="preserve">Demonſtratum eſt enim in ſecunda, tertia, & </s>
            <s xml:id="echoid-s4665" xml:space="preserve">quar-
              <lb/>
            ta figura rectam GF ad FD eſſe vt tranſuerſum latus ad rectum.</s>
            <s xml:id="echoid-s4666" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div464" type="section" level="1" n="191">
          <head xml:id="echoid-head196" xml:space="preserve">THEOR. XLV. PROP. XCI.</head>
          <p>
            <s xml:id="echoid-s4667" xml:space="preserve">Si Ellipſim quædam recta linea contingat inter axium extrema,
              <lb/>
            cui à tactu ducta ſit perpendicularis cum vtroque axe conueniens,
              <lb/>
            ſemper ipſius portio inter contactum, & </s>
            <s xml:id="echoid-s4668" xml:space="preserve">minorem axim intercepta,
              <lb/>
            eſt maior ſemi-axe maiori; </s>
            <s xml:id="echoid-s4669" xml:space="preserve">portio verò inter contactum, & </s>
            <s xml:id="echoid-s4670" xml:space="preserve">maio-
              <lb/>
            rem axim, maior eſt ſemi-recto latere maioris axis; </s>
            <s xml:id="echoid-s4671" xml:space="preserve">& </s>
            <s xml:id="echoid-s4672" xml:space="preserve">eadem por-
              <lb/>
            tio eſt minor ſemi-axe minori; </s>
            <s xml:id="echoid-s4673" xml:space="preserve">ac demum portio inter contactum,
              <lb/>
            & </s>
            <s xml:id="echoid-s4674" xml:space="preserve">minorem axim minor eſt ſemi-recto latere minoris axis.</s>
            <s xml:id="echoid-s4675" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4676" xml:space="preserve">SIt Ellipſis ABC, cuius maior axis BC, minor IL, centrum G, & </s>
            <s xml:id="echoid-s4677" xml:space="preserve">quædam
              <lb/>
            contingens MAE inter axium extrema, quæ ipſis occurret in E, M; </s>
            <s xml:id="echoid-s4678" xml:space="preserve">&</s>
            <s xml:id="echoid-s4679" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-0163-02" xlink:href="note-0163-02a" xml:space="preserve">25. pri-
                <lb/>
              mi conic.</note>
            ex A ducta ſit ADH contingenti perpendicularis, quæ vtrique axi occurret,
              <lb/>
            ſed priùs cum maiori in D, cum minori verò in H.</s>
            <s xml:id="echoid-s4680" xml:space="preserve"/>
          </p>
          <note symbol="c" position="right" xml:space="preserve">88. h.</note>
          <p>
            <s xml:id="echoid-s4681" xml:space="preserve">Dico primùm interceptam AH ſemper maiorem eſſe maiori ſemi-axe
              <lb/>
            G B.</s>
            <s xml:id="echoid-s4682" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4683" xml:space="preserve">Agatur HP æquidiſtans ad GE, & </s>
            <s xml:id="echoid-s4684" xml:space="preserve">AFO ad NH. </s>
            <s xml:id="echoid-s4685" xml:space="preserve">Et quoniam eſt HP ma-
              <lb/>
            ior GE, & </s>
            <s xml:id="echoid-s4686" xml:space="preserve">HO æqualis GF, erit rectangulum PHO, ſiue quadratum HA (in
              <lb/>
            triangulo rectangulo PAH) maius rectangulo EGF, ſiue quadrato
              <note symbol="d" position="right" xlink:label="note-0163-04" xlink:href="note-0163-04a" xml:space="preserve">37. pri-
                <lb/>
              mi conic.</note>
            hoc eſt linea AH maior ipſa GB. </s>
            <s xml:id="echoid-s4687" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s4688" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4689" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4690" xml:space="preserve">Ampliùs, dico AD eſſe pluſquam dimidium recti lateris axis BC.</s>
            <s xml:id="echoid-s4691" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4692" xml:space="preserve">Quoniam cum ſit GB minor AH, vt modò oſtendimus, habebit GD ad
              <lb/>
            AD minorem rationem quàm AH ad AD, vel quàm FG ad FD, vel quàm
              <lb/>
            eadem GB ſemi-tranſuerſum, ad ſemi-rectum; </s>
            <s xml:id="echoid-s4693" xml:space="preserve">vnde AD erit maior
              <note symbol="e" position="right" xlink:label="note-0163-05" xlink:href="note-0163-05a" xml:space="preserve">3. Co-
                <lb/>
              roll. 90. h.</note>
            ſemi-rectum latus maioris axis. </s>
            <s xml:id="echoid-s4694" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s4695" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4697" xml:space="preserve">Dico præterea eandem portionem AD minorem eſſe quam IG dimidium
              <lb/>
            minoris axis.</s>
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