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

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        <div xml:id="echoid-div495" type="section" level="1" n="201">
          <head xml:id="echoid-head206" xml:space="preserve">THEOR. IL. PROP. IIC.</head>
          <p>
            <s xml:id="echoid-s4924" xml:space="preserve">MAXIMORVM circulorum, ad puncta Parabolicę, aut Hy-
              <lb/>
            perbolicæ peripheriæ inſcriptorum, MINIMVS eſt, qui ad axis
              <lb/>
            verticem inſcribitur. </s>
            <s xml:id="echoid-s4925" xml:space="preserve">Aliorum verò is, cuius contactus magis
              <lb/>
            diſtat à vertice, maior eſt, neque datur MAXIMVS.</s>
            <s xml:id="echoid-s4926" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4927" xml:space="preserve">ESto Parabole, vel Hyperbole ABC, cuius axis B D, vertex B, & </s>
            <s xml:id="echoid-s4928" xml:space="preserve">in
              <lb/>
            eius peripheria ſumpta ſint quælibet puncta A, E extra verticem
              <lb/>
            B, à quo agantur contingentibus per-
              <lb/>
              <figure xlink:label="fig-0172-01" xlink:href="fig-0172-01a" number="138">
                <image file="0172-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0172-01"/>
              </figure>
            pendiculares AD, E G, & </s>
            <s xml:id="echoid-s4929" xml:space="preserve">ab axe
              <lb/>
            abſciſſa ſit B F, æqualis dimidio recti
              <lb/>
            datæ ſectionis. </s>
            <s xml:id="echoid-s4930" xml:space="preserve">Patet ſi cum centris
              <lb/>
            F, G, D, inueruallis verò FB, GE,
              <lb/>
            DA circuli deſcribantur, ipſos datæ
              <lb/>
            ſectioni ABC eſſe inſcriptos, atque
              <lb/>
            _MAXIMOS_ ad puncta B, E, A
              <note symbol="a" position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">1. Co-
                <lb/>
              roll. 20. h.
                <lb/>
              & 95. h.</note>
            ſcriptibilium. </s>
            <s xml:id="echoid-s4931" xml:space="preserve">Dico iam inter hos _MA-_
              <lb/>
            _XIMOS, MINIMVM_ eſſe eum, qui ad
              <lb/>
            verticem B inſcribitur. </s>
            <s xml:id="echoid-s4932" xml:space="preserve">Aliorum au-
              <lb/>
            tem illum, qui ad punctum E propin-
              <lb/>
            quius vertici, minorem eſſe eo, qui
              <lb/>
            ad A vertici remotius, inſcribitur.</s>
            <s xml:id="echoid-s4933" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4934" xml:space="preserve">Nam quælibet perpendicularis GE, DA, &</s>
            <s xml:id="echoid-s4935" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4936" xml:space="preserve">maior eſt dimidio
              <note symbol="b" position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">1. Co-
                <lb/>
              roll. 90. h.</note>
            cti, ſiue maior FB: </s>
            <s xml:id="echoid-s4937" xml:space="preserve">quare circulus ex FB erit _MINIMVS_, &</s>
            <s xml:id="echoid-s4938" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4939" xml:space="preserve">ſed G E,
              <lb/>
            quæ à contactu vertici propiori, minor eſt D A, que à remotiori: </s>
            <s xml:id="echoid-s4940" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-0172-03" xlink:href="note-0172-03a" xml:space="preserve">93. h.</note>
            re circulus ex G E, erit minor circulo ex G A, &</s>
            <s xml:id="echoid-s4941" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4942" xml:space="preserve">neque inter hos,
              <lb/>
            _MAXIMVS_ reperitur, cum ſectio Parabole, aut Hyperbole ad partes ver-
              <lb/>
            tici oppoſitas ſit infinitæ cxtenſionis, ac proinde vnquam ei inſcribi ne-
              <lb/>
            queat circulus tàm longi interualli, quin infra alij adhuc maioris inter-
              <lb/>
            ualli inſcribi poſſint. </s>
            <s xml:id="echoid-s4943" xml:space="preserve">Quod tandem erat demonſtrandum.</s>
            <s xml:id="echoid-s4944" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div498" type="section" level="1" n="202">
          <head xml:id="echoid-head207" xml:space="preserve">THEOR. L. PROP. IC.</head>
          <p>
            <s xml:id="echoid-s4945" xml:space="preserve">MAXIMORVM circulorum, ad puncta Ellipticæ peri-
              <lb/>
            pheriæ inſcriptorum, MAXIMVS eſt qui ad verticem mino-
              <lb/>
            ris axis inſcribitur. </s>
            <s xml:id="echoid-s4946" xml:space="preserve">MINIMVS verò, qui ad verticem maio-
              <lb/>
            ris. </s>
            <s xml:id="echoid-s4947" xml:space="preserve">Aliorum autem is, cuius contactus à vertice maioris axis
              <lb/>
            magis remouetur, maior eſt.</s>
            <s xml:id="echoid-s4948" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4949" xml:space="preserve">ESto Ellipſis ABCD, cuius axis maior BD, minor A C, centrum E,
              <lb/>
            ſitq; </s>
            <s xml:id="echoid-s4950" xml:space="preserve">DF æqualis dimidio recti, cuius tranſuerſum latus eſt BD; </s>
            <s xml:id="echoid-s4951" xml:space="preserve">& </s>
            <s xml:id="echoid-s4952" xml:space="preserve"/>
          </p>
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