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

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        <div xml:id="echoid-div587" type="section" level="1" n="238">
          <head xml:id="echoid-head246" xml:space="preserve">THEOR. XIII. PROP. XVIII.</head>
          <p>
            <s xml:id="echoid-s5666" xml:space="preserve">Si per centrum Ellipſis deſcribatur Hyperbole, cuius aſym-
              <lb/>
            ptoti coniugatis diametris æquidiſtent; </s>
            <s xml:id="echoid-s5667" xml:space="preserve">ipſa in duobus tantùm
              <lb/>
            punctis Ellipſis peripheriam ſecabit.</s>
            <s xml:id="echoid-s5668" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5669" xml:space="preserve">ESto Ellipſis A B C D, cuius centrum E, & </s>
            <s xml:id="echoid-s5670" xml:space="preserve">diametri coniugatæ ſint
              <lb/>
            A C, B D quibus ductæ ſint F G, H C ipſis diametris altera alteri ę-
              <lb/>
            quidiſtantes, & </s>
            <s xml:id="echoid-s5671" xml:space="preserve">ſimul occurrentes in G; </s>
            <s xml:id="echoid-s5672" xml:space="preserve">& </s>
            <s xml:id="echoid-s5673" xml:space="preserve">cum aſymptotis G F, G H, per
              <lb/>
            centrum E, deſcripta ſit Hyperbole I E L. </s>
            <s xml:id="echoid-s5674" xml:space="preserve">Dico hanc, Ellipſis periphe-
              <lb/>
            riam in duobus tantùm punctis ſecare.</s>
            <s xml:id="echoid-s5675" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5676" xml:space="preserve">Nam cum in Hyperbola I E L
              <lb/>
            ſumptum ſit punctum E, per
              <lb/>
              <figure xlink:label="fig-0203-01" xlink:href="fig-0203-01a" number="163">
                <image file="0203-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0203-01"/>
              </figure>
            quod ductæ ſunt A E C, D E B
              <lb/>
            aſymptotis æquidiſtantes, ipſæ
              <lb/>
            in puncto tantùm E ſectioni oc-
              <lb/>
            current, & </s>
            <s xml:id="echoid-s5677" xml:space="preserve">Hyperbole in angu-
              <lb/>
            lo B E A, inter E A, & </s>
            <s xml:id="echoid-s5678" xml:space="preserve">G F
              <lb/>
            ſemper incedet, pariterque in
              <lb/>
            angulo C E D, inter E D, & </s>
            <s xml:id="echoid-s5679" xml:space="preserve">
              <lb/>
            G H; </s>
            <s xml:id="echoid-s5680" xml:space="preserve">ſed anguli B E A, C E D
              <lb/>
            terminantur à peripherijs B A,
              <lb/>
            C D, quare Hyperbole ex vtra-
              <lb/>
            que parte producta ipſas peri-
              <lb/>
            pherias omninò ſecabit, vt in
              <lb/>
            I, L. </s>
            <s xml:id="echoid-s5681" xml:space="preserve">Si ergo ex I ducantur M
              <lb/>
            I N, O I F diametris æquidiſtã-
              <lb/>
            tes, ob eandem rationem ſupe-
              <lb/>
            riùs allatam ſectio E I P, in nullo alio puncto, quàm I cum rectis N I M,
              <lb/>
            F I O conueniet, ſed ipſæ N I M, F I O nil aliud commune habent
              <lb/>
            cum peripheria quadrantis A B, quàm idem punctum I, quare
              <lb/>
            Hyperbole E I P in vno tantùm puncto I Ellipſis periphe-
              <lb/>
            riam ſecabit in quadrante A B. </s>
            <s xml:id="echoid-s5682" xml:space="preserve">Cõſimili conſtructione,
              <lb/>
            & </s>
            <s xml:id="echoid-s5683" xml:space="preserve">argumento, oſtendetur ſectionem E L Q in
              <lb/>
            alio puncto quàm L peripheriam D C non
              <lb/>
            ſecare: </s>
            <s xml:id="echoid-s5684" xml:space="preserve">quare huiuſmodi Hyperbole in
              <lb/>
            duobus tantùm punctis ſecat El-
              <lb/>
            lipſis peripheriam. </s>
            <s xml:id="echoid-s5685" xml:space="preserve">Quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s5686" xml:space="preserve"/>
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