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

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        <div xml:id="echoid-div584" type="section" level="1" n="236">
          <head xml:id="echoid-head244" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s5644" xml:space="preserve">HInc, data ratione maioris inæqualitatis, hoc eſt D E, ad E H, & </s>
            <s xml:id="echoid-s5645" xml:space="preserve">
              <lb/>
            differentia A C inter duo s terminos ignotos A G, G C, qui de-
              <lb/>
            beant eſſe in data ratione, eruitur quomodo reperiantur ipſi termini A G,
              <lb/>
            G C. </s>
            <s xml:id="echoid-s5646" xml:space="preserve">Facta enim fuit vt D H differentia primorum, ad H E minorem ter-
              <lb/>
            minum, ita data differentia A C, ad aliam C G, & </s>
            <s xml:id="echoid-s5647" xml:space="preserve">reperti ſunt quæſiti
              <lb/>
            termini A G, G C, Nam ſtatim oſtenſum fuit eſſe A G ad G C, vt D E
              <lb/>
            ad E H.</s>
            <s xml:id="echoid-s5648" xml:space="preserve"/>
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        <div xml:id="echoid-div585" type="section" level="1" n="237">
          <head xml:id="echoid-head245" xml:space="preserve">THEOR. XII. PROP. XVII.</head>
          <p>
            <s xml:id="echoid-s5649" xml:space="preserve">Si fuerit in angulo rectilineo quælibet applicata, à qua hinc
              <lb/>
            inde ab eius termino æqualia ſegmenta ſint abſciſſa, & </s>
            <s xml:id="echoid-s5650" xml:space="preserve">per v-
              <lb/>
            num diuiſionis punctum deſcribatur Hyperbole, cuius aſympto-
              <lb/>
            ti ſint latera dati anguli, ipſa per alterum punctum neceſſariò
              <lb/>
            tranſibit.</s>
            <s xml:id="echoid-s5651" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5652" xml:space="preserve">SIt in angulo A B C applicata quæcunque A C, quæ inæqualiter ſece-
              <lb/>
            tur in D, & </s>
            <s xml:id="echoid-s5653" xml:space="preserve">ſumatur C E æqualis A D. </s>
            <s xml:id="echoid-s5654" xml:space="preserve">Dico ſi per punctum D de-
              <lb/>
            ſcribatur Hyperbole, cuius aſymptoti ſint B A, B C, ipſam omnino tran-
              <lb/>
            ſire per E.</s>
            <s xml:id="echoid-s5655" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5656" xml:space="preserve">Quod huiuſmodi Hyper-
              <lb/>
              <figure xlink:label="fig-0202-01" xlink:href="fig-0202-01a" number="162">
                <image file="0202-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0202-01"/>
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            bole tranſiens per D, alibi
              <lb/>
            ſecet applicatam A C, pa-
              <lb/>
            tet. </s>
            <s xml:id="echoid-s5657" xml:space="preserve">Nam ſi eam continge-
              <lb/>
            ret in D, eſſet A C æquali-
              <lb/>
            ter ſecta in D: </s>
            <s xml:id="echoid-s5658" xml:space="preserve">quod
              <note symbol="a" position="left" xlink:label="note-0202-01" xlink:href="note-0202-01a" xml:space="preserve">3. ſecun-
                <lb/>
              di conic.</note>
            contra hypoteſim. </s>
            <s xml:id="echoid-s5659" xml:space="preserve">Secet er-
              <lb/>
            go in F; </s>
            <s xml:id="echoid-s5660" xml:space="preserve">& </s>
            <s xml:id="echoid-s5661" xml:space="preserve">erit F C
              <note symbol="b" position="left" xlink:label="note-0202-02" xlink:href="note-0202-02a" xml:space="preserve">8. ibid.</note>
            lis A D, ſed eſt quoque E
              <lb/>
            C eidem A D ęqualis, qua-
              <lb/>
            re F C, E C ęquales erunt;
              <lb/>
            </s>
            <s xml:id="echoid-s5662" xml:space="preserve">hoc eſt punctum F congruet
              <lb/>
            cum ipſo E; </s>
            <s xml:id="echoid-s5663" xml:space="preserve">quare Hyper-
              <lb/>
            bole D F, quæ in angulo aſymptotali A B C deſcribitur per D, omnino
              <lb/>
            tranſit per E. </s>
            <s xml:id="echoid-s5664" xml:space="preserve">Quod erat demonſtrandum.</s>
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