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

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        <div xml:id="echoid-div676" type="section" level="1" n="270">
          <head xml:id="echoid-head279" xml:space="preserve">LEMMA XII. PROP. XXXIX.</head>
          <p>
            <s xml:id="echoid-s6498" xml:space="preserve">Si fuerit quodcunque quadrilaterum rectilineum A B C D, cu-
              <lb/>
            ius oppoſita latera A D, B C bifariam ſecta ſint in punctis F,
              <lb/>
            E, iunctaque ſit recta F E, in qua ſumptum ſit quodlibet pun-
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            ctum G, vel intra, vel extra quadrilaterum à quo ad terminos
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            alterius ęquidiſtantium veluti ad A, D, ductæ ſint G A, G D,
              <lb/>
            ac in triangulo A G D, ſit quædam H I ipſis A D, B C æquidi-
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            ſtans, & </s>
            <s xml:id="echoid-s6499" xml:space="preserve">E F ſecans in L. </s>
            <s xml:id="echoid-s6500" xml:space="preserve">Dico, ſi iungantur B H, C I, trian-
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            gula A B H, D C I inter ſe æqualia eſſe.</s>
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          <figure number="194">
            <image file="0232-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0232-01"/>
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            <s xml:id="echoid-s6502" xml:space="preserve">NAm totum quadrilaterum A B E F, æquale eſt integro quadrilatero
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            D C E F (vtrunque enim diuiditur per diagonales A E, D E, in
              <lb/>
            duo triangula alterum alteri æquale, eò quod ſint ſuper æqualibus baſi-
              <lb/>
            bus, ac inter eaſdem parallelas) eadem ratione quadrilaterum A H L F
              <lb/>
            æquale eſt quadrilatero D I L F, & </s>
            <s xml:id="echoid-s6503" xml:space="preserve">quadrilaterum B E L H æquale qua-
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            drilatero C E L I, ergo, & </s>
            <s xml:id="echoid-s6504" xml:space="preserve">reliquum triangulum A B H reliquo triangulo
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            D C I eſt æquale. </s>
            <s xml:id="echoid-s6505" xml:space="preserve">Quod erat demonſtrandum.</s>
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          <p style="it">
            <s xml:id="echoid-s6507" xml:space="preserve">His itaque præoſtenſis, ad inueſtigationem MAXIMARVM, MI-
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            NIMARV MQVE portionum per idem datum punctum ex qualibet coni-
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            ſectione abſciſſarum accedamus, præmiſſo tamen, ſuper figurastertij Sche-
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            matiſmi, ſequenti Theoremate, vniuerſalem, ſimulque facilem methodum
              <lb/>
            exhibente, qua æquales portiones de eadem coni-ſectione abſcindi poſſunt.</s>
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