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

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            <s xml:id="echoid-s7502" xml:space="preserve">
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            rectæ D H F æquidiſtabit, cum & </s>
            <s xml:id="echoid-s7503" xml:space="preserve">hæc quoque ſit eidem diametro ordina-
              <lb/>
            tim ducta.</s>
            <s xml:id="echoid-s7504" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7505" xml:space="preserve">Iam in ſingulis figuris erit portio L E M æqualis portioni A B C,
              <note symbol="a" position="right" xlink:label="note-0269-01" xlink:href="note-0269-01a" xml:space="preserve">40. h.</note>
            eſt quoque portio D E F eidem portioni A B C æqualis, ex hypotheſi,
              <lb/>
            quare duæ portiones L E M, D E F inter ſe æquales erunt, ſed vtraque eſt
              <lb/>
            de eadem ſectione, & </s>
            <s xml:id="echoid-s7506" xml:space="preserve">circa communem diametrum E H I, & </s>
            <s xml:id="echoid-s7507" xml:space="preserve">ſuper baſes
              <lb/>
            parallelas, ergo baſis L I M tota congruet cum baſi D H F, vnde & </s>
            <s xml:id="echoid-s7508" xml:space="preserve">pun-
              <lb/>
            ctum I cum puncto H; </s>
            <s xml:id="echoid-s7509" xml:space="preserve">quare ſegmenta E I, E H inter ſe æqualia erunt,
              <lb/>
            ac propterea erit, in prima, ſegmentum quoque E H æquale B G, & </s>
            <s xml:id="echoid-s7510" xml:space="preserve">in re-
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            liquis erit H E ad E O, vt G B ad B O. </s>
            <s xml:id="echoid-s7511" xml:space="preserve">Quod primò oſtendere propone-
              <lb/>
            batur.</s>
            <s xml:id="echoid-s7512" xml:space="preserve"/>
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            <image file="0269-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0269-01"/>
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            <s xml:id="echoid-s7513" xml:space="preserve">Sint iam in tertia figura duæ portiones æquales A N C, D P F ſemi- El-
              <lb/>
            lipſi maiores, quarum ſegmenta diametrorum ſint G N, H P, & </s>
            <s xml:id="echoid-s7514" xml:space="preserve">commune
              <lb/>
            centrum O. </s>
            <s xml:id="echoid-s7515" xml:space="preserve">Dico item eſſe G N ad N O, vt H P ad P O.</s>
            <s xml:id="echoid-s7516" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7517" xml:space="preserve">Producantur diametri N G, P H, ad B, E.</s>
            <s xml:id="echoid-s7518" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7519" xml:space="preserve">Et cum portiones A N C, D P F ſint æquales, & </s>
            <s xml:id="echoid-s7520" xml:space="preserve">ſemi- Ellipſi maiores
              <lb/>
            erunt quoque reliquæ A B C, D E F de eadem Ellipſi inter ſe æquales,
              <lb/>
            ſed ſemi- Ellipſi minores; </s>
            <s xml:id="echoid-s7521" xml:space="preserve">quare erit, vt ſupra oſtendimus, G B ad B O,
              <lb/>
            vt H E ad E O, & </s>
            <s xml:id="echoid-s7522" xml:space="preserve">conuertendo, & </s>
            <s xml:id="echoid-s7523" xml:space="preserve">diuidendo O G ad G B, vt O H ad
              <lb/>
            H E, & </s>
            <s xml:id="echoid-s7524" xml:space="preserve">eſt G B ad B O, vel ad O N, vt H E ad E O, vel ad O P, ergo,
              <lb/>
            ex æquali G O ad O N, vt H O ad O P, & </s>
            <s xml:id="echoid-s7525" xml:space="preserve">componendo, G N ad N O,
              <lb/>
            vt H P ad P O. </s>
            <s xml:id="echoid-s7526" xml:space="preserve">Quod vltimò erat, &</s>
            <s xml:id="echoid-s7527" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7528" xml:space="preserve"/>
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