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

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        <div xml:id="echoid-div952" type="section" level="1" n="380">
          <head xml:id="echoid-head389" xml:space="preserve">Pag. 53. Coroll. I. ita reſtituendum.</head>
          <p>
            <s xml:id="echoid-s9115" xml:space="preserve">HInc eſt, quod applicatæ ex terminis ęqualium diametrorum in Parabo-
              <lb/>
            la, vel (in reliquis ſectionibus) ex punctis proportionaliter diuiden-
              <lb/>
            tibus ſemi-diametros ad quemlibet angulum conſtitutas; </s>
            <s xml:id="echoid-s9116" xml:space="preserve">nempe quod baſes
              <lb/>
            equalium portionum de eadem coni-ſectione, vel circulo, omnino ſemu-
              <lb/>
            tuò ſecant inter diametros; </s>
            <s xml:id="echoid-s9117" xml:space="preserve">& </s>
            <s xml:id="echoid-s9118" xml:space="preserve">quod rectæ lineæ, tum harum applicatarum,
              <lb/>
            vel baſium portionum puncta media, tum extrema iungentes, rectæ ſemi-
              <lb/>
            diametrorum terminos iungentiæquidiſtant.</s>
            <s xml:id="echoid-s9119" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9120" xml:space="preserve">Demonſtratum eſt enim rectas H I, E C, quæ ſunt baſes æqualiũ portio-
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            num H E I, A B C, ſecare ſe mutuò in M inter diametros E D, B D; </s>
            <s xml:id="echoid-s9121" xml:space="preserve">& </s>
            <s xml:id="echoid-s9122" xml:space="preserve">iun-
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            ctas H C, G F, A I ipſi E B eſſe parallelas.</s>
            <s xml:id="echoid-s9123" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div953" type="section" level="1" n="381">
          <head xml:id="echoid-head390" xml:space="preserve">Pag. 59. poſt Coroll. adde ſequens</head>
          <head xml:id="echoid-head391" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s9124" xml:space="preserve">QVod in Ellipſi demonſtratum fuit de portionibus A B C, H M I, ſemi-
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            Ellipſi minoribus, idem ſequitur de maioribus A H C, H C I, qua-
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            rum baſes A C, H I ſimilem concentricam interiorem Ellipſim.
              <lb/>
            </s>
            <s xml:id="echoid-s9125" xml:space="preserve">contingunt; </s>
            <s xml:id="echoid-s9126" xml:space="preserve">nempe has quoque inter ſe æquales eſſe. </s>
            <s xml:id="echoid-s9127" xml:space="preserve">Nam ipſæ portiones
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            A H C, H C I ſunt partes ſuperſtites de eadem Ellipſi A B C H, demptis
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            æqualibus portionibus A B C, H M I.</s>
            <s xml:id="echoid-s9128" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div954" type="section" level="1" n="382">
          <head xml:id="echoid-head392" xml:space="preserve">Pag. 61. poſt Coroll. II.</head>
          <head xml:id="echoid-head393" xml:space="preserve">COROLL. III.</head>
          <p>
            <s xml:id="echoid-s9129" xml:space="preserve">PAtet denique in Parabolis parallelis, vel in ſimilibus concentricis Hy-
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            perbolis, aut Ellipſibus, vel Circulis A B C, D E F, omnia rectangu-
              <lb/>
            la ſub ſegmentis applicatarum, interſe, & </s>
            <s xml:id="echoid-s9130" xml:space="preserve">prædictæ contingenti A E C
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            æquidiſtantium (quorum vnum eſt rectangulum G D H, vel G F H) eſſe.
              <lb/>
            </s>
            <s xml:id="echoid-s9131" xml:space="preserve">inter ſe æqualia, cum quodlibet ipſorum æquale ſit eidem quadrato ſemi-
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            tangentis A E.</s>
            <s xml:id="echoid-s9132" xml:space="preserve"/>
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