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

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            quæ verò cum tranſuerſo, quod deficiat à CF, eſt quidem minor ipſa ABC,
              <note symbol="a" position="right" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve">4. Co-
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              roll. 19. h.</note>
            omnino ſecat Hyperbolæ portionem A N C ſupra baſim AD cum & </s>
            <s xml:id="echoid-s2050" xml:space="preserve">iuncta
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              roll. 19. h.</note>
            gula ſecet datæ portionis regulam M L ſupra A D. </s>
            <s xml:id="echoid-s2051" xml:space="preserve">Quare Ellipſis portio ABC
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            D eſt _MINIMA_ circumſcripta cum dato recto C E, Quod vltimò, &</s>
            <s xml:id="echoid-s2052" xml:space="preserve">c.</s>
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        <div xml:id="echoid-div188" type="section" level="1" n="91">
          <head xml:id="echoid-head96" xml:space="preserve">PROBL. XVI. PROP. XXXI.</head>
          <p>
            <s xml:id="echoid-s2054" xml:space="preserve">Datæ portioni circuli, vel Ellipſis, cum dato tranſuerſo latere,
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            quod excedat verſum, vel cum dato recto, quod minus ſit recto datæ
              <lb/>
            portionis, maius verò latitudine ſemi-applicatæ baſis portionis, per
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            eius verticem MAXIMAM Ellipſis portionem inſcribere. </s>
            <s xml:id="echoid-s2055" xml:space="preserve">Item.</s>
            <s xml:id="echoid-s2056" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2057" xml:space="preserve">Datæ portioni circuli, vel Ellipſis, cum dato tranſuerſo, quod mi-
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            nus ſit tranſuerſo, ſed maius diametro datæ portionis, vel cum dato
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            recto, quod excedat rectum datæ portionis, per eius verticem MI-
              <lb/>
            NIMAM Ellipſis portionem circumſcribere.</s>
            <s xml:id="echoid-s2058" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2059" xml:space="preserve">SIt data circuli, vel Ellipſis portio A B C D, cuius diameter C E, baſis A D,
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            verſum CF, rectum CG, & </s>
            <s xml:id="echoid-s2060" xml:space="preserve">regula CF. </s>
            <s xml:id="echoid-s2061" xml:space="preserve">Oportet per verticẽ C _MAXIMAM_
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            Ellipſis portionem inſcribere, cum dato tranſuerſo CH, quod ſit maius ipſo CF.</s>
            <s xml:id="echoid-s2062" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2063" xml:space="preserve">Applicata AE, & </s>
            <s xml:id="echoid-s2064" xml:space="preserve">producta occurrat regulæ FG
              <lb/>
              <figure xlink:label="fig-0083-01" xlink:href="fig-0083-01a" number="53">
                <image file="0083-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0083-01"/>
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            in I; </s>
            <s xml:id="echoid-s2065" xml:space="preserve">iunctaque HI, conueniat producta cum con-
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            tingente C G in L, & </s>
            <s xml:id="echoid-s2066" xml:space="preserve">cum dato tranſuerſo CH, re-
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            ctoq; </s>
            <s xml:id="echoid-s2067" xml:space="preserve">CL adſcribatur per C Ellipſis portio A M
              <note symbol="c" position="right" xlink:label="note-0083-03" xlink:href="note-0083-03a" xml:space="preserve">7. h.</note>
            D, quæ per extrema baſis A D tranſibit
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              roll. 19. h.</note>
            portioni erit inſcripta. </s>
            <s xml:id="echoid-s2068" xml:space="preserve">Iam dico hanc eſſe _MAXI-_
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            _MAM_. </s>
            <s xml:id="echoid-s2069" xml:space="preserve">Nam quæ adſcribitur cum eodem verſo C
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            H, ſed cum recto, quod minus ſit ipſo C L, minor
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              <note symbol="e" position="right" xlink:label="note-0083-05" xlink:href="note-0083-05a" xml:space="preserve">2. Co-
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              roll. 19. h.</note>
            eſt eſt ipſa A M C D; </s>
            <s xml:id="echoid-s2070" xml:space="preserve">quæ verò cum recto, quod excedat C L, eſt quidem maior AMCD, ſed vel
              <note symbol="f" position="right" xlink:label="note-0083-06" xlink:href="note-0083-06a" xml:space="preserve">ibidem.</note>
            tota cadit extra ABCD, tum cum eius rectũ
              <note symbol="g" position="right" xlink:label="note-0083-07" xlink:href="note-0083-07a" xml:space="preserve">20. h.</note>
            quet CG, tũ cũ ipſum excedat; </s>
            <s xml:id="echoid-s2071" xml:space="preserve">vel ſaltim ſecat datã
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            portionem ABCD ſupra baſim AD quando
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              roll. 19. h.</note>
            cadat inter CL, & </s>
            <s xml:id="echoid-s2072" xml:space="preserve">C G, quale eſt C O, nam iuncta
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            regula HO, ſecat omnino regulã I G ſupra eandem
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            AD. </s>
            <s xml:id="echoid-s2073" xml:space="preserve">Vnde Ellipſis portio A M C D eſt _MAXIMA_
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            inſcripta cum dato trãſuerſo CH. </s>
            <s xml:id="echoid-s2074" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s2075" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2076" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2077" xml:space="preserve">Iam, ijſdem poſitis, oporteat cum dato recto C L, quod minus ſit recto CG;
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            </s>
            <s xml:id="echoid-s2078" xml:space="preserve">maior verò latitudine E I, _MAXIMAM_ Ellipſis portionem inſcribere.</s>
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            <s xml:id="echoid-s2080" xml:space="preserve">Iungatur L I, & </s>
            <s xml:id="echoid-s2081" xml:space="preserve">producatur, conueniens cum diametro C E in H, & </s>
            <s xml:id="echoid-s2082" xml:space="preserve">cum
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            tranſuerſo CH, datoque recto CL adſcribatur per C Ellipſis portio A M C
              <note symbol="i" position="right" xlink:label="note-0083-09" xlink:href="note-0083-09a" xml:space="preserve">7. h.</note>
            quæ datæ portioni occurret in A, & </s>
            <s xml:id="echoid-s2083" xml:space="preserve">D, eique erit inſcripta. </s>
            <s xml:id="echoid-s2084" xml:space="preserve">Dico hanc
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              roll. 19. h.</note>
            _MAXIMAM_ quæſitam.</s>
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            <s xml:id="echoid-s2086" xml:space="preserve">Quæ enim adſcribitur cũ eodem recto CL, ſed cum verſo, quod minus ſit ipſo
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              roll. 19. h.</note>
            CH eſt minor portione AMCD; </s>
            <s xml:id="echoid-s2087" xml:space="preserve">quæ autem cum verſo, quod excedat C H, quale eſt C P, eſt quidem maior ipſa AMCD, ſed omnino ſecat Ellipſim A B
              <note symbol="n" position="right" xlink:label="note-0083-12" xlink:href="note-0083-12a" xml:space="preserve">ibid.</note>
            C D ſupra baſim A D cum iuncta regula P L, ſecet regulam I G ſupra
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              roll. 19. h.</note>
            </s>
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