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

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          <p>
            <s xml:id="echoid-s4241" xml:space="preserve">
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            ABC, erit DB æqualis BF; </s>
            <s xml:id="echoid-s4242" xml:space="preserve">cumque AH contingat AGC erit DG
              <note symbol="a" position="left" xlink:label="note-0150-01" xlink:href="note-0150-01a" xml:space="preserve">35. pri.
                <lb/>
              conic.</note>
            GH, ſed eſt DB maior DG ex conſtructione, quare, & </s>
            <s xml:id="echoid-s4243" xml:space="preserve">BF erit maior GH, & </s>
            <s xml:id="echoid-s4244" xml:space="preserve">
              <lb/>
            GF eò maior GH: </s>
            <s xml:id="echoid-s4245" xml:space="preserve">quod memento.</s>
            <s xml:id="echoid-s4246" xml:space="preserve"/>
          </p>
          <note symbol="b" position="left" xml:space="preserve">ibidem.</note>
          <p>
            <s xml:id="echoid-s4247" xml:space="preserve">Præterea, in ſecunda figura, cum ſit LB, æqualis MG, & </s>
            <s xml:id="echoid-s4248" xml:space="preserve">BD maior GD,
              <lb/>
            ex conſtructione, habebit LB ad BD minorem rationem, quàm MG ad GD,
              <lb/>
            & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">componendo LD ad DB, ſiue LF ad FB minorem quàm MD ad
              <note symbol="c" position="left" xlink:label="note-0150-03" xlink:href="note-0150-03a" xml:space="preserve">36. pri-
                <lb/>
              mi conic.</note>
            ſiue quàm MH ad HG, & </s>
            <s xml:id="echoid-s4250" xml:space="preserve">iterum componendo LB ad BF, minorem
              <note symbol="d" position="left" xlink:label="note-0150-04" xlink:href="note-0150-04a" xml:space="preserve">ibidem.</note>
            MG ad GH, ſed eſt LB æqualis MG, quare BF erit maior GH, & </s>
            <s xml:id="echoid-s4251" xml:space="preserve">eò magis
              <lb/>
            GF maior GH.</s>
            <s xml:id="echoid-s4252" xml:space="preserve"/>
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          <figure number="117">
            <image file="0150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0150-01"/>
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          <p>
            <s xml:id="echoid-s4253" xml:space="preserve">Intertia denique, cum ſit LB æqualis MG, & </s>
            <s xml:id="echoid-s4254" xml:space="preserve">DB maior DG, ex conſtru-
              <lb/>
            ctione, habebit LB ad BD minorem rationem, quàm MG ad GD, & </s>
            <s xml:id="echoid-s4255" xml:space="preserve">diui-
              <lb/>
            dendo LD ad DB ſiue LF ad FB, minorem quàm MD ad DG, vel
              <note symbol="e" position="left" xlink:label="note-0150-05" xlink:href="note-0150-05a" xml:space="preserve">36. pri-
                <lb/>
              mi conic.</note>
            MH ad HG, & </s>
            <s xml:id="echoid-s4256" xml:space="preserve">diuidendo iterum, LB ad BF minorem rationem, quàm MG
              <lb/>
              <note symbol="f" position="left" xlink:label="note-0150-06" xlink:href="note-0150-06a" xml:space="preserve">ibidem.</note>
            ad GH, ſed eſt LB æqualis MG, ergo BF maior erit GH, & </s>
            <s xml:id="echoid-s4257" xml:space="preserve">eò magis GF
              <lb/>
            maior GH.</s>
            <s xml:id="echoid-s4258" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4259" xml:space="preserve">Itaque cum demonſtratum ſit in qualibet figura eſſe GF maiorem GH,
              <lb/>
            punctum H incidet infra F; </s>
            <s xml:id="echoid-s4260" xml:space="preserve">ſed HAI contingit ſectionem AGC in A, qua-
              <lb/>
            re FA, quæ contingit ABC, ſi producatur ad partes E, ſecabit ipſam ſectio-
              <lb/>
            nem ABC, cum inter ſectionem, & </s>
            <s xml:id="echoid-s4261" xml:space="preserve">contingentem, ex puncto contactus al-
              <lb/>
            tera recta linea non cadat: </s>
            <s xml:id="echoid-s4262" xml:space="preserve">quare, &</s>
            <s xml:id="echoid-s4263" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4264" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s4265" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4266" xml:space="preserve"/>
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          <note symbol="g" position="left" xml:space="preserve">32. pri-
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          mi conic.</note>
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        <div xml:id="echoid-div414" type="section" level="1" n="174">
          <head xml:id="echoid-head179" xml:space="preserve">PROBL. XXXII. PROP. LXXXII.</head>
          <p>
            <s xml:id="echoid-s4267" xml:space="preserve">Dato angulo rectilineo, vel coni-ſectione
              <unsure/>
            , vel circulo, perter-
              <lb/>
            minos, cuiuſcunque in ipſo applicatæ, MAXIMAM Ellipſim in-
              <lb/>
            ſcribere, cuius tranſuerſum latus æquale ſit dato.</s>
            <s xml:id="echoid-s4268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4269" xml:space="preserve">Oportet autem, ſi data ſectio ſuerit Ellipſis, datum tranſuerſum
              <lb/>
            minus eſſe diametro datæ Ellipſis, ad quam data applicata ordi-
              <lb/>
            natim ducitur.</s>
            <s xml:id="echoid-s4270" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4271" xml:space="preserve">ESto ABC datus angulus, vt in prima figura, vel Parabole, vt in ſecunda;
              <lb/>
            </s>
            <s xml:id="echoid-s4272" xml:space="preserve">vel Hyperbole, vt in tertia; </s>
            <s xml:id="echoid-s4273" xml:space="preserve">vel tandem Ellipſis, aut circulus, vt </s>
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