Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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            ſupra A; </s>
            <s xml:id="echoid-s3435" xml:space="preserve">eſt igitur D major quam C, quod demonſtrare
              <lb/>
            oportuit.</s>
            <s xml:id="echoid-s3436" xml:space="preserve"/>
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        <div xml:id="echoid-div184" type="section" level="1" n="87">
          <head xml:id="echoid-head123" xml:space="preserve">PROP. XIX. THEOREMA.</head>
          <p>
            <s xml:id="echoid-s3437" xml:space="preserve">IIsdem poſitis; </s>
            <s xml:id="echoid-s3438" xml:space="preserve">ſit inter A & </s>
            <s xml:id="echoid-s3439" xml:space="preserve">B media harmonica E. </s>
            <s xml:id="echoid-s3440" xml:space="preserve">dico
              <lb/>
            C majorem eſſe quam E. </s>
            <s xml:id="echoid-s3441" xml:space="preserve">ex hujus 13, D eſt ad C ut C ad
              <lb/>
            E, ſed D major eſt quam C; </s>
            <s xml:id="echoid-s3442" xml:space="preserve">& </s>
            <s xml:id="echoid-s3443" xml:space="preserve">ideo C major eſt quam E,
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            quod demonſtrare oportuit.</s>
            <s xml:id="echoid-s3444" xml:space="preserve"/>
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        <div xml:id="echoid-div185" type="section" level="1" n="88">
          <head xml:id="echoid-head124" xml:space="preserve">CONSECTARIUM.</head>
          <p>
            <s xml:id="echoid-s3445" xml:space="preserve">Ex duabus præcedentibus manifeſtum eſt D majorem eſſe
              <lb/>
            quam E, hoc eſt mediam arithmeticam inter duas quantita-
              <lb/>
            tes inæquales majorem eſſe media harmonica inter eaſdem.</s>
            <s xml:id="echoid-s3446" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div186" type="section" level="1" n="89">
          <head xml:id="echoid-head125" xml:space="preserve">PROP. XX. THEOREMA.</head>
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            <s xml:id="echoid-s3447" xml:space="preserve">SInt duo polygona complicata
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              <note position="right" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">
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              A B # A
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              C D # C
                <lb/>
              E F # G
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              K L # H
                <lb/>
              Z # X
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            A, B, nempe A intra circuli
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            vel ellipſeos ſectorem, B extra.
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            </s>
            <s xml:id="echoid-s3448" xml:space="preserve">continuetur ſeries convergens ho-
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            rum polygonorum complicato-
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            rum ſecundum methodum no-
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            ſtram ſubduplam deſcriptorum; </s>
            <s xml:id="echoid-s3449" xml:space="preserve">
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            ita ut polygona intra circulum ſint A, C, E, K, &</s>
            <s xml:id="echoid-s3450" xml:space="preserve">c, & </s>
            <s xml:id="echoid-s3451" xml:space="preserve">ex-
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            tra circulum B, D, F, L, &</s>
            <s xml:id="echoid-s3452" xml:space="preserve">c; </s>
            <s xml:id="echoid-s3453" xml:space="preserve">ſitque ſeriei convergentis ter-
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            minatio ſeu circuli vel ellipſeos ſector Z. </s>
            <s xml:id="echoid-s3454" xml:space="preserve">dico Z majorem
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            eſſe quam C una cum triente exceſſus C ſupra A. </s>
            <s xml:id="echoid-s3455" xml:space="preserve">ſit exceſſus
              <lb/>
            G ſupra C quarta pars exceſſus C ſupra A, & </s>
            <s xml:id="echoid-s3456" xml:space="preserve">exceſſus H
              <lb/>
            ſupra G quarta pars exceſſus G ſupra C; </s>
            <s xml:id="echoid-s3457" xml:space="preserve">continueturque
              <lb/>
            hæc ſeries in infinitum, ut ejus terminatio ſit X. </s>
            <s xml:id="echoid-s3458" xml:space="preserve">Exceſſus
              <lb/>
            C ſupra A minor eſt quadruplo exceſſus E ſupra C; </s>
            <s xml:id="echoid-s3459" xml:space="preserve">& </s>
            <s xml:id="echoid-s3460" xml:space="preserve">ideo
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            exceſſus E ſupra C major eſt exceſſu G ſupra C, eſt ergo
              <lb/>
            E major quam G. </s>
            <s xml:id="echoid-s3461" xml:space="preserve">deinde exceſſus E ſupra C minor eſt qua-
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            druplo exceſſus K ſupra E, & </s>
            <s xml:id="echoid-s3462" xml:space="preserve">ideo exceſſus G ſupra C mul-
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            to minor eſt quadruplo exceſſus K ſupra E, eſt igitur </s>
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