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

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            jor eſt quam E, & </s>
            <s xml:id="echoid-s3371" xml:space="preserve">ideo A B ſeu C C major eſt quam A E,
              <lb/>
            & </s>
            <s xml:id="echoid-s3372" xml:space="preserve">igitur AE + CC minor eſt quam 2 CC: </s>
            <s xml:id="echoid-s3373" xml:space="preserve">atque AC + E C
              <lb/>
            eſt ad 2 CC ut A + E ad 2 C, ſed A + E minor eſt quam
              <lb/>
            2 C; </s>
            <s xml:id="echoid-s3374" xml:space="preserve">& </s>
            <s xml:id="echoid-s3375" xml:space="preserve">ideo A C + E C minor eſt quam 2 CC; </s>
            <s xml:id="echoid-s3376" xml:space="preserve">proinde
              <lb/>
            A C + E C + A E + CC minor eſt quam 4 CC; </s>
            <s xml:id="echoid-s3377" xml:space="preserve">& </s>
            <s xml:id="echoid-s3378" xml:space="preserve">igitur
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            C - A minor eſt quadruplo ipſius E - C, quod demon-
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            ſtrare oportuit.</s>
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        <div xml:id="echoid-div178" type="section" level="1" n="84">
          <head xml:id="echoid-head120" xml:space="preserve">PROP. XVI. THEOREMA.</head>
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            <s xml:id="echoid-s3380" xml:space="preserve">SInt duo Polygona complicata A, B;
              <lb/>
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              A # B
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              C # D
                <lb/>
              E # F
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              </note>
            nempe A extra hyperbolæ ſecto-
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            rem & </s>
            <s xml:id="echoid-s3382" xml:space="preserve">B intra: </s>
            <s xml:id="echoid-s3383" xml:space="preserve">Continuetur ſeries con-
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            vergens horum polygonorum complica-
              <lb/>
            torum ſecundum noſtram methodum
              <lb/>
            ſubduplam deſcriptorum, ita ut polygona extra hyperbolem
              <lb/>
            ſint A, C, E, &</s>
            <s xml:id="echoid-s3384" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3385" xml:space="preserve">& </s>
            <s xml:id="echoid-s3386" xml:space="preserve">intra hyperbolem B, D, F &</s>
            <s xml:id="echoid-s3387" xml:space="preserve">c; </s>
            <s xml:id="echoid-s3388" xml:space="preserve">Dico A
              <lb/>
            + E majorem eſſe quam 2 C. </s>
            <s xml:id="echoid-s3389" xml:space="preserve">ex prædictis manifeſtæ ſunt ſe-
              <lb/>
            quentes duæ Analogiæ, prima quoniam A, C, B, ſunt con-
              <lb/>
            tinue proportionales; </s>
            <s xml:id="echoid-s3390" xml:space="preserve">& </s>
            <s xml:id="echoid-s3391" xml:space="preserve">ſecunda, quoniam C, D, B, ſunt
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            harmonicè proportionales; </s>
            <s xml:id="echoid-s3392" xml:space="preserve">& </s>
            <s xml:id="echoid-s3393" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">
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              A - C:C - B::A:C
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              C - B:C - D::A + C:A
                <lb/>
              </note>
            proinde exceſſus A ſupra C,
              <lb/>
            hoc eſt A - C, eſt ad ex ceſſum
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            C ſupra D ſeu C - D; </s>
            <s xml:id="echoid-s3394" xml:space="preserve">In ratione
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            compoſita ex proportione A ad C & </s>
            <s xml:id="echoid-s3395" xml:space="preserve">ex proportione A + C
              <lb/>
            ad A hoc eſt in ratione A + C ad C, at A + C eſt ma-
              <lb/>
            jor quam C & </s>
            <s xml:id="echoid-s3396" xml:space="preserve">ideo exceſſus A ſupra C eſt major exceſſu C
              <lb/>
            ſupra D, eſt autem E major quam D; </s>
            <s xml:id="echoid-s3397" xml:space="preserve">& </s>
            <s xml:id="echoid-s3398" xml:space="preserve">proinde exceſſus A
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            ſupra C multo major eſt exceſſu C ſupra E; </s>
            <s xml:id="echoid-s3399" xml:space="preserve">manifeſtum eſt
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            igitur A + E majorem eſſe quam 2 C, quod demonſtrare
              <lb/>
            oportuit.</s>
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