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

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            C, G; </s>
            <s xml:id="echoid-s3575" xml:space="preserve">& </s>
            <s xml:id="echoid-s3576" xml:space="preserve">ideo terminatio ſeriei A, C, E, nempe Z, major
              <lb/>
            erit terminatione ſeriei A, C, G, nempè X; </s>
            <s xml:id="echoid-s3577" xml:space="preserve">at ex Archime-
              <lb/>
            dis quadratura parabolæ conſtat X æqualem eſſe ipſi C dem-
              <lb/>
            pto triente exceſſus A ſupra C, & </s>
            <s xml:id="echoid-s3578" xml:space="preserve">proinde Z eadem major
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            eſt, quod demonſtrare oportuit.</s>
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        <div xml:id="echoid-div195" type="section" level="1" n="94">
          <head xml:id="echoid-head130" xml:space="preserve">PROP. XXIV. THEOREMA.</head>
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            <s xml:id="echoid-s3580" xml:space="preserve">IIsdem poſitis; </s>
            <s xml:id="echoid-s3581" xml:space="preserve">dico Z ſeu ſe-
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              A B # A B
                <lb/>
              C D # G H
                <lb/>
              E F # M N
                <lb/>
              K L # O P
                <lb/>
              Z # X
                <lb/>
              </note>
            ctorem hyperbolæ minorem eſ-
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            ſe quam minor duarum mediarum
              <lb/>
            arithmeticè continuè proportio-
              <lb/>
            nalium inter A & </s>
            <s xml:id="echoid-s3582" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3583" xml:space="preserve">Inter A & </s>
            <s xml:id="echoid-s3584" xml:space="preserve">
              <lb/>
            B ſit media arithmetica G, & </s>
            <s xml:id="echoid-s3585" xml:space="preserve">in-
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            ter G & </s>
            <s xml:id="echoid-s3586" xml:space="preserve">B ſit media Arithmetica
              <lb/>
            H, Item inter G & </s>
            <s xml:id="echoid-s3587" xml:space="preserve">H ſit media Arithmetica M, & </s>
            <s xml:id="echoid-s3588" xml:space="preserve">inter M
              <lb/>
            & </s>
            <s xml:id="echoid-s3589" xml:space="preserve">H ſit media Arithmetica N: </s>
            <s xml:id="echoid-s3590" xml:space="preserve">continueturque hæc ſeries con-
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            vergens A B, G H, M N, O P, in infinitum, ut fiat ejus termi-
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            natio X. </s>
            <s xml:id="echoid-s3591" xml:space="preserve">ſatis patet ex prædictis G majorem eſſe quam C;
              <lb/>
            </s>
            <s xml:id="echoid-s3592" xml:space="preserve">atque H media arithmetica inter G & </s>
            <s xml:id="echoid-s3593" xml:space="preserve">B major eſt media har-
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            monica inter easdem G & </s>
            <s xml:id="echoid-s3594" xml:space="preserve">B; </s>
            <s xml:id="echoid-s3595" xml:space="preserve">media autem harmonica inter
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            G & </s>
            <s xml:id="echoid-s3596" xml:space="preserve">B; </s>
            <s xml:id="echoid-s3597" xml:space="preserve">major eſt media harmonica inter C & </s>
            <s xml:id="echoid-s3598" xml:space="preserve">B, nempe D, quo-
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            niam G major eſt quam C; </s>
            <s xml:id="echoid-s3599" xml:space="preserve">& </s>
            <s xml:id="echoid-s3600" xml:space="preserve">ideo media Arithmetica inter G
              <lb/>
            & </s>
            <s xml:id="echoid-s3601" xml:space="preserve">B nempe H major eſt quam D media harmonica inter C & </s>
            <s xml:id="echoid-s3602" xml:space="preserve">B
              <lb/>
            eodem modo M media Arithmetica inter G & </s>
            <s xml:id="echoid-s3603" xml:space="preserve">H major eſt me-
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            dia geometrica inter eaſdem G & </s>
            <s xml:id="echoid-s3604" xml:space="preserve">H; </s>
            <s xml:id="echoid-s3605" xml:space="preserve">& </s>
            <s xml:id="echoid-s3606" xml:space="preserve">quoniam G eſt ma-
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            jor quam C & </s>
            <s xml:id="echoid-s3607" xml:space="preserve">H quam D, media geometrica inter G & </s>
            <s xml:id="echoid-s3608" xml:space="preserve">H
              <lb/>
            major eſt quam E media geometrica inter C & </s>
            <s xml:id="echoid-s3609" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3610" xml:space="preserve">& </s>
            <s xml:id="echoid-s3611" xml:space="preserve">proin-
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            de M major eſt quam E. </s>
            <s xml:id="echoid-s3612" xml:space="preserve">Deinde N media Arithmetica in-
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            ter M & </s>
            <s xml:id="echoid-s3613" xml:space="preserve">H major eſt media harmonica inter easdem; </s>
            <s xml:id="echoid-s3614" xml:space="preserve">& </s>
            <s xml:id="echoid-s3615" xml:space="preserve">quo-
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            niam H major eſt quam D & </s>
            <s xml:id="echoid-s3616" xml:space="preserve">M quam E, media harmonica
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            inter M & </s>
            <s xml:id="echoid-s3617" xml:space="preserve">H major eſt quam F media harmonica inter E & </s>
            <s xml:id="echoid-s3618" xml:space="preserve">
              <lb/>
            D; </s>
            <s xml:id="echoid-s3619" xml:space="preserve">& </s>
            <s xml:id="echoid-s3620" xml:space="preserve">ideo N eadem F major eſt. </s>
            <s xml:id="echoid-s3621" xml:space="preserve">eodem modo utramque
              <lb/>
            ſeriem in infinitum continuando, ſemper demonſtratur ter-
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            minum quemlibet ſeriei A B, C D, minorem eſſe quam idem
              <lb/>
            numero terminum ſeriei A B, G H; </s>
            <s xml:id="echoid-s3622" xml:space="preserve">& </s>
            <s xml:id="echoid-s3623" xml:space="preserve">igitur terminatio ſe-
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            riei A B, C D, nempe Z, minor erit terminatione ſeriei A </s>
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