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

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              <pb o="439" file="0157" n="166" rhead="ET HYPERBOLÆ QUADRATURA."/>
            ceſſus K ſupra E major exceſſus H ſupra G; </s>
            <s xml:id="echoid-s3463" xml:space="preserve">cumque E ma-
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            <s xml:id="echoid-s3464" xml:space="preserve">eodem prorſus modo demonſtratur in omni ſerierum A, C,
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            E; </s>
            <s xml:id="echoid-s3465" xml:space="preserve">A, C, G, continuatione, terminum quemcunque ſeriei
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            A, C, E, majorem eſſe quam idem numero terminus ſeriei
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            A, C, G; </s>
            <s xml:id="echoid-s3466" xml:space="preserve">& </s>
            <s xml:id="echoid-s3467" xml:space="preserve">ideo terminatio ſeriei A, C, E, nempe Z ma-
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            medis quadratura parabloæ conſtat X æqualem eſſe ipſi C
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            major eſt, quod demonſtrare oportuit.</s>
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          <head xml:id="echoid-head126" xml:space="preserve">PROP. XXI. THEOREMA.</head>
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            <s xml:id="echoid-s3470" xml:space="preserve">IIsdem poſitis quæ ſupra; </s>
            <s xml:id="echoid-s3471" xml:space="preserve">dico Z
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              A B # A B
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              C D # G H
                <lb/>
              E F # M N
                <lb/>
              K L # O P
                <lb/>
              Z # X
                <lb/>
              </note>
            ſeu ſectorem circuli vel ellipſeos
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            minorem eſſe quam major duarum
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            mediarum continuè proportionalium
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            arithmeticè inter A & </s>
            <s xml:id="echoid-s3472" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">inter A & </s>
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              <lb/>
            B ſit media Arithmetica G, & </s>
            <s xml:id="echoid-s3475" xml:space="preserve">inter
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            G & </s>
            <s xml:id="echoid-s3476" xml:space="preserve">B ſit media Arithmetica H; </s>
            <s xml:id="echoid-s3477" xml:space="preserve">item
              <lb/>
            inter G & </s>
            <s xml:id="echoid-s3478" xml:space="preserve">H ſit media Arithmetica M, & </s>
            <s xml:id="echoid-s3479" xml:space="preserve">inter M & </s>
            <s xml:id="echoid-s3480" xml:space="preserve">H ſed me-
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            dia Arithmetica N; </s>
            <s xml:id="echoid-s3481" xml:space="preserve">continueturque hæc ſeries convergens A B,
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            G H, M N, O P, in infinitum, ut fiat ejus terminatio X. </s>
            <s xml:id="echoid-s3482" xml:space="preserve">ſatis
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            pater ex prædictis G majorem eſſe quam C, atque H media
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            Arithmetica inter G & </s>
            <s xml:id="echoid-s3483" xml:space="preserve">B major eſt media harmonica inter eas-
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            dem G, B; </s>
            <s xml:id="echoid-s3484" xml:space="preserve">media autem harmonica inter G & </s>
            <s xml:id="echoid-s3485" xml:space="preserve">B major eſt quam
              <lb/>
            D media harmonica inter C & </s>
            <s xml:id="echoid-s3486" xml:space="preserve">B, quoniam G major eſt quam
              <lb/>
            C; </s>
            <s xml:id="echoid-s3487" xml:space="preserve">& </s>
            <s xml:id="echoid-s3488" xml:space="preserve">ideo media Arithmetica inter G & </s>
            <s xml:id="echoid-s3489" xml:space="preserve">B, hoc eſt H, major
              <lb/>
            eſt quam D media harmonica inter C & </s>
            <s xml:id="echoid-s3490" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3491" xml:space="preserve">eodem modo M
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            media arithmetica inter G & </s>
            <s xml:id="echoid-s3492" xml:space="preserve">H major eſt media geometrica
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            inter easdem G & </s>
            <s xml:id="echoid-s3493" xml:space="preserve">H: </s>
            <s xml:id="echoid-s3494" xml:space="preserve">& </s>
            <s xml:id="echoid-s3495" xml:space="preserve">quoniam G eſt major quam C, & </s>
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            H quam D; </s>
            <s xml:id="echoid-s3497" xml:space="preserve">media geometrica inter G & </s>
            <s xml:id="echoid-s3498" xml:space="preserve">H major eſt quam
              <lb/>
            E media geometrica inter C & </s>
            <s xml:id="echoid-s3499" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3500" xml:space="preserve">& </s>
            <s xml:id="echoid-s3501" xml:space="preserve">proinde M major
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            eſt quam E. </s>
            <s xml:id="echoid-s3502" xml:space="preserve">deinde N media arithmetica inter M & </s>
            <s xml:id="echoid-s3503" xml:space="preserve">H ma-
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            jor eſt media harmonica inter eaſdem, & </s>
            <s xml:id="echoid-s3504" xml:space="preserve">quoniam H major
              <lb/>
            eſt quam D & </s>
            <s xml:id="echoid-s3505" xml:space="preserve">M quam E, media harmonica inter M & </s>
            <s xml:id="echoid-s3506" xml:space="preserve">H
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            major eſt quam F media harmonica inter E & </s>
            <s xml:id="echoid-s3507" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3508" xml:space="preserve">& </s>
            <s xml:id="echoid-s3509" xml:space="preserve">ideo </s>
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