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

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              <pb o="467" file="0187" n="197" rhead="JAC. GREG. RESPONS."/>
            perientiam enim feci ſolummodo de primis & </s>
            <s xml:id="echoid-s4054" xml:space="preserve">ſecundis ter-
              <lb/>
            minis, non conſiderando tertios cum primis coincidere, nam
              <lb/>
            ratiociniis inſiſtebam, de exemplis parum ſolicitus. </s>
            <s xml:id="echoid-s4055" xml:space="preserve">Ut au-
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            tem appareat in hoc nihil contineri contra noſtram Doctri-
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            nam, agedum hoc loco 10: </s>
            <s xml:id="echoid-s4056" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s4057" xml:space="preserve">totidem verbis, ſed cum
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            legitimo exemplo repetamus.</s>
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        <div xml:id="echoid-div226" type="section" level="1" n="112">
          <head xml:id="echoid-head154" xml:space="preserve">PROP. X. PROBLEMA.</head>
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            <s xml:id="echoid-s4059" xml:space="preserve">Ex data quantitate eodem modo compoſita à duobus
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            terminis convergentibus cujuſcunque ſeriei convergen-
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            tis, quo componitur ex terminis convergentibus ejuſ-
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            dem ſeriei immediate ſequentibus; </s>
            <s xml:id="echoid-s4060" xml:space="preserve">ſeriei propoſitæ
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            terminationem invenire.</s>
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          <p>
            <s xml:id="echoid-s4062" xml:space="preserve">Sit ſeries convergens, cujus duo termini convergentes qui-
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            cunque ſint a, b, & </s>
            <s xml:id="echoid-s4063" xml:space="preserve">termini convergentes immediatè ſe-
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            quentes {2 a b/a + b}, {a + b/2}, termini priores inter ſe multiplicati effi-
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            ciunt eandem a b, item ſequentes inter ſe multiplicati effi-
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            ciunt eandem a b; </s>
            <s xml:id="echoid-s4064" xml:space="preserve">ex his invenienda ſit propoſitæ ſeriei ter-
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            minatio. </s>
            <s xml:id="echoid-s4065" xml:space="preserve">Manifeſtum eſt, quantitatem a b eodem modo
              <lb/>
            fieri à terminis convergentibus a, b, quo à terminis conver-
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            gentibus immediatè ſequentibus {2 a b/a + b}, {a + b/z}: </s>
            <s xml:id="echoid-s4066" xml:space="preserve">& </s>
            <s xml:id="echoid-s4067" xml:space="preserve">quoniam quan-
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            titates a, b, indefinitè ponuntur pro quibuslibet totius ſe-
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            riei terminis convergentibus, evidens eſt, duos quoſcunque
              <lb/>
            terminos convergentes propoſitæ ſeriei inter ſe multiplica-
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            tos idem efficere productum, quod faciunt termini imme-
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            diatè ſequentes etiam inter ſe multiplicati; </s>
            <s xml:id="echoid-s4068" xml:space="preserve">cumque duo ter-
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            mini convergentes duos terminos convergentes ſemper im-
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            mediatè ſequantur, manifeſtum eſt, duos quoſcunque ter-
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            minos convergentes inter ſe multiplicatos idem ſemper effi-
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            cere productum, nempe a b; </s>
            <s xml:id="echoid-s4069" xml:space="preserve">atque ultimi termini conver-
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            gentes ſunt æquales, & </s>
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          <head xml:id="echoid-head155" style="it" xml:space="preserve">Tom. II. Nnn</head>
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            <s xml:id="echoid-s4070" xml:space="preserve">proinde ſit ultimus ille terminus, ſeu
              <lb/>
            ſeriei terminatio Z, quæ in ſe ipſam multiplicata facit
              <lb/>
            </s>
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