Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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              <pb o="468" file="0188" n="198" rhead="JAC. GREG. RESPONSUM"/>
            Z
              <emph style="super">2</emph>
            = a b; </s>
            <s xml:id="echoid-s4071" xml:space="preserve">eſt igitur Z. </s>
            <s xml:id="echoid-s4072" xml:space="preserve">ſeu ſeriei terminatio r
              <emph style="super">2</emph>
            a b, quam invenire oportuit: </s>
            <s xml:id="echoid-s4073" xml:space="preserve">& </s>
            <s xml:id="echoid-s4074" xml:space="preserve">proinde ad inveniendam cujuſcunque ſeriei convergentis terminationem opus eſt ſolummodo inve- nire quantitatem eodem modo compoſitam ex terminis con- vergentibus primis, quo componitur eadem quantitas ex ter- minis convergentibus ſecundis.</s>
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        <div xml:id="echoid-div228" type="section" level="1" n="114">
          <head xml:id="echoid-head156" xml:space="preserve">CONSECTARIUM.</head>
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            <s xml:id="echoid-s4076" xml:space="preserve">Quoniam non refert in Problemate, ſive termini con-
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            vergentes, a, b, ſint primi, ſecundi vel tertii,
              <lb/>
            &</s>
            <s xml:id="echoid-s4077" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4078" xml:space="preserve">manifeſtum eſt, omnis ſeriei convergentis ter-
              <lb/>
            minationem eodem modo eſſe compoſitam ex termi-
              <lb/>
            nis convergentibus primis, quo ex ſecundis, ter-
              <lb/>
            tiis, &</s>
            <s xml:id="echoid-s4079" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4080" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4081" xml:space="preserve">Si quis aliud Exemplum deſideret, ſint primi termini a, b,
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            ſecundi r
              <emph style="super">7</emph>
            a
              <emph style="super">5</emph>
            b
              <emph style="super">2</emph>
            , r2 a b, quantitas eodem modo compo-
              <lb/>
            ſita &</s>
            <s xml:id="echoid-s4082" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4083" xml:space="preserve">eſt a
              <emph style="super">7</emph>
            b
              <emph style="super">4</emph>
            & </s>
            <s xml:id="echoid-s4084" xml:space="preserve">ſeriei terminatio r
              <emph style="super">11</emph>
            a
              <emph style="super">7</emph>
            b
              <emph style="super">4</emph>
            : </s>
            <s xml:id="echoid-s4085" xml:space="preserve">videat Huge-
              <lb/>
            nius, duo exempla legitima hic adducta inquiſitionem Septi-
              <lb/>
            mæ non admittere; </s>
            <s xml:id="echoid-s4086" xml:space="preserve">ope tamen prop. </s>
            <s xml:id="echoid-s4087" xml:space="preserve">decimæ (ſuppoſita ter-
              <lb/>
            tia illa quantitate) facilè reſolvuntur, neque ullo modo con-
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            ſectarium reſpuunt, quod ſolummodo eſſe momenti ſatis
              <lb/>
            ſit indicaſſe; </s>
            <s xml:id="echoid-s4088" xml:space="preserve">plura autem exempla deſideranti millena affe-
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            ram.</s>
            <s xml:id="echoid-s4089" xml:space="preserve"/>
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            <s xml:id="echoid-s4090" xml:space="preserve">Ad primam Hugenii objectionem quod ſpectat, miror
              <lb/>
            eum non conſiderâſſe præcedens conſectarium, ubi illa,
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            quæ deſiderat, evidenter deduco ex prop. </s>
            <s xml:id="echoid-s4091" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4092" xml:space="preserve">At agnoſcit
              <lb/>
            hoc verum eſſe in illis ſeriebus, quæ ope noſtræ methodi
              <lb/>
            terminantur: </s>
            <s xml:id="echoid-s4093" xml:space="preserve">velim certè ut aſſignet mihi Nobiliſſimus Vir
              <lb/>
            ſeriem aliquam convergentem cum ſua terminatione, quæ
              <lb/>
            conſectarium noſtrum reſpuat; </s>
            <s xml:id="echoid-s4094" xml:space="preserve">vel ſi eam aſſignare non poſ-
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            ſit, ſolidam dubitandi rationem tantum deſidero. </s>
            <s xml:id="echoid-s4095" xml:space="preserve">Ut au-
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            tem funditus evertatur hæc objectio, ſequentem exhibeo de-
              <lb/>
            monſtrationem Geometricam.</s>
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