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

Table of Notes

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            <s xml:id="echoid-s2968" xml:space="preserve">
              <pb o="421" file="0139" n="148" rhead="ET HYPERBOLÆ QUADRATURA."/>
            ter C & </s>
            <s xml:id="echoid-s2969" xml:space="preserve">D, manifeſtum eſt differentiam inter A & </s>
            <s xml:id="echoid-s2970" xml:space="preserve">B majo-
              <lb/>
            rem eſſe duplo differentiæ inter C & </s>
            <s xml:id="echoid-s2971" xml:space="preserve">D, hoc eſt differen-
              <lb/>
            tiam inter triangulum A B P & </s>
            <s xml:id="echoid-s2972" xml:space="preserve">trapezium A B F P majo-
              <lb/>
            rem eſſe duplo differentiæ inter trapezium A B I P, & </s>
            <s xml:id="echoid-s2973" xml:space="preserve">po-
              <lb/>
            lygonum A B D L P, quod demonſtrare oportuit.</s>
            <s xml:id="echoid-s2974" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div157" type="section" level="1" n="72">
          <head xml:id="echoid-head107" xml:space="preserve">SCHOLIUM.</head>
          <p>
            <s xml:id="echoid-s2975" xml:space="preserve">Eodem prorſus modo demonſtratur differentiam inter tra-
              <lb/>
            pezium A B I P & </s>
            <s xml:id="echoid-s2976" xml:space="preserve">polygonum A B D L P majorem
              <lb/>
            eſſe duplo differentiæ inter polygonum A B E I O P & </s>
            <s xml:id="echoid-s2977" xml:space="preserve">poly-
              <lb/>
            gonum A B C G K N P. </s>
            <s xml:id="echoid-s2978" xml:space="preserve">denique eodem modo demonſtra-
              <lb/>
            ri poteſt hic differentiarum exceſſus in ſubdupla noſtra poly-
              <lb/>
            gonorum complicatorum deſcriptione in infinitum; </s>
            <s xml:id="echoid-s2979" xml:space="preserve">differen-
              <lb/>
            tia enim priorum nempe inſcripti & </s>
            <s xml:id="echoid-s2980" xml:space="preserve">circumſcripti major ſem-
              <lb/>
            per erit duplo differentiæ immediatè ſequentium nimirum in-
              <lb/>
            ſcripti quoque & </s>
            <s xml:id="echoid-s2981" xml:space="preserve">circumſcripti, & </s>
            <s xml:id="echoid-s2982" xml:space="preserve">proinde aufertur majus
              <lb/>
            quam dimidium a priorum differentia ut fiat differentia im-
              <lb/>
            mediatè ſequentium; </s>
            <s xml:id="echoid-s2983" xml:space="preserve">& </s>
            <s xml:id="echoid-s2984" xml:space="preserve">igitur continuando ſubduplam po-
              <lb/>
            lygonorum deſcriptionem, inveniri poſſunt duo polygona
              <lb/>
            complicata, quorum differentia ſit minor qualibet exhibita
              <lb/>
            quantitate, ut in præcedentis Scholio aſſumpſimus.</s>
            <s xml:id="echoid-s2985" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2986" xml:space="preserve">Sint duæ quantitates indefinitæ
              <emph style="super">a</emph>
            minor
              <emph style="sub">b</emph>
            major, ſintque
              <lb/>
            datæ duæ rationes majoris inæqualitatis
              <emph style="super">c</emph>
            ad
              <emph style="super">d</emph>
            , & </s>
            <s xml:id="echoid-s2987" xml:space="preserve">
              <emph style="super">c</emph>
            ad
              <emph style="super">e</emph>
            ; </s>
            <s xml:id="echoid-s2988" xml:space="preserve">de-
              <lb/>
            inde ſit ut
              <emph style="super">c</emph>
            ad
              <emph style="super">d</emph>
            ita
              <emph style="super">b - a</emph>
            ad {bd - ad/c} cui addatur quantitas
              <emph style="sub">a</emph>
            ut
              <lb/>
            fiat {ca + bd - ad/c}, quæ quantitas ponatur immediate ſub a: </s>
            <s xml:id="echoid-s2989" xml:space="preserve">fiatque
              <lb/>
            ut
              <emph style="super">c</emph>
            ad
              <emph style="sub">e</emph>
            ita
              <emph style="super">b</emph>
            -
              <emph style="sub">a</emph>
            ad {be - ae/c}, quæ quantitas ſubſtrahatur ex
              <emph style="super">b</emph>
            & </s>
            <s xml:id="echoid-s2990" xml:space="preserve">
              <lb/>
            relictum nempe {bc - be + ae/c} ponatur ſub
              <emph style="sub">b.</emph>
            continuetur de-
              <lb/>
            inde ſeries convergens cujus pri-
              <lb/>
              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">
                <lb/>
              # d
                <lb/>
              c # e # a # b
                <lb/>
              ## {ca + bd - ad/c} # {bc - be + ae/ c}
                <lb/>
              </note>
            mi termini convergentes ſunt
              <emph style="super">a, b</emph>
            ,
              <lb/>
            & </s>
            <s xml:id="echoid-s2991" xml:space="preserve">ſecundi termini convergentes
              <lb/>
            {ca + bd - ad/c}, {bc - be + ae/c}. </s>
            <s xml:id="echoid-s2992" xml:space="preserve">manifeſtum eſt terminum {ca + bd - ad/c} </s>
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