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

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            <s xml:id="echoid-s1243" xml:space="preserve">
              <pb o="361" file="0069" n="73" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            rectis A D, D C & </s>
            <s xml:id="echoid-s1244" xml:space="preserve">arcu A B C comprehenſum majus erit
              <lb/>
            portionis A B C dimidio. </s>
            <s xml:id="echoid-s1245" xml:space="preserve">Ac proinde triangulum A D C
              <lb/>
            majus quam portionis A B C ſeſquialterum. </s>
            <s xml:id="echoid-s1246" xml:space="preserve">Quod erat de-
              <lb/>
            monſtrandum.</s>
            <s xml:id="echoid-s1247" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div62" type="section" level="1" n="28">
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            <emph style="sc">Theor</emph>
          . V.
            <emph style="sc">Prop</emph>
          . V.</head>
          <p style="it">
            <s xml:id="echoid-s1248" xml:space="preserve">OMnis circulus major eſt pylogono æqualium
              <lb/>
            laterum ſibi inſcripto & </s>
            <s xml:id="echoid-s1249" xml:space="preserve">triente exceſſus quo
              <lb/>
            id polygonum ſuperat aliud inſcriptum ſubduplo la-
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            terum numero.</s>
            <s xml:id="echoid-s1250" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1251" xml:space="preserve">Eſto circulus centro C; </s>
            <s xml:id="echoid-s1252" xml:space="preserve">ſitque ipſi inſcriptum polygonum
              <lb/>
              <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">TAB. XXXVIII.
                <lb/>
              Fig. 5.</note>
            æqualium laterum, quorum unum ſit A B. </s>
            <s xml:id="echoid-s1253" xml:space="preserve">Atque alterum
              <lb/>
            item polygonum ſit inſcriptum, cujus bina latera A D, D B,
              <lb/>
            ſubtendat A B. </s>
            <s xml:id="echoid-s1254" xml:space="preserve">Hoc igitur priore polygono majus eſt. </s>
            <s xml:id="echoid-s1255" xml:space="preserve">Sit
              <lb/>
            autem exceſſus trienti æquale H ſpatium. </s>
            <s xml:id="echoid-s1256" xml:space="preserve">Dico circulum ma-
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            jorem eſſe polygono A D B una cum ſpatio H. </s>
            <s xml:id="echoid-s1257" xml:space="preserve">Ducantur
              <lb/>
            enim ex centro rectæ C A, C B. </s>
            <s xml:id="echoid-s1258" xml:space="preserve">Quoniam igitur portio
              <lb/>
            circuli A D B major eſt quam ſeſquitertia trianguli A D B ſibi
              <lb/>
            inſcripti ; </s>
            <s xml:id="echoid-s1259" xml:space="preserve">erunt portiones A D, D B, ſimul majores
              <note symbol="*" position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">per. 3. huj.</note>
            ente trianguli A D B. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">Quamobrem & </s>
            <s xml:id="echoid-s1261" xml:space="preserve">ſector C A B major
              <lb/>
            erit utriſque ſimul quadrilatero C A D B & </s>
            <s xml:id="echoid-s1262" xml:space="preserve">triente trian-
              <lb/>
            guli A D B. </s>
            <s xml:id="echoid-s1263" xml:space="preserve">Sicut autem ſector C A B ad circulum totum,
              <lb/>
            ita eſt quadrilaterum C D B A ad polygonum A D B, & </s>
            <s xml:id="echoid-s1264" xml:space="preserve">
              <lb/>
            ita quoque triens trianguli A D B ad trientem exceſſus po-
              <lb/>
            lygoni A D B ſupra polygonum A B. </s>
            <s xml:id="echoid-s1265" xml:space="preserve">Ergo manifeſtum eſt
              <lb/>
            circulum quoque totum majorem fore polygono A D B una
              <lb/>
            cum triente exceſſus quo polygonum A D B ſuperat poly-
              <lb/>
            gonum A B, hoc eſt, unà cum ſpatio H. </s>
            <s xml:id="echoid-s1266" xml:space="preserve">Quod erat demon-
              <lb/>
            ſtrandum.</s>
            <s xml:id="echoid-s1267" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div64" type="section" level="1" n="29">
          <head xml:id="echoid-head50" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . VI.
            <emph style="sc">Prop</emph>
          . VI.</head>
          <p style="it">
            <s xml:id="echoid-s1268" xml:space="preserve">Omnis circulus minor eſt duabus tertiis polygo-
              <lb/>
            ni æqualium laterum ſibi circumſcripti & </s>
            <s xml:id="echoid-s1269" xml:space="preserve">tri-
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            ente polygoni ſimilis inſcripti.</s>
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