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

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        <div xml:id="echoid-div64" type="section" level="1" n="29">
          <pb o="362" file="0070" n="74" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s1271" xml:space="preserve">Eſto circulus cujus centrum A, & </s>
            <s xml:id="echoid-s1272" xml:space="preserve">inſcribatur ipſi polygo-
              <lb/>
              <note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">TAB. XXXVIII.
                <lb/>
              Fig. 6.</note>
            num lateribus æqualibus, quorum unum ſit B C; </s>
            <s xml:id="echoid-s1273" xml:space="preserve">& </s>
            <s xml:id="echoid-s1274" xml:space="preserve">ali-
              <lb/>
            ud ſimile circumſcribatur F E G, cujus latera circulum con-
              <lb/>
            tingant ad occurſum angulorum polygoni prioris. </s>
            <s xml:id="echoid-s1275" xml:space="preserve">Dico cir-
              <lb/>
            culum minorem eſſe duabus tertiis polygoni F E G ſimul
              <lb/>
            cum triente polygoni B C. </s>
            <s xml:id="echoid-s1276" xml:space="preserve">Ducantur namque ex centro re-
              <lb/>
            ctæ A B, A C. </s>
            <s xml:id="echoid-s1277" xml:space="preserve">Igitur quoniam ſuper baſi portionis B D C
              <lb/>
            conſiſtit triangulum B E C, cujus latera portionem contin-
              <lb/>
            gunt, erit ipſa minor duabus tertiis trianguli B E C . </s>
            <s xml:id="echoid-s1278" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">per. 4. huj.</note>
            taque ſi triangulo A B C addantur duæ tertiæ trianguli B E C,
              <lb/>
            hoc eſt, duæ tertiæ exceſſus quadrilateri A B E C ſupra tri-
              <lb/>
            angulum A B C, ex utriſque compoſitum ſpatium majus
              <lb/>
            erit ſectore circuli A B C. </s>
            <s xml:id="echoid-s1279" xml:space="preserve">Idem eſt autem, ſive triangulo
              <lb/>
            A B C addantur duæ tertiæ exceſſus dicti, ſive addantur duæ
              <lb/>
            tertiæ quadrilateri A B E C, contraque auferantur duæ ter-
              <lb/>
            tiæ trianguli A B C: </s>
            <s xml:id="echoid-s1280" xml:space="preserve">hinc autem fiunt duæ tertiæ quadri-
              <lb/>
            lateri A B E C cum triente trianguli A B C. </s>
            <s xml:id="echoid-s1281" xml:space="preserve">Ergo apparet
              <lb/>
            ſectorem A B C minorem eſſe duabus tertiis quadrilateri
              <lb/>
            A B E C & </s>
            <s xml:id="echoid-s1282" xml:space="preserve">triente trianguli A B C. </s>
            <s xml:id="echoid-s1283" xml:space="preserve">Quare ſumptis omni-
              <lb/>
            bus quoties ſector A B C circulo continetur, totus quoque
              <lb/>
            circulus minor erit duabus tertiis polygoni circumſcripti
              <lb/>
            F E G & </s>
            <s xml:id="echoid-s1284" xml:space="preserve">triente inſcripti B C. </s>
            <s xml:id="echoid-s1285" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s1286" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div66" type="section" level="1" n="30">
          <head xml:id="echoid-head51" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . VII.
            <emph style="sc">Prop</emph>
          . VII.</head>
          <p style="it">
            <s xml:id="echoid-s1287" xml:space="preserve">OMnis circuli circumferentia major eſt perime-
              <lb/>
            tro polygoni æqualium laterum ſibi inſcripti,
              <lb/>
            & </s>
            <s xml:id="echoid-s1288" xml:space="preserve">triente exceſſus quo perimeter eadem ſuperat pe-
              <lb/>
            rimetrum alterius polygoni inſcripti ſubduplo late-
              <lb/>
            terum numero.</s>
            <s xml:id="echoid-s1289" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1290" xml:space="preserve">Eſto circulus A B, centro O, cui inſcribatur polygonum
              <lb/>
              <note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">TAB. XXXVIII.
                <lb/>
              Fig. 7.</note>
            æquilaterum A C D, atque alterum duplo laterum nume-
              <lb/>
            ro A E C B D F. </s>
            <s xml:id="echoid-s1291" xml:space="preserve">Sitque recta G I æqualis perimetro po-
              <lb/>
            lygoni A E C B D F, G H vero æqualis perimetro </s>
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