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

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        <div xml:id="echoid-div58" type="section" level="1" n="26">
          <pb o="360" file="0068" n="72" rhead="CHRISTIANI HUGENII"/>
        </div>
        <div xml:id="echoid-div60" type="section" level="1" n="27">
          <head xml:id="echoid-head48" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . IV.
            <emph style="sc">Prop</emph>
          . IV.</head>
          <p style="it">
            <s xml:id="echoid-s1223" xml:space="preserve">Omnis circuli portio, ſemicirculo minor, minor
              <lb/>
            eſt duabus tertiis trianguli eandem cum ipſa
              <lb/>
            baſin babentis, & </s>
            <s xml:id="echoid-s1224" xml:space="preserve">latera portionem contingentia.</s>
            <s xml:id="echoid-s1225" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1226" xml:space="preserve">Eſto circuli portio, ſemicirculo minor, A B C, & </s>
            <s xml:id="echoid-s1227" xml:space="preserve">contin-
              <lb/>
              <note position="left" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve">TAB. XXXVIII.
                <lb/>
              Fig. 4.</note>
            gant ipſam ad terminos baſis rectæ A D, C D, quæ con-
              <lb/>
            veniant in puncto D. </s>
            <s xml:id="echoid-s1228" xml:space="preserve">Dico Portionem A B C minorem eſſe
              <lb/>
            duabus tertiis trianguli A D C. </s>
            <s xml:id="echoid-s1229" xml:space="preserve">Ducatur enim E F quæ por-
              <lb/>
            tionem contingat in vertice B, & </s>
            <s xml:id="echoid-s1230" xml:space="preserve">inſcribatur ipſi triangu-
              <lb/>
            lum maximum A B C. </s>
            <s xml:id="echoid-s1231" xml:space="preserve">Quum igitur triangulum E D F ma-
              <lb/>
            jus ſit dimidio trianguli A B C , manifeſtum eſt ab
              <note symbol="*" position="left" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve">per. 2. huj.</note>
            partem abſcindi poſſe, ita ut reliquum tamen majus ſit di-
              <lb/>
            midio dicti A B C trianguli. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">Sit igitur hoc pacto abſciſſum
              <lb/>
            triangulum E D G. </s>
            <s xml:id="echoid-s1233" xml:space="preserve">Et ducantur porro rectæ H I, K L,
              <lb/>
            quæ portiones reliquas A M B, B N C in verticibus ſuis
              <lb/>
            contingant, ipſiſque portionibus triangula maxima inſcri-
              <lb/>
            bantur. </s>
            <s xml:id="echoid-s1234" xml:space="preserve">Idemque prorſus circa reliquas portiones fieri intel-
              <lb/>
            ligatur, donec tandem portiones reſiduæ ſimul minores ſint
              <lb/>
            quam duplum trianguli E D G. </s>
            <s xml:id="echoid-s1235" xml:space="preserve">Erit igitur inſcripta portio-
              <lb/>
            ni figura quædam rectilinea, atque alia circumſcripta. </s>
            <s xml:id="echoid-s1236" xml:space="preserve">Et
              <lb/>
            quoniam triangulum E G F majus eſt dimidio trianguli
              <lb/>
            A B C; </s>
            <s xml:id="echoid-s1237" xml:space="preserve">& </s>
            <s xml:id="echoid-s1238" xml:space="preserve">rurſus triangula H E I, K F L, majora quam
              <lb/>
            dimidia triangulorum A M B, B N C; </s>
            <s xml:id="echoid-s1239" xml:space="preserve">idque eadem ſem-
              <lb/>
            per ratione in reliquis locum habet, ut triangula ſuper por-
              <lb/>
            tionum verticibus conſtituta, eorum quæ intra portiones i-
              <lb/>
            pſas deſcripta ſunt, majora ſint quam ſubdupla: </s>
            <s xml:id="echoid-s1240" xml:space="preserve">apparet tri-
              <lb/>
            angula omnia extra portionem poſita etiam abſque triangu-
              <lb/>
            lo E G D majora ſimul eſſe quam dimidia triangulorum o-
              <lb/>
            mnium intra portionem deſcriptorum. </s>
            <s xml:id="echoid-s1241" xml:space="preserve">Atqui ſegmentorum in
              <lb/>
            portione reliquorum triangulum quoque E G D majus eſt
              <lb/>
            quam ſubduplum. </s>
            <s xml:id="echoid-s1242" xml:space="preserve">Ergo triangulum E D F ſimul cum reli-
              <lb/>
            quis triangulis, quæ ſunt extra portionem, majus erit dimi-
              <lb/>
            dio portionis totius A B C. </s>
            <s xml:id="echoid-s1243" xml:space="preserve">Quare multo magis ſpatium </s>
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