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

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          <p>
            <s xml:id="echoid-s1166" xml:space="preserve">
              <pb o="358" file="0066" n="70" rhead="CHRISTIANI HUGENII"/>
            anguli E B F. </s>
            <s xml:id="echoid-s1167" xml:space="preserve">Huic autem triangulo æquantur ſingula A E B,
              <lb/>
            B F C. </s>
            <s xml:id="echoid-s1168" xml:space="preserve">Ergo utriuſque ſimul triangulum A B C minus erit
              <lb/>
            quam quadruplum. </s>
            <s xml:id="echoid-s1169" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s1170" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div56" type="section" level="1" n="25">
          <head xml:id="echoid-head46" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . II.
            <emph style="sc">Prop</emph>
          . II.</head>
          <p style="it">
            <s xml:id="echoid-s1171" xml:space="preserve">Si fuerit circuli portio, ſemicirculo minor, & </s>
            <s xml:id="echoid-s1172" xml:space="preserve">ſu-
              <lb/>
            per eadem baſi triangulum, cujus latera portio-
              <lb/>
            nem contingant; </s>
            <s xml:id="echoid-s1173" xml:space="preserve">ducatur autem quæ contingat por-
              <lb/>
            tionem in vertice: </s>
            <s xml:id="echoid-s1174" xml:space="preserve">Hæc à triangulo dicto triangu-
              <lb/>
            lum abſcindet majus dimidio maximi trianguli in-
              <lb/>
            tra portionem deſcripti.</s>
            <s xml:id="echoid-s1175" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1176" xml:space="preserve">Eſto circuli portio ſemicirculo minor A B C, cujus vertex
              <lb/>
              <note position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">TAB. XXXVIII.
                <lb/>
              Fig. 2.</note>
            B. </s>
            <s xml:id="echoid-s1177" xml:space="preserve">Et contingant portionem ad terminos baſis rectæ A E,
              <lb/>
            C E, quæ conveniant in E: </s>
            <s xml:id="echoid-s1178" xml:space="preserve">convenient enim quia portio ſe-
              <lb/>
            micirculo minor eſt. </s>
            <s xml:id="echoid-s1179" xml:space="preserve">Porro ducatur F G, quæ contingati-
              <lb/>
            pſam in vertice B; </s>
            <s xml:id="echoid-s1180" xml:space="preserve">& </s>
            <s xml:id="echoid-s1181" xml:space="preserve">jungantur A B, B C. </s>
            <s xml:id="echoid-s1182" xml:space="preserve">Oſtendendum eſt
              <lb/>
            itaque, triangulum F E G majus eſſe dimidio trianguli
              <lb/>
            A B C. </s>
            <s xml:id="echoid-s1183" xml:space="preserve">Conſtat triangula A E C, F E G, item A F B,
              <lb/>
            B G C æquicruria eſſe, dividique F G ad B bifariam. </s>
            <s xml:id="echoid-s1184" xml:space="preserve">Utra-
              <lb/>
            que autem ſimul F E, E G, major eſt quam F G; </s>
            <s xml:id="echoid-s1185" xml:space="preserve">ergo
              <lb/>
            E F major quam F B, vel quam F A. </s>
            <s xml:id="echoid-s1186" xml:space="preserve">Tota igitur A E minor
              <lb/>
            quam dupla F E. </s>
            <s xml:id="echoid-s1187" xml:space="preserve">Quare triangulum F E G majus erit quarta
              <lb/>
            parte trianguli A E C. </s>
            <s xml:id="echoid-s1188" xml:space="preserve">Sicut autem F A ad A E, ita eſt al-
              <lb/>
            titudo trianguli A B C ad altitudinem trianguli A E C, & </s>
            <s xml:id="echoid-s1189" xml:space="preserve">
              <lb/>
            baſis utrique eadem A C. </s>
            <s xml:id="echoid-s1190" xml:space="preserve">Ergo, quum F A ſit minor quam
              <lb/>
            ſubdupla totius A E, erit triangulum A B C minus dimi-
              <lb/>
            dio triangulo A E C. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">Hujus vero quarta parte majus erat
              <lb/>
            triangulum F E G. </s>
            <s xml:id="echoid-s1192" xml:space="preserve">Ergo triangulum F E G majus dimidio
              <lb/>
            trianguli A B C. </s>
            <s xml:id="echoid-s1193" xml:space="preserve">Quod oſtendendum fuit.</s>
            <s xml:id="echoid-s1194" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div58" type="section" level="1" n="26">
          <head xml:id="echoid-head47" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . III.
            <emph style="sc">Prop</emph>
          . III.</head>
          <p style="it">
            <s xml:id="echoid-s1195" xml:space="preserve">OMnis circuli portio, ſemicirculo minor, ad ma-
              <lb/>
            ximum triangulum inſcriptum majorem ratio-
              <lb/>
            nem habet quam ſeſquitertiam.</s>
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