Cataneo, Girolamo, Hier. Cataneus de arte bellica, sive, de designandis ac construendis arcibus & propugnaculis, necnon & de iis oppugnandis, expugnandis ac propugnandis : de itinere exercitus, ac castrametatione, quando expediat manus cum hoste conserere, 1600

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        <div xml:id="echoid-div24" type="section" level="1" n="21">
          <head xml:id="echoid-head25" xml:space="preserve">SEPTIMA OPERATIO.</head>
          <p>
            <s xml:id="echoid-s407" xml:space="preserve">
              <emph style="sc">Indagare</emph>
            mediam proportionalem in-
              <lb/>
            ter duas lineas.</s>
            <s xml:id="echoid-s408" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s409" xml:space="preserve">Verbi gratia, deſidero mediam proportionalem in-
              <lb/>
            ter lineam E -- F, & </s>
            <s xml:id="echoid-s410" xml:space="preserve">F -- G, jun-
              <lb/>
            gam eas in directum, faciamq́; </s>
            <s xml:id="echoid-s411" xml:space="preserve">ex eis vnicam lineam,
              <lb/>
            quæ erit
              <emph style="sc">E -- F -- G</emph>
            , æ quipollens
              <lb/>
            ſcilicet E F & </s>
            <s xml:id="echoid-s412" xml:space="preserve">F G.</s>
            <s xml:id="echoid-s413" xml:space="preserve"> Diuidemus deinde integram lineam
              <lb/>
              <emph style="sc">EG</emph>
            in duas partes æ quales in puncto
              <emph style="sc">O</emph>
            , vt hîc apparet,
              <lb/>
              <emph style="sc">E -- F -- O -- G</emph>
            , figemusq́; </s>
            <s xml:id="echoid-s414" xml:space="preserve">pedem im-
              <lb/>
            mobilem circini in puncto
              <emph style="sc">O</emph>
            , alterum extendendo ad
              <lb/>
            alterutram extremitatum
              <emph style="sc">E</emph>
            vel
              <emph style="sc">G</emph>
            , ſemicirculumq́; </s>
            <s xml:id="echoid-s415" xml:space="preserve">de-
              <lb/>
            ſcribemus: </s>
            <s xml:id="echoid-s416" xml:space="preserve">deinde à puncto
              <emph style="sc">F</emph>
            erigemus perpendicu-
              <lb/>
            larem, vt in ſecunda operatione factum eſt, quæ erit
              <lb/>
            linea
              <emph style="sc">FH</emph>
            , quam dico mediam eſſe proportionalem in-
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            ter duas lineas EF, & </s>
            <s xml:id="echoid-s417" xml:space="preserve">FG, vt docet nona ſexti Eucli-
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            dis.</s>
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            <image file="0022-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/archimedes_repository/large/catan_belli_502_la_1600/figures/0022-01"/>
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