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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            <s xml:id="echoid-s381" xml:space="preserve">
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            lineam
              <emph style="sc">EF</emph>
            , paſſus 25 longam:</s>
            <s xml:id="echoid-s382" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s383" xml:space="preserve">E -- F.</s>
            <s xml:id="echoid-s384" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s385" xml:space="preserve">Ad hoc agendum formabimus angulum fortuitum
              <lb/>
              <emph style="sc">GHI</emph>
            , & </s>
            <s xml:id="echoid-s386" xml:space="preserve">à linea
              <emph style="sc">HI</emph>
            , ſecabimus duas lineas. </s>
            <s xml:id="echoid-s387" xml:space="preserve">Prior erit
              <emph style="sc">HK</emph>
              <lb/>
            æqualis
              <emph style="sc">AB</emph>
            : </s>
            <s xml:id="echoid-s388" xml:space="preserve">altera
              <emph style="sc">KL</emph>
            æqualis
              <emph style="sc">CD</emph>
            . </s>
            <s xml:id="echoid-s389" xml:space="preserve">Et à linea
              <emph style="sc">HG</emph>
            ſecabi-
              <lb/>
            mus aliam æqualem
              <emph style="sc">EF</emph>
            , quæ erit
              <emph style="sc">HM</emph>
            : </s>
            <s xml:id="echoid-s390" xml:space="preserve">intra duo item
              <lb/>
            puncta
              <emph style="sc">K</emph>
            & </s>
            <s xml:id="echoid-s391" xml:space="preserve">
              <emph style="sc">M</emph>
            , ducemus lineam rectam, quæ erit
              <emph style="sc">KM</emph>
            : </s>
            <s xml:id="echoid-s392" xml:space="preserve">ac
              <lb/>
            à puncto
              <emph style="sc">L</emph>
            ducemus lineam æquidiſtantem lineæ
              <emph style="sc">KM</emph>
            ,
              <lb/>
            vt docet quarta operatio, quæ erit linea
              <emph style="sc">LN</emph>
            : </s>
            <s xml:id="echoid-s393" xml:space="preserve">linea au-
              <lb/>
            tem
              <emph style="sc">MN</emph>
            erit quarta proportionalis ad tres lineas
              <emph style="sc">AB</emph>
            ,
              <lb/>
              <emph style="sc">CD</emph>
            , & </s>
            <s xml:id="echoid-s394" xml:space="preserve">
              <emph style="sc">EF</emph>
            , vt docet duodecima ſexti Euclidis Itaque li-
              <lb/>
            nea
              <emph style="sc">EF</emph>
            , quum ſit æqualis lineæ
              <emph style="sc">HM</emph>
            , eandem habebit
              <lb/>
            proportionem ad lineam
              <emph style="sc">MN</emph>
            , quam habet linea
              <emph style="sc">AB</emph>
            ,
              <lb/>
            æqualis exiſtens lineæ
              <emph style="sc">HK</emph>
            , ad
              <emph style="sc">KL</emph>
            , quæ æqualis eſt
              <emph style="sc">CD</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s395" xml:space="preserve">Iam ſumemus mediam proportionalem inter lineam
              <lb/>
              <emph style="sc">HM</emph>
            & </s>
            <s xml:id="echoid-s396" xml:space="preserve">
              <emph style="sc">MN</emph>
            , per nonam ſexti Euclidis, quæ erit linea
              <lb/>
              <emph style="sc">OP</emph>
            ,
              <emph style="sc">O -- P</emph>
              <lb/>
            partiemurq́; </s>
            <s xml:id="echoid-s397" xml:space="preserve">lineam
              <emph style="sc">OP</emph>
            , in paſſus 25, prout erat diuiſa
              <lb/>
            linea
              <emph style="sc">EF</emph>
            , deſcribendoq́; </s>
            <s xml:id="echoid-s398" xml:space="preserve">ichnographiam ſimilem datæ,
              <lb/>
            cum ſcala
              <emph style="sc">OP</emph>
            , ichnographia quarta parte major erit
              <lb/>
            quàm prior, vt docet decima nona ſexti Euclidis. </s>
            <s xml:id="echoid-s399" xml:space="preserve">Ex
              <lb/>
            hoc eodem canone deſcribi poterit ichnographia
              <lb/>
            major vel minor, in quacumq; </s>
            <s xml:id="echoid-s400" xml:space="preserve">proportione libuerit. </s>
            <s xml:id="echoid-s401" xml:space="preserve">
              <lb/>
            Ne quis autem conqueratur quòd paſſus linearũ
              <emph style="sc">HM</emph>
            ,
              <lb/>
            & </s>
            <s xml:id="echoid-s402" xml:space="preserve">
              <emph style="sc">MN</emph>
            inæquales ſint paſſibus linearum
              <emph style="sc">HK</emph>
            , & </s>
            <s xml:id="echoid-s403" xml:space="preserve">
              <emph style="sc">KL</emph>
            : </s>
            <s xml:id="echoid-s404" xml:space="preserve">ſi
              <lb/>
            enim vtrobique æqualitas à nobis obſeruata ſuiſſet,
              <lb/>
            aut in nimiam longitudinem excreuiſſet typus ſeu fi-
              <lb/>
            gura, aut æquidiſtantia linearum
              <emph style="sc">KM</emph>
            & </s>
            <s xml:id="echoid-s405" xml:space="preserve">
              <emph style="sc">LN</emph>
            diſcerni
              <lb/>
            nequiuiſſet.</s>
            <s xml:id="echoid-s406" xml:space="preserve"/>
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