Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div705" type="section" level="1" n="247">
          <pb o="250" file="280" n="280" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s11582" xml:space="preserve">
              <emph style="sc">Datvm</emph>
            præterea ſit rectilineum ABCD, ex puncto E, dato in latere AB, di-
              <lb/>
            uidendum in duas partes, quarum prior ad B, vergens ad poſteriorem partem
              <lb/>
            habeat proportionem datam K, ad L. </s>
            <s xml:id="echoid-s11583" xml:space="preserve">Ductis ex dato puncto E, ad omnes an-
              <lb/>
              <figure xlink:label="fig-280-01" xlink:href="fig-280-01a" number="183">
                <image file="280-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/280-01"/>
              </figure>
            gulos oppoſitos rectis diuidentibus rectilineum in tot triangula vno minus,
              <lb/>
            quotlatera figura habet; </s>
            <s xml:id="echoid-s11584" xml:space="preserve">inueniantur rectæ FH, HI, IG, triangulis EBC, ECD, EDA, proportionales. </s>
            <s xml:id="echoid-s11585" xml:space="preserve">Secta deindetota FG, in M, ſecundum datam propor-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-280-01" xlink:href="note-280-01a" xml:space="preserve">3. hui{us}.</note>
            tionem K, ad L: </s>
            <s xml:id="echoid-s11586" xml:space="preserve">quoniam diuiſionis punctum M, incidit in primam linea F H,
              <lb/>
            diuidemus primi trianguli E B C, baſem BC, dato puncto E, oppoſitam in X, vt
              <lb/>
            FH, ſecta eſt in M. </s>
            <s xml:id="echoid-s11587" xml:space="preserve">Iuncta namq; </s>
            <s xml:id="echoid-s11588" xml:space="preserve">recta EX, erit triangulum EBX, ad
              <note symbol="b" position="left" xlink:label="note-280-02" xlink:href="note-280-02a" xml:space="preserve">1. hui{us}.</note>
            EXCDAE, vt FM, ad MG, hoc eſt, vt K, ad L: </s>
            <s xml:id="echoid-s11589" xml:space="preserve">propterea quod triangula E B C,
              <lb/>
            ECD, EDA, rectis FH, HI, IG, proportionalia ſunt ex conſtructione; </s>
            <s xml:id="echoid-s11590" xml:space="preserve">& </s>
            <s xml:id="echoid-s11591" xml:space="preserve">primæ
              <lb/>
            partes EBC, FH, ſectæ ſunt per rectam EX, & </s>
            <s xml:id="echoid-s11592" xml:space="preserve">in M, proportionaliter; </s>
            <s xml:id="echoid-s11593" xml:space="preserve">cum
              <note symbol="c" position="left" xlink:label="note-280-03" xlink:href="note-280-03a" xml:space="preserve">1. ſexti.</note>
            EBX, ad EXC, vt BX, ad XC, hoc eſt, vt FM, ad MH. </s>
            <s xml:id="echoid-s11594" xml:space="preserve">Conſtat ergo propoſitũ.</s>
            <s xml:id="echoid-s11595" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11596" xml:space="preserve">
              <emph style="sc">Si</emph>
            proportio data ſit N, ad O; </s>
            <s xml:id="echoid-s11597" xml:space="preserve">ſecta FG, in P, ſecundum proportionem N,
              <lb/>
            ad O, cadet diuiſionis punctum P, in ſecundam lineam HI. </s>
            <s xml:id="echoid-s11598" xml:space="preserve">Igitur ſi ſecundi tri-
              <lb/>
            anguli ECD, baſis CD, dato puncto E, oppoſita ſecetur in Q, vt ſecta eſt HI, in
              <lb/>
            P, nectatur que recta EQ, erit rurſus figura EBCQE, ad figuram EQDA, vt
              <note symbol="d" position="left" xlink:label="note-280-04" xlink:href="note-280-04a" xml:space="preserve">1. hui{us}.</note>
            ad PG, hoc eſt, vt N, ad O.</s>
            <s xml:id="echoid-s11599" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11600" xml:space="preserve">
              <emph style="sc">Si</emph>
            denique data ſit proportio R, ad S; </s>
            <s xml:id="echoid-s11601" xml:space="preserve">ſecta FG, in V, ſecundum proportio-
              <lb/>
            nem R, ad S, cadet diuiſionis punctum V, in tertiam lineam I G. </s>
            <s xml:id="echoid-s11602" xml:space="preserve">Quamobrem
              <lb/>
            ſi tertij trianguli EDA, baſis DA, dato puncto E, oppoſita ſecetur in T, vt ſecta
              <lb/>
            eſt IG, in V, iungaturque recta ET; </s>
            <s xml:id="echoid-s11603" xml:space="preserve"> erit rurſus figura EBCDTE, ad
              <note symbol="e" position="left" xlink:label="note-280-05" xlink:href="note-280-05a" xml:space="preserve">hui{us}.</note>
            ETA, vt FV, ad VG, hoc eſt, vt R, ad S.</s>
            <s xml:id="echoid-s11604" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11605" xml:space="preserve">
              <emph style="sc">Atqve</emph>
            hac via procedendum eſt in omnibus alijs figuris, quæ latera toti-
              <lb/>
            dem habeant, quot angulos, id eſt, in quibus omnes anguli introrſum vergant.</s>
            <s xml:id="echoid-s11606" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11607" xml:space="preserve">
              <emph style="sc">Idem</emph>
            hoc problema efficiemus in rectilineo, cuius anguli partim extror-
              <lb/>
            ſum vergant, & </s>
            <s xml:id="echoid-s11608" xml:space="preserve">partim introrſum, dummodo ab angulo, vel puncto dato in la-
              <lb/>
            tere ducipoſsint lineæ rectæ diuidentes rectilineum in triangula quæ nullũ ipſi-
              <lb/>
            us latus ſecent. </s>
            <s xml:id="echoid-s11609" xml:space="preserve">Vt in hac figura octo laterum ABCDEFGH, cuius quinque an-
              <lb/>
            guli B, C, D, F, H, introrſum vergunt, & </s>
            <s xml:id="echoid-s11610" xml:space="preserve">reliquitres BAH, DEF, FGH, extrorſum.
              <lb/>
            </s>
            <s xml:id="echoid-s11611" xml:space="preserve">ductæ ſunt rectæ ex angulo A, ad omnes angulos, præter quam ad duos </s>
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