Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div703" type="section" level="1" n="246">
          <p>
            <s xml:id="echoid-s11500" xml:space="preserve">
              <pb o="248" file="278" n="278" rhead="GEOMETR. PRACT."/>
            tuor rectangulis, vel parallelogrammis conſtituitur vnum totum, vt ex demõ-
              <lb/>
            ſtratione propoſ 45. </s>
            <s xml:id="echoid-s11501" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11502" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11503" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s11504" xml:space="preserve">manifeſtum eſt, propter angulos I, S R T, V-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-278-01" xlink:href="note-278-01a" xml:space="preserve">1. ſexti.</note>
            TX, YXM, æquales: </s>
            <s xml:id="echoid-s11505" xml:space="preserve">ac proinde omnia quatuor eandem habent altitudinem.</s>
            <s xml:id="echoid-s11506" xml:space="preserve"> Igitur rectæ IR, RT, TX, XM, proportionales ſunt parallelogrammis, ideo que
              <lb/>
            & </s>
            <s xml:id="echoid-s11507" xml:space="preserve">triangulis, ſiue figuris, quod eſt propoſitum.</s>
            <s xml:id="echoid-s11508" xml:space="preserve"/>
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        <div xml:id="echoid-div705" type="section" level="1" n="247">
          <head xml:id="echoid-head272" xml:space="preserve">PROBL. 3. PROPOS. 4.</head>
          <p>
            <s xml:id="echoid-s11509" xml:space="preserve">DATVM rectilineum per rectam à quouis angulo, vel puncto in ali-
              <lb/>
            quo latere ductam in proportionem datam diuidere: </s>
            <s xml:id="echoid-s11510" xml:space="preserve">ita vt antece-
              <lb/>
            dens proportionis, in quam malueris partem, vergat.</s>
            <s xml:id="echoid-s11511" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11512" xml:space="preserve">
              <emph style="sc">Sit</emph>
            primum triangulum quodcunque ABC, per rectam ex angulo A, diui-
              <lb/>
            dendum in duas partes: </s>
            <s xml:id="echoid-s11513" xml:space="preserve">ita vt pars ad B, vergẽs ad reliquam partẽ habeat
              <unsure/>
            pro-
              <lb/>
              <figure xlink:label="fig-278-01" xlink:href="fig-278-01a" number="181">
                <image file="278-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/278-01"/>
              </figure>
            portionem datam D, ad E. </s>
            <s xml:id="echoid-s11514" xml:space="preserve">Secetur latus B C,
              <lb/>
            dato angulo oppoſitum, per ea, quæin ſcholio
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s11515" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11516" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11517" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11518" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s11519" xml:space="preserve">docuimus, in F, ita vt
              <lb/>
            eadem ſit proportio BF, ad FC, quæ D, ad E, du-
              <lb/>
            caturque recta A F. </s>
            <s xml:id="echoid-s11520" xml:space="preserve">Dico eſſe vt D, ad E, ita tri-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-278-02" xlink:href="note-278-02a" xml:space="preserve">1. ſexti.</note>
            angulum ABF, ad triangulum AFC. </s>
            <s xml:id="echoid-s11521" xml:space="preserve">Eſt enim triangulum ABF, ad triangulum AFC, vt BF, ad
              <lb/>
            FC, hoc eſT, vt D, ad E.</s>
            <s xml:id="echoid-s11522" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11523" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            ſit idem triangulum ABC, diuidendum in duas partes, per rectam
              <lb/>
            ex puncto F, dato in latere BC, ita vt pars verſus B, ad reliquam partem habeat
              <lb/>
            proportionem datam D, ad E. </s>
            <s xml:id="echoid-s11524" xml:space="preserve">Ducta ex dato puncto F, ad angulum oppo-
              <lb/>
            ſitum A, recta FA, vt totum triangulum in duo triangula ſit ſectum: </s>
            <s xml:id="echoid-s11525" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-278-03" xlink:href="note-278-03a" xml:space="preserve">3. hui{us}.</note>
            tur duæ rectæ GH, HI, habentes eandem proportionem, quam triangulum A-
              <lb/>
            BF, ad triangulum AFC: </s>
            <s xml:id="echoid-s11526" xml:space="preserve">tota que GI, ſecetur in H, vt eadem ſit proportio GH,
              <lb/>
            ad HI, quæ D, ad E. </s>
            <s xml:id="echoid-s11527" xml:space="preserve">Et quia punctum H, cadit in extremum primæ lineæ GH;
              <lb/>
            </s>
            <s xml:id="echoid-s11528" xml:space="preserve">eſtque vt GH, ad HI, hoc eſt, vt D, ad E, ita triangulum ABF, ad triangulum A-
              <lb/>
            FC: </s>
            <s xml:id="echoid-s11529" xml:space="preserve">diuidet recta F A, ex dato puncto F, ad oppoſitum angulum A, ducta tri-
              <lb/>
            angulum ABC, in duas partes in data proportione D, ad E.</s>
            <s xml:id="echoid-s11530" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11531" xml:space="preserve">
              <emph style="sc">Sit</emph>
            rurſus data proportio K, ad L, diuidendumque ſit triangulum ABC, ex
              <lb/>
            puncto F, in duas partes eiuſdem proportionis. </s>
            <s xml:id="echoid-s11532" xml:space="preserve">Diuidatur tota GI, in M, ita vt
              <lb/>
            eadem ſit proportio GM, ad MI, quæ K, ad L. </s>
            <s xml:id="echoid-s11533" xml:space="preserve">Et quoniam diuiſionis punctum
              <lb/>
            M, cadit in primam partem GH, totius lineæ GI, ſecabimus BA, baſem primitri-
              <lb/>
            anguli dato puncto F, oppoſitam, in N, vt eadem ſit proportio BN, ad NA, quę
              <lb/>
            GM, ad MH. </s>
            <s xml:id="echoid-s11534" xml:space="preserve">Dico ductam rectam FN, problema efficere, hoc eſt, ita eſſe tri-
              <lb/>
            angulum BFN, ad trapezium FNAC, vt K, ad L. </s>
            <s xml:id="echoid-s11535" xml:space="preserve">Quoniam enim rectæ GH, HI,
              <lb/>
            triangulis ABF, AFC, proportionales inuentæ ſunt: </s>
            <s xml:id="echoid-s11536" xml:space="preserve">& </s>
            <s xml:id="echoid-s11537" xml:space="preserve">tam primam partem GH,
              <lb/>
            in M, quam primum triangulum ABF, per rectam FN, ſecuimus proportionali-
              <lb/>
              <note symbol="d" position="left" xlink:label="note-278-04" xlink:href="note-278-04a" xml:space="preserve">1. ſexti.</note>
            ter, cum ſit triangulum BFN, ad triangulum NFA, vt BN, ad NA, hoc eſt,
              <note symbol="e" position="left" xlink:label="note-278-05" xlink:href="note-278-05a" xml:space="preserve">1. hui{us}.</note>
            GM, ad MH, erit vt GM, ad MI, id eſt, vt K, ad L, ita BFN, triangulum ad tra- pezium FNAC. </s>
            <s xml:id="echoid-s11538" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s11539" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11540" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            data ſit proportio O, ad P, ſecandum que ſit triangulum ABC,
              <lb/>
            in duas partes eiuſdem proportionis. </s>
            <s xml:id="echoid-s11541" xml:space="preserve">Diuiſatota G I, in Q, ita vt eadem </s>
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