Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div319" type="section" level="1" n="133">
          <pb o="128" file="158" n="158" rhead="GEOMETR. PRACT."/>
        </div>
        <div xml:id="echoid-div322" type="section" level="1" n="134">
          <head xml:id="echoid-head137" xml:space="preserve">PROBLEMA XVII.</head>
          <p>
            <s xml:id="echoid-s4989" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4990" xml:space="preserve">
              <emph style="sc">In</emph>
            Plano Horizontis AB, iaceat interuallum C D, in tranſuerſum, pesau-
              <lb/>
            tem menſoris in E, ita vt longitudo C D, in vtramque partem producta per E,
              <lb/>
            non tranſeat. </s>
            <s xml:id="echoid-s4991" xml:space="preserve">Nam quando recta C D, è directo menſoris iacet, inueſtigabitur
              <lb/>
            ea, per problema 11. </s>
            <s xml:id="echoid-s4992" xml:space="preserve">Itaque vt tranſuerſum interuallum C D, cognoſcatur, in-
              <lb/>
            quirenda erit primum vtriuſque extremi puncti C,
              <lb/>
              <figure xlink:label="fig-158-01" xlink:href="fig-158-01a" number="86">
                <image file="158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/158-01"/>
              </figure>
            D, diſtantia à pede menſoris E, vt Num. </s>
            <s xml:id="echoid-s4993" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4994" xml:space="preserve">proble-
              <lb/>
            matis 15. </s>
            <s xml:id="echoid-s4995" xml:space="preserve">traditum eſt, per vnicam ſtationem. </s>
            <s xml:id="echoid-s4996" xml:space="preserve">Dein-
              <lb/>
            de angulus C E D, explorandus, quod fiet, ſi vnum
              <lb/>
            latus quadrati rectæ E C, congruat, & </s>
            <s xml:id="echoid-s4997" xml:space="preserve">dioptra rectæ
              <lb/>
            E D. </s>
            <s xml:id="echoid-s4998" xml:space="preserve">Nam vmbra abſciſſa inter latus illud, ac dio-
              <lb/>
            ptram oſtendet quantitatem anguli CED, vt in pro-
              <lb/>
            blemate 1. </s>
            <s xml:id="echoid-s4999" xml:space="preserve">dictũ eſt: </s>
            <s xml:id="echoid-s5000" xml:space="preserve">qui quidem acutus erit, ſi alterũ latus vltra rectam E D, exi-
              <lb/>
            ſtet: </s>
            <s xml:id="echoid-s5001" xml:space="preserve">rectus verò ſi præcisè rectę E D, congruet: </s>
            <s xml:id="echoid-s5002" xml:space="preserve">obtuſus denique, ſi citra re-
              <lb/>
            ctam E D, cadet; </s>
            <s xml:id="echoid-s5003" xml:space="preserve">quem cognoſcemus, ſi recto angulo adiiciemus reliquum
              <lb/>
            acutum, qui deprehendetur, vt in pręcedenti problemate docuimus. </s>
            <s xml:id="echoid-s5004" xml:space="preserve">Quoniam
              <lb/>
            ergo triangulum habemus C E D, cuius duo latera E C, E D, cognita ſunt, vna
              <lb/>
            cum angulo comprehenſo E: </s>
            <s xml:id="echoid-s5005" xml:space="preserve"> cognitum quo que erit tertium latus C D,
              <note symbol="a" position="left" xlink:label="note-158-01" xlink:href="note-158-01a" xml:space="preserve">12. triang.
                <lb/>
              rectil.</note>
            partibus rectarum E C, ED.</s>
            <s xml:id="echoid-s5006" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5007" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            recta C D, cognita erit, ſi in rectis E C, E D, ſeorſum deſcriptis cum
              <lb/>
            angulo E, inuento ſumantur partes ipſis EC, ED, proportionales, &</s>
            <s xml:id="echoid-s5008" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5009" xml:space="preserve">vt Num.
              <lb/>
            </s>
            <s xml:id="echoid-s5010" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5011" xml:space="preserve">pręcedentis problematis factum eſt.</s>
            <s xml:id="echoid-s5012" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5013" xml:space="preserve">DISTANTIAM alicuius ſigni in Horizonte poſiti à ſummitate turris,
              <lb/>
            vel muri alicuius, licet ad ipſum ſignum acceſſus non pateat, per qua-
              <lb/>
            dratum eruere, vbicunque menſor exiſtat.</s>
            <s xml:id="echoid-s5014" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div324" type="section" level="1" n="135">
          <head xml:id="echoid-head138" xml:space="preserve">PROBLEMA XVIII.</head>
          <p>
            <s xml:id="echoid-s5015" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5016" xml:space="preserve">
              <emph style="sc">In</emph>
            Horizontis plano punctum A, diſtet à ſummitate D, alicuius altitudi-
              <lb/>
            nis per rectam A D, quam ſic venabimur. </s>
            <s xml:id="echoid-s5017" xml:space="preserve">Vbicunque oculus menſoris exiſtat,
              <lb/>
            nimirum in B, indagentur per problema 15. </s>
            <s xml:id="echoid-s5018" xml:space="preserve">diſtantię
              <lb/>
              <figure xlink:label="fig-158-02" xlink:href="fig-158-02a" number="87">
                <image file="158-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/158-02"/>
              </figure>
            punctorum A, D, ab oculo menſoris B. </s>
            <s xml:id="echoid-s5019" xml:space="preserve">Deinde angu-
              <lb/>
            lus exploretur A B D, vt in problemate 16. </s>
            <s xml:id="echoid-s5020" xml:space="preserve">do cuimus.
              <lb/>
            </s>
            <s xml:id="echoid-s5021" xml:space="preserve">Nam ſic habebimus triangulum A B D, cuius duo la-
              <lb/>
            tera nota ſunt BA, BD, vna cum angulo B. </s>
            <s xml:id="echoid-s5022" xml:space="preserve"> Igitur
              <note symbol="b" position="left" xlink:label="note-158-02" xlink:href="note-158-02a" xml:space="preserve">12. triang.
                <lb/>
              rectil,</note>
            tium quo que latus AD, cognitum erit.</s>
            <s xml:id="echoid-s5023" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5024" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            etiam inuenietur, vt Num. </s>
            <s xml:id="echoid-s5025" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5026" xml:space="preserve">problem. </s>
            <s xml:id="echoid-s5027" xml:space="preserve">16. </s>
            <s xml:id="echoid-s5028" xml:space="preserve">docuimus, ſi in rectis B A,
              <lb/>
            B D, cum angulo B, ſeorſum ductis ſumentur partes ipſis B A, B D, proportio-
              <lb/>
            nales, &</s>
            <s xml:id="echoid-s5029" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5030" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5031" xml:space="preserve">ALTITVDINEM inacceſſibile
              <unsure/>
            m, cuius baſis non videatur; </s>
            <s xml:id="echoid-s5032" xml:space="preserve">& </s>
            <s xml:id="echoid-s5033" xml:space="preserve">ad
              <lb/>
            quam per nullum ſpatium ſecundum rectam lineam accedere poſſit
              <lb/>
            menſor, autrecedere, vt duæſtationes fieri poſſint, ſed ſolum ad </s>
          </p>
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