Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div158" type="section" level="1" n="69">
          <p>
            <s xml:id="echoid-s2601" xml:space="preserve">
              <pb o="68" file="096" n="96" rhead="GEOMETR. PRACT."/>
            nor B, à maiori ADF, differt, ad BD, differentiam ſtationum: </s>
            <s xml:id="echoid-s2602" xml:space="preserve">ita ſinus anguli B,
              <lb/>
            in remotiori ſtatione. </s>
            <s xml:id="echoid-s2603" xml:space="preserve">ad D A.</s>
            <s xml:id="echoid-s2604" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2605" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2606" xml:space="preserve">
              <emph style="sc">Distantia</emph>
            verò à puncto A, ad pedem menſoris C, hoc eſt, recta AC,
              <lb/>
            cognoſcetur per Problema 12. </s>
            <s xml:id="echoid-s2607" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s2608" xml:space="preserve">rectil. </s>
            <s xml:id="echoid-s2609" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s2610" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2611" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2612" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2613" xml:space="preserve">cum in triangulo obli-
              <lb/>
            quangulo ABC, duo latera AB, BC, nota ſint, nimirum diſtantia inuenta, & </s>
            <s xml:id="echoid-s2614" xml:space="preserve">ſta-
              <lb/>
            tura menſoris, comprehendantque angulum ABC, notum, vtpote conflatum
              <lb/>
            ex recto CBD, & </s>
            <s xml:id="echoid-s2615" xml:space="preserve">angulo obſeruationis ABD.</s>
            <s xml:id="echoid-s2616" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2617" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2618" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde punctum A, vt in muro HI, infra oculum B. </s>
            <s xml:id="echoid-s2619" xml:space="preserve">Inſpecto pun-
              <lb/>
            cto A, obſeruetur angulus CBA. </s>
            <s xml:id="echoid-s2620" xml:space="preserve">quem latus pinnacidiorum cum perpendiculi
              <lb/>
            filo, vel dio ptræ linea fiduciæ cum BC, facit: </s>
            <s xml:id="echoid-s2621" xml:space="preserve">Deinde accede verſus A. </s>
            <s xml:id="echoid-s2622" xml:space="preserve">vſque ad
              <lb/>
            D, & </s>
            <s xml:id="echoid-s2623" xml:space="preserve">iterum conſidera angulum EDA: </s>
            <s xml:id="echoid-s2624" xml:space="preserve">exiſtentque rectæ AB, AD BD, BC, DE,
              <lb/>
            in vno eodemque plano, in eo videlicet, quod per ſta-
              <lb/>
              <figure xlink:label="fig-096-01" xlink:href="fig-096-01a" number="29">
                <image file="096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/096-01"/>
              </figure>
            turas menſoris BC, DE, & </s>
            <s xml:id="echoid-s2625" xml:space="preserve">per punctum A, ducitur.
              <lb/>
            </s>
            <s xml:id="echoid-s2626" xml:space="preserve"> Et quoniam angulus FDA, complementi anguli
              <note symbol="a" position="left" xlink:label="note-096-01" xlink:href="note-096-01a" xml:space="preserve">32. primi.</note>
            ſeruationis in propinquiore ſtatione æqualis eſt duo-
              <lb/>
            bus DBA, DAB; </s>
            <s xml:id="echoid-s2627" xml:space="preserve">ſi DBA, angulus complementi an-
              <lb/>
            guli remotioris ſtationis dematur ex angulo A D F,
              <lb/>
            complementi anguli ſtationis propinquioris, reliquus
              <lb/>
            fiet notus BAD. </s>
            <s xml:id="echoid-s2628" xml:space="preserve"> Si ergo fiat,</s>
          </p>
          <note symbol="b" position="left" xml:space="preserve">10. Triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſinus anguli BAD, dif- \\ ferentiæ inter angulos com \\ plementorum angulorum \\ obſeruationum # ad B D, diffe- \\ rentiam ſta- \\ tionum: # Ita ſinus anguli ADB, con- \\ flati ex recto B D E, & \\ ex angulo obſeruationis \\ A D E, in propinquiore \\ ſtatione # ad AB di- \\ ſtantiam \\ quæſitã.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2629" xml:space="preserve">cognita erit diſtantia A B, quam quærimus, in partibus differentiæ ſtatio-
              <lb/>
            num B D.</s>
            <s xml:id="echoid-s2630" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2631" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi oculus ponatur in D, & </s>
            <s xml:id="echoid-s2632" xml:space="preserve">recedatur à puncto D, vſque ad B, repe-
              <lb/>
            rietur eodem modo diſtantia DA, ſi pro angulo BDA, aſſumes angulum DBA,
              <lb/>
            complementianguli ABC, obſeruationis in remotiore ſtatione, vt manifeſtum
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s2633" xml:space="preserve"> Nam eſt, vt ſinus anguli BAD, differentiæ inter angulos
              <note symbol="c" position="left" xlink:label="note-096-04" xlink:href="note-096-04a" xml:space="preserve">10. Triang.
                <lb/>
              rectil.</note>
            rum angulorum obſeruationum, ad BD, differentiam ſtationum: </s>
            <s xml:id="echoid-s2634" xml:space="preserve">ita ſinus angu-
              <lb/>
            li DBA, complementi anguli ABC, in remotiore ſtatione, ad DA.</s>
            <s xml:id="echoid-s2635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2636" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2637" xml:space="preserve">
              <emph style="sc">Vt</emph>
            autem diſtantia CA, à pede ad punctum A, inueniatur, ita progredie-
              <lb/>
            mur. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">Quoniam in triangulo rectangulo ABG, (ſi ex puncto A, concipiatur
              <lb/>
            ducta ad BC, ſtaturam menſoris perpendicularis AG,) baſis AB, nota eſt per in-
              <lb/>
            uentionem, & </s>
            <s xml:id="echoid-s2639" xml:space="preserve">angulus BAG, notus, quippe cum ſit complementum anguli
              <lb/>
            obſeruationis ABG; </s>
            <s xml:id="echoid-s2640" xml:space="preserve"> Si fiat,</s>
          </p>
          <note symbol="d" position="left" xml:space="preserve">2. Triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſinus \\ totus # ad baſem A B, proximè \\ inuentam: # Ita ſinus anguli B A G, complemen- \\ ti anguli obſeruationis, # ad B G,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2641" xml:space="preserve">cognoſcetur BG, in partibus baſis AB, hoc eſt, in partibus differentiæ ſtationum
              <lb/>
            BD, in quibus AB, inuenta fuit. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">Ablata autem BG, ex menſoris ſtatura BC, no-
              <lb/>
            ta fiet reliqua CG. </s>
            <s xml:id="echoid-s2643" xml:space="preserve"> Item ſi fiat,</s>
          </p>
          <note symbol="e" position="left" xml:space="preserve">2. Triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſinus to- \\ tus # ad baſem A B, nu- \\ per inuentam: # Ita ſinus anguli obſeruatio- \\ nis A B G, # ad A G,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2644" xml:space="preserve">nota etiam fiet A G, in partibus eiuſdem baſis A B, vel differentiæ </s>
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