Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div155" type="section" level="1" n="67">
          <pb o="65" file="095" n="95" rhead="LIBER SECVNDVS."/>
        </div>
        <div xml:id="echoid-div157" type="section" level="1" n="68">
          <head xml:id="echoid-head71" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s2573" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2574" xml:space="preserve">Per ſolos ſinus eandem altitudinem G F, adipiſcemur, ſi prius hypote-
              <lb/>
            nuſam G D, venabimur, hoc modo. </s>
            <s xml:id="echoid-s2575" xml:space="preserve"> Fiat,</s>
          </p>
          <note symbol="a" position="right" xml:space="preserve">10. triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} anguli D G E, diffe- \\ rentiæ angulorum obſer- \\ uationum # ad D E, ſpa- \\ tium cogni- \\ tum # Ita ſin{us} anguli E, com- \\ plementi maioris an- \\ guli obſeruationis # ad hypotenu- \\ ſam G D,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2576" xml:space="preserve">Numerus enim productus dabit hypotenuſam GD, in partibus ſpatii DE, no-
              <lb/>
            tam. </s>
            <s xml:id="echoid-s2577" xml:space="preserve"> Si ergo rurſus fiat,</s>
          </p>
          <note symbol="b" position="right" xml:space="preserve">10. triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} tot{us} an- \\ guli recti F, # ad hypotenuſam \\ G D, proximè \\ inuentam: # Ita ſin{us} anguli D, comple- \\ menti minoris anguli ob- \\ ſeruationis # ad G F, altitu- \\ dinem,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2578" xml:space="preserve">producetur altitudo GF, in partibus hypotenuſæ GD, ſiue ſpatij DE, nota.</s>
            <s xml:id="echoid-s2579" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Solutio pro-
            <lb/>
          blematis ſine
            <lb/>
          numeris.</note>
          <p>
            <s xml:id="echoid-s2580" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2581" xml:space="preserve">
              <emph style="sc">Sine</emph>
            numeris agendum erit, vt in problemate 1. </s>
            <s xml:id="echoid-s2582" xml:space="preserve">declaratum eſt.</s>
            <s xml:id="echoid-s2583" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2584" xml:space="preserve">DISTANTIAM ab oculo, vel pede menſoris ad quoduis punctum
              <lb/>
            in aliqua altitudine notatum, per duas ſtationes in plano factas me-
              <lb/>
            tiri.</s>
            <s xml:id="echoid-s2585" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div158" type="section" level="1" n="69">
          <head xml:id="echoid-head72" xml:space="preserve">PROBLEMA VI.</head>
          <p>
            <s xml:id="echoid-s2586" xml:space="preserve">1
              <emph style="sc">Sit</emph>
            inqui@enda diſtantia puncti A, in muro G H, ſiue perpendiculari ad
              <lb/>
            Horizontem, ſiue inclinato, vel etiam in tecto quo piam; </s>
            <s xml:id="echoid-s2587" xml:space="preserve">ab oculo B, vel pe-
              <lb/>
            de C, poſita ſtatura menſoris B C. </s>
            <s xml:id="echoid-s2588" xml:space="preserve">Concipiatur ducta B D, ipſi plano C E, pa-
              <lb/>
            ſallela, ſitque primo punctum A, altius,
              <lb/>
              <figure xlink:label="fig-095-01" xlink:href="fig-095-01a" number="28">
                <image file="095-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/095-01"/>
              </figure>
            quam oculus B. </s>
            <s xml:id="echoid-s2589" xml:space="preserve">Inſpecto puncto A, no-
              <lb/>
            tetur angulus ABD, quem latus pinnaci-
              <lb/>
            diorum in quadrante pendulo, vel linea
              <lb/>
            fiduciæ in dioptra Quadrantis ſtabilis
              <lb/>
            cum recta BD, facit. </s>
            <s xml:id="echoid-s2590" xml:space="preserve">Deinde accede ver-
              <lb/>
            ſrus punctum A, quotlibet palmis aut pe-
              <lb/>
            dibus vſque ad D, vt BD, differentia ſta-
              <lb/>
            tionum nota ſit. </s>
            <s xml:id="echoid-s2591" xml:space="preserve">Rurſumque ex D, pun-
              <lb/>
            ctum A, inſpiciatur, notato diligenter angulo ADF: </s>
            <s xml:id="echoid-s2592" xml:space="preserve">exiſtentque rectæ AB, AD,
              <lb/>
            B D, B C, D E, in eodem plano, in eo videlicet, quod per ſtaturas menſoris B C,
              <lb/>
            D E, & </s>
            <s xml:id="echoid-s2593" xml:space="preserve">per punctum A, ducitur, Et quia angulus A D F, duobus B, & </s>
            <s xml:id="echoid-s2594" xml:space="preserve">B A
              <note symbol="c" position="right" xlink:label="note-095-06" xlink:href="note-095-06a" xml:space="preserve">32. primi.</note>
            eſt æqualis: </s>
            <s xml:id="echoid-s2595" xml:space="preserve">ſi angulus B, in remotiore ſtatione auferatur ex angulo D, in pro-
              <lb/>
            pinquiore, notus fiet reliquus angulus A. </s>
            <s xml:id="echoid-s2596" xml:space="preserve"> Siigitur fiat,</s>
          </p>
          <note symbol="d" position="right" xml:space="preserve">10. triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} anguli \\ A, quo angu- \\ l{us} minor B, à \\ maiori differt, # ad B D, diffe- \\ rentiam ſta- \\ tionum: # Ita ſin{us} anguli A D B, qui comple- \\ mentum eſt maioris anguli D, ad \\ duos rectos, # ad A B, di- \\ ſtantiã quæ- \\ ſitam,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2597" xml:space="preserve">reperta erit quæſita diſtantia A B, in partibus differentiæ ſtationum.</s>
            <s xml:id="echoid-s2598" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2599" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi oculus exiſtat in D, & </s>
            <s xml:id="echoid-s2600" xml:space="preserve">recedatur à puncto D, vſque ad B, inue-
              <lb/>
            nietur eadem arte diſtantia D A, ſi loco anguli A D B, ſumatur angulus B, in
              <lb/>
              <note symbol="e" position="right" xlink:label="note-095-09" xlink:href="note-095-09a" xml:space="preserve">10. triang,
                <lb/>
              rectil.</note>
            remotiore ſtatione, vt liquet. </s>
            <s xml:id="echoid-s2601" xml:space="preserve"> Eſt enim vt ſinus anguli A, quo angulus </s>
          </p>
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