Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div185" type="section" level="1" n="79">
          <pb o="73" file="103" n="103" rhead="LIBER SECVNDVS."/>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} t@- \\ t{us} AC, # ad AB, Tangentem an- \\ guli obſeruati ACB: # Ita longitudo A C, per \\ problema 10. inuenta # Ad AB, alt@- \\ tudinem,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2875" xml:space="preserve">prodibit nota altitudo AB, in partibus, in quibus AC, inuenta fuit.</s>
            <s xml:id="echoid-s2876" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2877" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2878" xml:space="preserve">
              <emph style="sc">Non</emph>
            erit autem difficile problema hoc ſine numerorum auxilio exequi,
              <lb/>
            ſi ſuperiora præcepta conſulantur.</s>
            <s xml:id="echoid-s2879" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2880" xml:space="preserve">ALTITVDINEM inacceſſibilem, quando neque diſtantia à loco
              <lb/>
            menſoris ad eius baſem nota eſt, neque è directo ipſius duæ ſtationes
              <lb/>
            in plano fieri poſſunt, neque denique baſis appareat, per Quadran-
              <lb/>
            tem notam reddere. </s>
            <s xml:id="echoid-s2881" xml:space="preserve">Atque hinc obiter ipſam quoque diſtantiam e-
              <lb/>
            licere.</s>
            <s xml:id="echoid-s2882" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div186" type="section" level="1" n="80">
          <head xml:id="echoid-head83" xml:space="preserve">PROBLEMA XV.</head>
          <p>
            <s xml:id="echoid-s2883" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2884" xml:space="preserve">
              <emph style="sc">Sit</emph>
            altitudo A B, locus menſoris C, diſtantia CB, incognita: </s>
            <s xml:id="echoid-s2885" xml:space="preserve">baſis B, non
              <lb/>
            appareat, & </s>
            <s xml:id="echoid-s2886" xml:space="preserve">à loco C, non liceat accedere ad A B, nequerecedere, vt duæ ſta-
              <lb/>
            tiones fiantin plano. </s>
            <s xml:id="echoid-s2887" xml:space="preserve">Erigatur haſta C E, ſi non præſtò ſit turris aliqua C O, & </s>
            <s xml:id="echoid-s2888" xml:space="preserve">
              <lb/>
            ſtatura menſoris ſit CD. </s>
            <s xml:id="echoid-s2889" xml:space="preserve">Sumpta deinde portione haſtæ D E, notarum partium,
              <lb/>
            concipiantur ductæ DM, EN, ipſi CB, pa-
              <lb/>
              <figure xlink:label="fig-103-01" xlink:href="fig-103-01a" number="39">
                <image file="103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/103-01"/>
              </figure>
            rallelæ, obſeruenturq; </s>
            <s xml:id="echoid-s2890" xml:space="preserve">per Quadrantem
              <lb/>
            anguli ADM, AEN. </s>
            <s xml:id="echoid-s2891" xml:space="preserve">Sumptis quoq; </s>
            <s xml:id="echoid-s2892" xml:space="preserve">rectis
              <lb/>
            æqualibus EF, DG, pro ſinubus totis, eri-
              <lb/>
            gantur perpendiculares FH, GI, pro Tã-
              <lb/>
            gentibus angulorum obſeruationũ. </s>
            <s xml:id="echoid-s2893" xml:space="preserve">Sum
              <lb/>
            pta item A L, æqualiipſi D E, ducaturre-
              <lb/>
            cta D L, quæ parallela erit ipſi E A,
              <note symbol="a" position="right" xlink:label="note-103-02" xlink:href="note-103-02a" xml:space="preserve">33. primi.</note>
            bitq; </s>
            <s xml:id="echoid-s2894" xml:space="preserve">GI, in K. </s>
            <s xml:id="echoid-s2895" xml:space="preserve"> Quoniam vero
              <note symbol="b" position="right" xlink:label="note-103-03" xlink:href="note-103-03a" xml:space="preserve">29. primi.</note>
            DKG, angulo DLB, & </s>
            <s xml:id="echoid-s2896" xml:space="preserve">hic angulo EAB,
              <lb/>
            & </s>
            <s xml:id="echoid-s2897" xml:space="preserve">hic angulo EHF, æqualis eſt; </s>
            <s xml:id="echoid-s2898" xml:space="preserve">erit angu-
              <lb/>
            lus DKG, angulo EHF, æqualis: </s>
            <s xml:id="echoid-s2899" xml:space="preserve">Eſt au-
              <lb/>
            tem & </s>
            <s xml:id="echoid-s2900" xml:space="preserve">rectus G, recto F, æqualis, & </s>
            <s xml:id="echoid-s2901" xml:space="preserve">latus
              <lb/>
            DG, lateri EF, æquale; </s>
            <s xml:id="echoid-s2902" xml:space="preserve"> erunt quoq; </s>
            <s xml:id="echoid-s2903" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-103-04" xlink:href="note-103-04a" xml:space="preserve">26. primi.</note>
            ra GK, FH, æqualia, & </s>
            <s xml:id="echoid-s2904" xml:space="preserve">anguli D, E, æqua-
              <lb/>
            les: </s>
            <s xml:id="echoid-s2905" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s2906" xml:space="preserve">IK, differentia erit inter Tan-
              <lb/>
            gentes GI, GK, angulorum GDI, GDK,
              <lb/>
            ſiue F E H. </s>
            <s xml:id="echoid-s2907" xml:space="preserve"> Et quia eſt, vt I K, ad K G. </s>
            <s xml:id="echoid-s2908" xml:space="preserve">ita A L, ad L M; </s>
            <s xml:id="echoid-s2909" xml:space="preserve">erit per contrariam compoſitionem à nobis in ſcholio propoſ. </s>
            <s xml:id="echoid-s2910" xml:space="preserve">18.
              <lb/>
            </s>
            <s xml:id="echoid-s2911" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-103-05" xlink:href="note-103-05a" xml:space="preserve">ſchol. 4. ſe-
                <lb/>
              xti.</note>
            lib. </s>
            <s xml:id="echoid-s2912" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2913" xml:space="preserve">demonſtratam, ita quo que IK, ad IG, vt AL, hoc eſt, vt ED, differentia ſta-
              <lb/>
            tionum, ad altitudinem AM. </s>
            <s xml:id="echoid-s2914" xml:space="preserve"># Igitur ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt I K, differen- \\ tia Tangentium # ad I G, Tangen- \\ te maiorem: # Ita AL, vel ED, differen- \\ tia ſtationum # Ad A M, alti- \\ tudinem,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2915" xml:space="preserve">gignetur altitudo AM, cui ſi apponaturſtatura menſoris MB, tota altitudo AB,
              <lb/>
            nota efficietur. </s>
            <s xml:id="echoid-s2916" xml:space="preserve"> Iam ſi fiat,</s>
          </p>
          <note symbol="e" position="right" xml:space="preserve">4. ſexti.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt G I, ſi- \\ n{us} tot{us} # ad G D, Tangentem complementi ma- \\ ioris anguli obſeruationis: # Ita altitudo in- \\ uenta A M, # ad M D, di- \\ ſtantiam,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2917" xml:space="preserve">inuenta erit diſtantia D M, vel C B.</s>
            <s xml:id="echoid-s2918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2919" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2920" xml:space="preserve">
              <emph style="sc">Per</emph>
            ſolos ſinus idem problema conficiemus, ſi prius inueſtigetur hy-
              <lb/>
              <note symbol="f" position="right" xlink:label="note-103-09" xlink:href="note-103-09a" xml:space="preserve">10. Triang.
                <lb/>
              rectil.</note>
            potenuſa AD, hoc modo. </s>
            <s xml:id="echoid-s2921" xml:space="preserve"> Fiat,</s>
          </p>
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