Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div194" type="section" level="1" n="85">
          <p>
            <s xml:id="echoid-s3046" xml:space="preserve">
              <pb o="77" file="107" n="107" rhead="LIBER SECVNDVS."/>
            nor FB, ex maiore DE, per problema 18. </s>
            <s xml:id="echoid-s3047" xml:space="preserve">vel 19. </s>
            <s xml:id="echoid-s3048" xml:space="preserve">exploranda erit. </s>
            <s xml:id="echoid-s3049" xml:space="preserve">Nam rurſus FB,
              <lb/>
            detracta ex AB, notam relinquet portionem AF.</s>
            <s xml:id="echoid-s3050" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3051" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3052" xml:space="preserve">
              <emph style="sc">Non</emph>
            ſecus per problema 18. </s>
            <s xml:id="echoid-s3053" xml:space="preserve">vel 19. </s>
            <s xml:id="echoid-s3054" xml:space="preserve">indaganda erit vtraque altitudo mi-
              <lb/>
            nor F B, GB, ex maiore D E, vtillarum differentia F G, quæ quæritur, colliga-
              <lb/>
            tur nota.</s>
            <s xml:id="echoid-s3055" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3056" xml:space="preserve">ALTITVDINEM, cuius baſis impoſita ſit alteri altitudini, & </s>
            <s xml:id="echoid-s3057" xml:space="preserve">vtra-
              <lb/>
            que illius extremitas cerni poſſit, etiamſi infimum punctum alterius,
              <lb/>
            cui imponitur, lateat, & </s>
            <s xml:id="echoid-s3058" xml:space="preserve">eiuſdem puncti infimi diſtantia à loco men-
              <lb/>
            ſoris cognita non ſit, per Quadrantem ex valle, aut ex plano Horizon-
              <lb/>
            tis explorare.</s>
            <s xml:id="echoid-s3059" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div196" type="section" level="1" n="86">
          <head xml:id="echoid-head89" xml:space="preserve">PROBLEMA XXI.</head>
          <p>
            <s xml:id="echoid-s3060" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3061" xml:space="preserve">
              <emph style="sc">Hvivscemodi</emph>
            altitudo eſt tur-
              <lb/>
              <figure xlink:label="fig-107-01" xlink:href="fig-107-01a" number="44">
                <image file="107-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/107-01"/>
              </figure>
            ris ſupra montem poſita, & </s>
            <s xml:id="echoid-s3062" xml:space="preserve">portio ali-
              <lb/>
            cuius ædificij inter duas feneſtras, vel duo
              <lb/>
            ſigna, quorum alterum altero ſuperius eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s3063" xml:space="preserve">Sit igitur ſupra montem altitudo turris
              <lb/>
            A B, propoſita. </s>
            <s xml:id="echoid-s3064" xml:space="preserve">Ex aliquoloco E, in pla-
              <lb/>
            nitie, aut valle, vnde vtrumque extremum
              <lb/>
            A, B, videatur, obſeruentur per Quadran-
              <lb/>
            tem anguli A D C, B D C, quos radij D A,
              <lb/>
            DB, cũ recta D C, quæ ex D, ad AB, pro-
              <lb/>
            ductam intra montẽ eſt perpendicularis: </s>
            <s xml:id="echoid-s3065" xml:space="preserve">
              <lb/>
            ita vt ſtatura menſoris ſit D E. </s>
            <s xml:id="echoid-s3066" xml:space="preserve">Deinde
              <lb/>
            per problema 6. </s>
            <s xml:id="echoid-s3067" xml:space="preserve">inueſtigetur longitudo
              <lb/>
            vtriuſque radij D A, D B. </s>
            <s xml:id="echoid-s3068" xml:space="preserve"> Nam ſi fiat
              <note symbol="a" position="right" xlink:label="note-107-01" xlink:href="note-107-01a" xml:space="preserve">10. Triang.
                <lb/>
              rectil.</note>
            triangulo A B D,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} anguli B A D, \\ qui complèmentum eſt \\ maioris anguli ADC, \\ obſeruati, # adradium DB, \\ proximè inuẽ- \\ tum: # Ita ſin{us} anguli A D B, \\ qui differentia est an- \\ gulorum obſeruationũ \\ ADC, BDC, # ad A B, alti- \\ tudinem,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3069" xml:space="preserve">inuenta erit altitudo AB, quæſita, in partibus, in quibus cognitus eſt radius
              <lb/>
            DB. </s>
            <s xml:id="echoid-s3070" xml:space="preserve"> Sic etiam, ſi 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} anguli A B D, vel (quod \\ idem eſt) anguli D B C, qui \\ complementum est minoris \\ anguli obſeruati B D C, # ad radium \\ D A, proxi- \\ mè inuen- \\ tum # Ita ſin{us} anguli A B D, \\ differentiæ angulorum \\ obſeruatorum A D C, \\ B D C, # ad A B, \\ altitu- \\ dinem
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3071" xml:space="preserve">pro dibit rurſus altitudo quæſita A B, in partibus radij inuenti D A.</s>
            <s xml:id="echoid-s3072" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div198" type="section" level="1" n="87">
          <head xml:id="echoid-head90" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s3073" xml:space="preserve">2,
              <emph style="sc">Per</emph>
            problema 2. </s>
            <s xml:id="echoid-s3074" xml:space="preserve">vel 15. </s>
            <s xml:id="echoid-s3075" xml:space="preserve">inueſtigetur tam altitudo inacceſsibilis A </s>
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