Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div137" type="section" level="1" n="60">
          <p>
            <s xml:id="echoid-s2441" xml:space="preserve">
              <pb o="61" file="091" n="91" rhead="LIBER SECVNDVS."/>
            rentiam ſtationum, vt eſt P Q, Tangens maior ad diſtantiam N L, vt paulo an-
              <lb/>
            te oſtenſum eſt, facilius demonſtrabimus, ſi ducatur recta I T, quæ producta
              <lb/>
            ſecet N L, in S. </s>
            <s xml:id="echoid-s2442" xml:space="preserve">Nam in triangulis IP T, K O R, duo latera IP, P T, duobus la-
              <lb/>
            teribus KO, OR, æqualia ſunt, angulo ſque continent æquales, vtp ote rectos.
              <lb/>
            </s>
            <s xml:id="echoid-s2443" xml:space="preserve"> Igitur anguli T, R, ęquales ſunt; </s>
            <s xml:id="echoid-s2444" xml:space="preserve"> ideo que KL, IS, parallelæ. </s>
            <s xml:id="echoid-s2445" xml:space="preserve"> Et quia
              <note symbol="a" position="right" xlink:label="note-091-01" xlink:href="note-091-01a" xml:space="preserve">4. primi.</note>
            I K, æqualis eſt & </s>
            <s xml:id="echoid-s2446" xml:space="preserve">ipſi SL, & </s>
            <s xml:id="echoid-s2447" xml:space="preserve">differentiæ ſtationum HG, vel NM, liquido
              <note symbol="b" position="right" xlink:label="note-091-02" xlink:href="note-091-02a" xml:space="preserve">28. primi.</note>
            ſtat, ita eſſe T Q, differentiam Tangentium ad S L, quæ differentię ſtationum
              <lb/>
              <note symbol="c" position="right" xlink:label="note-091-03" xlink:href="note-091-03a" xml:space="preserve">34. primi.</note>
            I K, vel H G, æqualis eſt, vt eſt P Q, Tangens maior ad diſtantiam NL,</s>
          </p>
          <note symbol="d" position="right" xml:space="preserve">ſchol. 4.
            <lb/>
          ſext.</note>
        </div>
        <div xml:id="echoid-div142" type="section" level="1" n="61">
          <head xml:id="echoid-head64" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s2448" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2449" xml:space="preserve">
              <emph style="sc">Per</emph>
            ſolos ſinus ita Problema efficiemus. </s>
            <s xml:id="echoid-s2450" xml:space="preserve">Primum inquiremus hypote-
              <lb/>
              <note symbol="e" position="right" xlink:label="note-091-05" xlink:href="note-091-05a" xml:space="preserve">32. primi.</note>
            nuſas I L, K L, hoc modo. </s>
            <s xml:id="echoid-s2451" xml:space="preserve"> Quoniam angulus L K V, duobus angulis L I K, I L K, æqualis eſt; </s>
            <s xml:id="echoid-s2452" xml:space="preserve">ſi L I K, angulus complementi maioris anguli obſeruationis
              <lb/>
            L I N, auferatur ex L K V, angulo complementi minoris anguli obſeruationis
              <lb/>
            L K M, reliquus fiet angulus I K L. </s>
            <s xml:id="echoid-s2453" xml:space="preserve"> Si ergo fiat.</s>
            <s xml:id="echoid-s2454" xml:space="preserve"/>
          </p>
          <note symbol="f" position="right" xml:space="preserve">10. triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} anguli I K L, dif- \\ ferentiæ inter duos an- \\ gulos complementorum \\ angulorum obſeruatio- \\ num # ad I K, \\ differẽ- \\ tiam \\ ſtatio- \\ num: # Ita ſin{us} anguli I K L, conflati ex \\ recto, & angulo obſeruationis \\ minore, vel # ad I L,
            <lb/>
          # # Ita ſin{us} anguli LIK, complemen- \\ ti maioris anguli obſeruationis. # ad K L,
            <lb/>
          </note>
          <note position="right" xml:space="preserve">Hypotenu-
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          ſarum inuẽ-
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          tio.</note>
          <p>
            <s xml:id="echoid-s2455" xml:space="preserve">euadet nota tam I L, quam K L, in menſura differentiæ ſtationum. </s>
            <s xml:id="echoid-s2456" xml:space="preserve"> Igitur ſi fiat,</s>
          </p>
          <note symbol="g" position="right" xml:space="preserve">10. triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} tot{us} \\ angulire- \\ cti N, # ad Hypotenuſam \\ proxime inuen- \\ tam I L, # Ita ſin{us} anguli I L N, complementi \\ maioris anguli obſeruationis # ad I N,
            <lb/>
          #### Vel
            <lb/>
          Vt ſin{us} tot{us} an- \\ guli recti M, # ad hypotenuſam K L, \\ nuper inuentam: # Ita ſin{us} anguli K L M, complemen- \\ ti minoris anguli obſeruationis # ad \\ K M,
            <lb/>
          </note>
          <note position="right" xml:space="preserve">Altitudinis
            <lb/>
          inuentio per
            <lb/>
          ſolos ſinus.</note>
          <p>
            <s xml:id="echoid-s2457" xml:space="preserve">cognita fiet altitudò
              <unsure/>
            I N, vel KM, ex qua ſi dematur ſtatura menſoris, altitudo
              <lb/>
            quæſita relinquetur H N, vel G M, hoc eſt, E F.</s>
            <s xml:id="echoid-s2458" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2459" xml:space="preserve">
              <emph style="sc">Distantia</emph>
            autem vtraque N L, M L, reperietur, ſi fiat.</s>
            <s xml:id="echoid-s2460" xml:space="preserve"/>
          </p>
          <note symbol="h" position="right" xml:space="preserve">10. triang.
            <lb/>
          rectil.</note>
          <note position="right" xml:space="preserve">Diſtantiæ in-
            <lb/>
          uentio per
            <lb/>
          ſolos ſinus.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} tot{us} \\ anguli recti \\ N, vel M, # ad Hypotenuſam \\ inuentam I L, \\ vel K L, # Ita ſin{us} anguli maioris ob- \\ ſeruati NIL, vel \\ ad N L, diſtan- \\ tiam
            <lb/>
          # # Ita ſin{us} anguli minoris ob- \\ ſeruati M K L, # ad M L, diſtan- \\ </note>
          <p>
            <s xml:id="echoid-s2461" xml:space="preserve">
              <emph style="sc">Sine</emph>
            numeris eædem rectæ IN, N L, IL, K L, &</s>
            <s xml:id="echoid-s2462" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2463" xml:space="preserve">reperientur, vt in ſupe-
              <lb/>
              <note position="right" xlink:label="note-091-15" xlink:href="note-091-15a" xml:space="preserve">Quo pacto
                <lb/>
              problema
                <lb/>
              conficiatur ſi-
                <lb/>
              ne numeris.</note>
            rioribus: </s>
            <s xml:id="echoid-s2464" xml:space="preserve">ſi nimirum (vtemur figura huius problematis, ne nouam conſtruere
              <lb/>
            cogamur) ſumptarecta IK, tot partium, quot palmi, pedeſuein differentia ſta-
              <lb/>
            tionum exiſtunt, fiant anguli VKL, VIL, complementorum angulorum MKL,
              <lb/>
            NIL, obſeruationum, & </s>
            <s xml:id="echoid-s2465" xml:space="preserve">concurſus L, notetur, ex quo ducatur LN, ipſi IK, pa-
              <lb/>
            rallela, & </s>
            <s xml:id="echoid-s2466" xml:space="preserve">ad hanc perpendicularis in I, excitetur IN, &</s>
            <s xml:id="echoid-s2467" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2468" xml:space="preserve">Vel ſi angulus rectus
              <lb/>
            conſtituatur INL, & </s>
            <s xml:id="echoid-s2469" xml:space="preserve">in aſſumpto puncto L, vbi concurſum eſſe volumus, </s>
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