Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div167" type="section" level="1" n="71">
          <pb o="69" file="099" n="99" rhead="LIBER SECVNDVS."/>
        </div>
        <div xml:id="echoid-div171" type="section" level="1" n="72">
          <head xml:id="echoid-head75" xml:space="preserve">PROBLEMA IX.</head>
          <p>
            <s xml:id="echoid-s2718" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2719" xml:space="preserve">
              <emph style="sc">Sit</emph>
            longitudo AB, è directo menſoris in C, exiſtentis, ita vt recta B A,
              <lb/>
            pro ducta tranſeat per C. </s>
            <s xml:id="echoid-s2720" xml:space="preserve">Sit quo que CD, vel ſta-
              <lb/>
              <figure xlink:label="fig-099-01" xlink:href="fig-099-01a" number="32">
                <image file="099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/099-01"/>
              </figure>
            tura menſoris, vel altitudo quæpiam nota. </s>
            <s xml:id="echoid-s2721" xml:space="preserve">Siigi-
              <lb/>
            tur per præcedens problema 8. </s>
            <s xml:id="echoid-s2722" xml:space="preserve">inquiratur vtra que
              <lb/>
            longitudo CB, CA, & </s>
            <s xml:id="echoid-s2723" xml:space="preserve">CA, ex CB, detrahatur, reli-
              <lb/>
            qua fiet AB, ac proinde cognita.</s>
            <s xml:id="echoid-s2724" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div173" type="section" level="1" n="73">
          <head xml:id="echoid-head76" xml:space="preserve">ALITER</head>
          <p>
            <s xml:id="echoid-s2725" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2726" xml:space="preserve">
              <emph style="sc">Posito</emph>
            ſinu toto CD, ſi termini A, B, per angulos CDA, CDB, ſpectẽ-
              <lb/>
            tur, erit C A, Tangens minoris anguli, & </s>
            <s xml:id="echoid-s2727" xml:space="preserve">C B, maioris, at A B, differentia earum
              <lb/>
            Tangentium. </s>
            <s xml:id="echoid-s2728" xml:space="preserve">Quare ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſinus to- \\ tus CD, # Ad AB, differentiam Tangentium \\ angulorum obſeruationum # Ita C D, alti- \\ tudo nota # Ad AB, lon- \\ gitudinem.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2729" xml:space="preserve">efficietur longitudo AB, nota in partibus altitudinis notæ C D.</s>
            <s xml:id="echoid-s2730" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div174" type="section" level="1" n="74">
          <head xml:id="echoid-head77" xml:space="preserve">ALITER</head>
          <p>
            <s xml:id="echoid-s2731" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2732" xml:space="preserve">
              <emph style="sc">Per</emph>
            ſolos ſinus eandem longitudinem A B, cognoſcemus: </s>
            <s xml:id="echoid-s2733" xml:space="preserve">ſed prius in-
              <lb/>
            uenienda eſt AD, hac ratione fiat,</s>
          </p>
          <note symbol="a" position="right" xml:space="preserve">5. triang. re-
            <lb/>
          ctil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſinus anguli CAD, comple- \\ menti minoris anguli obſerua- \\ tionis # ad C D, altitudi- \\ nem notam: # Ita ſinus totus \\ anguli recti C, # ad A D,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2734" xml:space="preserve">Productus enim numerus dabit A D, notam in partibus altitudinis notæ CD,
              <note symbol="b" position="right" xlink:label="note-099-04" xlink:href="note-099-04a" xml:space="preserve">10. triang re-
                <lb/>
              ctil.</note>
            Siergo rurſus fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſinus anguli CBD, com- \\ plementi maioris anguli \\ obſeruationis # Ad A D, pro- \\ xime inuen- \\ tam # Ita ſinus anguli A D B, \\ differentia inter duos an- \\ gulos obſeruatos # ad AB, \\ longi- \\ tudinẽ,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2735" xml:space="preserve">prodibit nota longitudo AB, in partibus rectę AD, hoc eſt, altitudinis notæ CD,
              <lb/>
            in quibus recta AD, fuit inuenta.</s>
            <s xml:id="echoid-s2736" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2737" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2738" xml:space="preserve">
              <emph style="sc">Sine</emph>
            numeris rem perficies, quemadmodum in præcedentibus, vt li-
              <lb/>
            quet.</s>
            <s xml:id="echoid-s2739" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2740" xml:space="preserve">LONGITVDINEM tranſuerſam in Horizonte, cuius vtrum{q́ue} ex-
              <lb/>
            tremum inſpici poteſt, notam efficere.</s>
            <s xml:id="echoid-s2741" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div176" type="section" level="1" n="75">
          <head xml:id="echoid-head78" xml:space="preserve">PROBLEMA X.</head>
          <p>
            <s xml:id="echoid-s2742" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2743" xml:space="preserve">
              <emph style="sc">Sit</emph>
            planum Horizontis AB, in quo jaceat longitudo CD, in tranſuerſum,
              <lb/>
            pes autem menſoris ſit in E, ita vt recta DC, per pedes menſoris in E, non tranſe-
              <lb/>
            at. </s>
            <s xml:id="echoid-s2744" xml:space="preserve">Quando namque longitudo D C, è directo menſoris ſita eſt, inueſtigabitur
              <lb/>
            ea per problema 9. </s>
            <s xml:id="echoid-s2745" xml:space="preserve">præcedens. </s>
            <s xml:id="echoid-s2746" xml:space="preserve">Vt ergo tranuserſa longitudo CD, nota effi-
              <lb/>
            ciatur, inueſtiganda primum erit vtriuſque puncti extremi C, D, diſtantia à pede
              <lb/>
            menſoris E, & </s>
            <s xml:id="echoid-s2747" xml:space="preserve">qu@dem per vnicam ſtationem in E, factã, vt problemate 6. </s>
            <s xml:id="echoid-s2748" xml:space="preserve">Num.</s>
            <s xml:id="echoid-s2749" xml:space="preserve"/>
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