Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div176" type="section" level="1" n="75">
          <p>
            <s xml:id="echoid-s2749" xml:space="preserve">
              <pb o="70" file="100" n="100" rhead="GEOMETR. PRACT."/>
            5. </s>
            <s xml:id="echoid-s2750" xml:space="preserve">dictum eſt. </s>
            <s xml:id="echoid-s2751" xml:space="preserve">Deinde per Quadrantem cum dioptra angulus C E D, exquiren-
              <lb/>
            dus in plano Horizontis. </s>
            <s xml:id="echoid-s2752" xml:space="preserve">quod fiet, ſi Quadrantis
              <lb/>
              <figure xlink:label="fig-100-01" xlink:href="fig-100-01a" number="33">
                <image file="100-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/100-01"/>
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            planum erectum tranſeat ſemel per puncta E, C, & </s>
            <s xml:id="echoid-s2753" xml:space="preserve">
              <lb/>
            iterum per puncta E, D, vt deſignari poſsint partes
              <lb/>
            rectarum E C, E D. </s>
            <s xml:id="echoid-s2754" xml:space="preserve">Quadrantis enim vno latere in-
              <lb/>
            cumbente rectæ E C, dioptra vero rectæ E D, ſi an-
              <lb/>
            gulus eſt acutus, indicabit arcus inter illud latus, ac
              <lb/>
            dioptram, angulum C E D. </s>
            <s xml:id="echoid-s2755" xml:space="preserve">Quod ſi alterum Qua-
              <lb/>
            drantis latus rectæ ED, congruet erit angulus CED rectus: </s>
            <s xml:id="echoid-s2756" xml:space="preserve">Si vero recta ED. </s>
            <s xml:id="echoid-s2757" xml:space="preserve">vl-
              <lb/>
            tra alterum latus Quadrantis extiterit, dictus angulus obtuſus erit, qui cogni-
              <lb/>
            tus erit, ſi recto angulo ad datur reliquus inter alterum latus, & </s>
            <s xml:id="echoid-s2758" xml:space="preserve">rectam ED: </s>
            <s xml:id="echoid-s2759" xml:space="preserve">Qui
              <lb/>
            quidem reliquus angulus per Quadrantem explorabitur vt de acuto diximus in
              <lb/>
            problemate 7. </s>
            <s xml:id="echoid-s2760" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s2761" xml:space="preserve">ita habebimus triangulum ECD, cuius duo latera nota ſunt
              <lb/>
            EC, E D, angulumq; </s>
            <s xml:id="echoid-s2762" xml:space="preserve">notum comprehendunt C E D. </s>
            <s xml:id="echoid-s2763" xml:space="preserve"> Igitur, & </s>
            <s xml:id="echoid-s2764" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-100-01" xlink:href="note-100-01a" xml:space="preserve">12. triang.
                <lb/>
              rectil.</note>
            C D, cognitum erit.</s>
            <s xml:id="echoid-s2765" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2766" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2767" xml:space="preserve">
              <emph style="sc">Qvo</emph>
            pacto autem ſine ope numerorum problema perſiciendum ſit, tra-
              <lb/>
            ditum eſt in problemate 7. </s>
            <s xml:id="echoid-s2768" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s2769" xml:space="preserve">2.</s>
            <s xml:id="echoid-s2770" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2771" xml:space="preserve">LONGITVDINEM in Horizonte inter turrim aliquam, & </s>
            <s xml:id="echoid-s2772" xml:space="preserve">aliud
              <lb/>
            quodpiam ſignum, ex turri per duas ſtationes in faſtigio factas: </s>
            <s xml:id="echoid-s2773" xml:space="preserve">vel in
              <lb/>
            duabus feneſtris, quarum vna ſit ſub altera ad perpendiculum, quan-
              <lb/>
            do ſpatium inter illas feneſtras notum eſt, etiamſi totius turris altitu-
              <lb/>
            do ignota ſit, demetiri. </s>
            <s xml:id="echoid-s2774" xml:space="preserve">Atque hinc obiter altitudinem turris patefa-
              <lb/>
            cere.</s>
            <s xml:id="echoid-s2775" xml:space="preserve"/>
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        <div xml:id="echoid-div178" type="section" level="1" n="76">
          <head xml:id="echoid-head79" xml:space="preserve">PROBLEMA XI.</head>
          <p>
            <s xml:id="echoid-s2776" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2777" xml:space="preserve">
              <emph style="sc">Qvamvis</emph>
            problema hoc ſolutum iam ſit in
              <lb/>
              <figure xlink:label="fig-100-02" xlink:href="fig-100-02a" number="34">
                <image file="100-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/100-02"/>
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            problemate 3. </s>
            <s xml:id="echoid-s2778" xml:space="preserve">& </s>
            <s xml:id="echoid-s2779" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2780" xml:space="preserve">occaſione altitu dinis inquirendæ,
              <lb/>
            libet tamen idem hic per ſe, & </s>
            <s xml:id="echoid-s2781" xml:space="preserve">paulo aliter expedire.
              <lb/>
            </s>
            <s xml:id="echoid-s2782" xml:space="preserve">Sit ergo turris A B CD, & </s>
            <s xml:id="echoid-s2783" xml:space="preserve">longitudo propoſita C E: </s>
            <s xml:id="echoid-s2784" xml:space="preserve">
              <lb/>
            ſtatura autem menſoris B G, vel AF. </s>
            <s xml:id="echoid-s2785" xml:space="preserve">Inſpecto extre-
              <lb/>
            mo E, in prima ſtatione per angulum C G E, & </s>
            <s xml:id="echoid-s2786" xml:space="preserve">in ſe-
              <lb/>
            cũda per angulum DFE, ducatur FH, ipſi G E, paral-
              <lb/>
            lela. </s>
            <s xml:id="echoid-s2787" xml:space="preserve">Et quia in triangulis F D H, G C E, anguli D, C,
              <lb/>
              <note symbol="b" position="left" xlink:label="note-100-02" xlink:href="note-100-02a" xml:space="preserve">29. primi.</note>
            recti ſunt, & </s>
            <s xml:id="echoid-s2788" xml:space="preserve">H, E, æquales latuſque FD, lateri GC.</s>
            <s xml:id="echoid-s2789" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-100-03" xlink:href="note-100-03a" xml:space="preserve">34. primi.</note>
            æquale: </s>
            <s xml:id="echoid-s2790" xml:space="preserve"> erunt quo que & </s>
            <s xml:id="echoid-s2791" xml:space="preserve">anguli G, DFH,
              <note symbol="d" position="left" xlink:label="note-100-04" xlink:href="note-100-04a" xml:space="preserve">26. primi.</note>
            & </s>
            <s xml:id="echoid-s2792" xml:space="preserve">latera D H, C E. </s>
            <s xml:id="echoid-s2793" xml:space="preserve">Poſito autem ſinu toto F D, erit
              <lb/>
            DE, Tangens maioris anguli obſeruationis D F E, & </s>
            <s xml:id="echoid-s2794" xml:space="preserve">
              <lb/>
            D H, Tangens anguli D F H, hoc eſt, anguli æqualis
              <lb/>
            G, in prima ſtatione obſeruati: </s>
            <s xml:id="echoid-s2795" xml:space="preserve">ac proinde H E, differentia erit earum Tangen-
              <lb/>
            tium, quæ quidem æqualis eſt differentiæ ſtationum F G, vel AB, vel DC. </s>
            <s xml:id="echoid-s2796" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-100-05" xlink:href="note-100-05a" xml:space="preserve">34. primi.</note>
            igitur fiat,</s>
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          Vt H E, differentia Tan- \\ gentium angulorumob- \\ ſeruationum # Ad CE, Tangentem \\ min@ris anguli ob- \\ ſeruationis CGE. # Ita HE, vel FG, \\ differentia ſtatio- \\ num # ad G E, \\ longitu- \\ dinem, \\ gigne-
            <lb/>
          </note>
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