Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div158" type="section" level="1" n="69">
          <p>
            <s xml:id="echoid-s2644" xml:space="preserve">
              <pb o="67" file="097" n="97" rhead="LIBER SECVNDVS."/>
            BD. </s>
            <s xml:id="echoid-s2645" xml:space="preserve">Quia ergo in triangulo rectangulo ACG, duo latera AG, GC, per inuen-
              <lb/>
            tionem nota fa cta ſunt; </s>
            <s xml:id="echoid-s2646" xml:space="preserve"> cognoſcetur quoq; </s>
            <s xml:id="echoid-s2647" xml:space="preserve">baſis AC, quod eſt propoſitum.</s>
            <s xml:id="echoid-s2648" xml:space="preserve"/>
          </p>
          <note symbol="a" position="right" xml:space="preserve">3. triang.
            <lb/>
          rectil.</note>
          <p>
            <s xml:id="echoid-s2649" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2650" xml:space="preserve">
              <emph style="sc">Manifestvm</emph>
            autem eſt, eodem pacto vtramque diſtantiam AB, AC,
              <lb/>
            reperiri, etiamſi punctum A, in plano ſit, in quo menſor conſiſtit, nimirum in
              <lb/>
            Horizonte, qui ponatur tranſire per rectam AG, ita vt ſtatura menſoris ſit B G,
              <lb/>
            Immo tunc per vnicam ſtationem vtraque diſtantia AB, AG, rep erietur. </s>
            <s xml:id="echoid-s2651" xml:space="preserve">Nam
              <lb/>
            poſito ſinu toto B G, ſtatura menſoris; </s>
            <s xml:id="echoid-s2652" xml:space="preserve">A B, ſecans eſt anguli obſeruationis
              <lb/>
            ABG, & </s>
            <s xml:id="echoid-s2653" xml:space="preserve">AG, Tangens. </s>
            <s xml:id="echoid-s2654" xml:space="preserve">Quo circa ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt BG, ſinus \\ totus # ad B A, ſecantem anguli obſer- \\ @ationis A B G, # Ita BG, ſtatura \\ menſoris # ad B A,
            <lb/>
          #### Vel
            <lb/>
          # ad GA, Tangentem anguli ob- \\ ſeruationis A B G: # # ad G A,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2655" xml:space="preserve">vtraque diſtantia & </s>
            <s xml:id="echoid-s2656" xml:space="preserve">BA, ab oculo B, & </s>
            <s xml:id="echoid-s2657" xml:space="preserve">G A, à G, pede menſoris cognita fiet.</s>
            <s xml:id="echoid-s2658" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2659" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2660" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò ſine numeris operabimur, vt in præcedentibus, vt manifeſtum
              <lb/>
              <note position="right" xlink:label="note-097-03" xlink:href="note-097-03a" xml:space="preserve">Quo pacto ꝓ-
                <lb/>
              blema ſine nu-
                <lb/>
              meris ſit ſol-
                <lb/>
              uendum.</note>
            eſt, ſi rectè figura conſtruatur, quemadmodum Num. </s>
            <s xml:id="echoid-s2661" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2662" xml:space="preserve">& </s>
            <s xml:id="echoid-s2663" xml:space="preserve">8. </s>
            <s xml:id="echoid-s2664" xml:space="preserve">problematis 1. </s>
            <s xml:id="echoid-s2665" xml:space="preserve">di-
              <lb/>
            ctum eſt.</s>
            <s xml:id="echoid-s2666" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2667" xml:space="preserve">INTER VALLVM inter duo puncta in quolibet plano eleuato, ſiuc
              <lb/>
            illud ad Horizontem rectum ſit, ſiue inclinatum, metiri.</s>
            <s xml:id="echoid-s2668" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div164" type="section" level="1" n="70">
          <head xml:id="echoid-head73" xml:space="preserve">PROBLEMA VII.</head>
          <p>
            <s xml:id="echoid-s2669" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2670" xml:space="preserve">
              <emph style="sc">In</emph>
            plano quolibet eleuato AB. </s>
            <s xml:id="echoid-s2671" xml:space="preserve">prop oſitum ſit interuallum CD, quod
              <lb/>
            ex plano EB, inueſtigandum ſit. </s>
            <s xml:id="echoid-s2672" xml:space="preserve">Poſito oculo in G, vt ſtatura menſoris ſit, GE,
              <lb/>
            inueſtiget ur per præcedens problema 6. </s>
            <s xml:id="echoid-s2673" xml:space="preserve">vtraque diſtantia G C, G D, in parti-
              <lb/>
            bus ſtaturæ menſoris G E, ſiue differentiæ
              <lb/>
              <figure xlink:label="fig-097-01" xlink:href="fig-097-01a" number="30">
                <image file="097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/097-01"/>
              </figure>
            duarum ſtationum, è quibus ipſæ diſtan-
              <lb/>
            tiæ inueſtigantur. </s>
            <s xml:id="echoid-s2674" xml:space="preserve">Deinde applicato Qua-
              <lb/>
            drante ſtabili ad oculum G, ita vt eius pla-
              <lb/>
            num per puncta CD, tranſeat, & </s>
            <s xml:id="echoid-s2675" xml:space="preserve">vna eius
              <lb/>
            ſemidiameter ad punctum D, vergat,
              <lb/>
            (quod fiet, ſi poſita linea fiduciæ dioptræ
              <lb/>
            ſupra illam ſemidiametrum, punctum D,
              <lb/>
            per foramina pinnacidiorum conſpicia-
              <lb/>
            tur) vertatur dioptra, donec per eam punctum C, appareat, arcuſque in-
              <lb/>
            ter dictam ſemidiametrum, & </s>
            <s xml:id="echoid-s2676" xml:space="preserve">lineam fiduciæ interceptus notetur. </s>
            <s xml:id="echoid-s2677" xml:space="preserve">hic enim
              <lb/>
            angulum G, metietur. </s>
            <s xml:id="echoid-s2678" xml:space="preserve">Quod ſi altera ſemidiameter Quadrantis vltra re-
              <lb/>
            ctam G C, exiſtat, erit angulus acutus C G D: </s>
            <s xml:id="echoid-s2679" xml:space="preserve">Si verò altera illa ſemidia-
              <lb/>
            meter citra rectam G C, extiterit, dictus angulus erit obtuſus, qui cogno-
              <lb/>
            ſcetur, ſi ad rectum adiiciatur reliquus angulus inter alteram illam ſemidia-
              <lb/>
            metrum, & </s>
            <s xml:id="echoid-s2680" xml:space="preserve">rectam G C; </s>
            <s xml:id="echoid-s2681" xml:space="preserve">quem quidem reliquum inueſtigabimus per
              <lb/>
            Quadrantem, vt de acuto C G D, diximus, ſi videlicet in recta C D,
              <lb/>
            mente notemus punctum, in quod altera illa ſemidiameter incurre-
              <lb/>
            ret producta. </s>
            <s xml:id="echoid-s2682" xml:space="preserve">Si namque tunc ſemidiameter illa rectæ G C, </s>
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