Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div164" type="section" level="1" n="70">
          <p>
            <s xml:id="echoid-s2682" xml:space="preserve">
              <pb o="68" file="098" n="98" rhead="GEOMETR. PRACT."/>
            & </s>
            <s xml:id="echoid-s2683" xml:space="preserve">dioptra ad illud punctum mente notatum dirigatur, indicabunt gradus in-
              <lb/>
            ter illam ſemidiametrum, & </s>
            <s xml:id="echoid-s2684" xml:space="preserve">dioptram prædictum angulum reliquum. </s>
            <s xml:id="echoid-s2685" xml:space="preserve">Si deni-
              <lb/>
            que altera illa ſemidiameter præcisè in C, tendat, angulus C G D, rectus erit.
              <lb/>
            </s>
            <s xml:id="echoid-s2686" xml:space="preserve">Quia ergo in triangulo G C D, obliquangulo latera nota G C, G D, continent
              <lb/>
            angulum notum G; </s>
            <s xml:id="echoid-s2687" xml:space="preserve">cognoſcetur latus C D, per problema 12. </s>
            <s xml:id="echoid-s2688" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s2689" xml:space="preserve">rectil. </s>
            <s xml:id="echoid-s2690" xml:space="preserve">
              <lb/>
            cap. </s>
            <s xml:id="echoid-s2691" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2692" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2693" xml:space="preserve">1.</s>
            <s xml:id="echoid-s2694" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2695" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2696" xml:space="preserve">
              <emph style="sc">Absqve</emph>
            numeris facile problema ſoluetur, ſi fiat angulus G, æqualis
              <lb/>
            ei, qui per Quadrantem obſeruatus fuit, & </s>
            <s xml:id="echoid-s2697" xml:space="preserve">in rectis G C, GD, ex inſtrumento
              <lb/>
              <note position="left" xlink:label="note-098-01" xlink:href="note-098-01a" xml:space="preserve">Problematis
                <lb/>
              ſolutio ſine
                <lb/>
              numeris.</note>
            partium tot particulæ ſumantur, quot palmi, aut pedes in diſtantiis G C, GD,
              <lb/>
            inuenti ſunt, & </s>
            <s xml:id="echoid-s2698" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2699" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2700" xml:space="preserve">LONGITVDINEM lineæ rectę, quando menſor in vno eius extre-
              <lb/>
            mo, vel in aliqua altitudine nota, quę perpendicularis ſit in eo extre-
              <lb/>
            mo ad planum, in quo linea iacet, exiſtens alterum extremum videre
              <lb/>
            poteſt, per Quadrantem comprehendere.</s>
            <s xml:id="echoid-s2701" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div167" type="section" level="1" n="71">
          <head xml:id="echoid-head74" xml:space="preserve">PROBLEMA VIII.</head>
          <p>
            <s xml:id="echoid-s2702" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2703" xml:space="preserve">
              <emph style="sc">Sit</emph>
            exquirenda longitudo A B, hoc eſt, diſtan-
              <lb/>
              <figure xlink:label="fig-098-01" xlink:href="fig-098-01a" number="31">
                <image file="098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/098-01"/>
              </figure>
            tia inter A, & </s>
            <s xml:id="echoid-s2704" xml:space="preserve">B, etiamſi puncta intermedia ſiue propter
              <lb/>
            tumores interiectos, ſiue propter valles, cerninequeant,
              <lb/>
            dummodo in extremo A, exiſtens menſor, vel in aliqua
              <lb/>
            altitudine cognita ad planum, in quo linea A B, perpen-
              <lb/>
            diculari, ita vt A C, ſit vel ſtatura menſoris, vel haſta ali-
              <lb/>
            qua erecta, vel turris. </s>
            <s xml:id="echoid-s2705" xml:space="preserve">Inſpecto extremo B, obſeruetur angulus C. </s>
            <s xml:id="echoid-s2706" xml:space="preserve">Et quia po-
              <lb/>
            ſito ſinu toto AC, diſtantia AB, eſt Tangens anguli obſeruati C: </s>
            <s xml:id="echoid-s2707" xml:space="preserve">ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſinus totus \\ AC, # ad AB, tangentem anguli \\ obſeruati C. # Ita AC, ſtatura menſoris, \\ vel altitudo nota, # Ad AB, longi- \\ tudinem.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2708" xml:space="preserve">procreabitur longitudo A B, in partibus altitudinis notæ A C. </s>
            <s xml:id="echoid-s2709" xml:space="preserve">Quæ per ſolos
              <lb/>
              <note symbol="a" position="left" xlink:label="note-098-03" xlink:href="note-098-03a" xml:space="preserve">4. Triang.
                <lb/>
              rectil.</note>
            ſinus etiam producetur, ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſinus anguli B, com- \\ plenti anguli C, ob- \\ ſeruati # Ad AC, ſtaturam menſo- \\ ris, vel altitudinem no- \\ tam # Ita ſinus angu- \\ li C, obſerua- \\ uationis # ad AB, longi- \\ tudinem
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2710" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2711" xml:space="preserve">
              <emph style="sc">Sine</emph>
            numeris eadem longitudo AB, cognoſcetur, vt in præcedentibus
              <lb/>
              <note position="left" xlink:label="note-098-05" xlink:href="note-098-05a" xml:space="preserve">Solutio pro-
                <lb/>
              blematis ſine
                <lb/>
              numeris.</note>
            dictum eſt: </s>
            <s xml:id="echoid-s2712" xml:space="preserve">ſi videlicet ex inſtrumento partium accipiatur A C, tot particula-
              <lb/>
            rum, quot palmi, pedeſue in altitudine AC, exiſtunt, conſtituatur que angulus
              <lb/>
            obſeruationis C, ac tandem ad AC, perpendicularis excitetur AB, & </s>
            <s xml:id="echoid-s2713" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2714" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2715" xml:space="preserve">LONGITVDINEM, ad cuius extrema accedere non liceat, dum-
              <lb/>
            modo ea appareant, & </s>
            <s xml:id="echoid-s2716" xml:space="preserve">ipſa longitudo producta ad pedes menſoris
              <lb/>
            pertingat, ex altitudine aliqua nota dim@tiri:</s>
            <s xml:id="echoid-s2717" xml:space="preserve"/>
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