Clavius, Christoph, Geometria practica

Table of Notes

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            <s xml:id="echoid-s2322" xml:space="preserve">
              <pb o="57" file="087" n="87" rhead="LIBER SECVNDVS."/>
            ſeruationis GDF, & </s>
            <s xml:id="echoid-s2323" xml:space="preserve">diſtantiam DF, quam per angulum obſeruationis GEF, & </s>
            <s xml:id="echoid-s2324" xml:space="preserve">
              <lb/>
            diſtantiam EF. </s>
            <s xml:id="echoid-s2325" xml:space="preserve">Vtroque enim modo inuenta eſt altitudo GF.</s>
            <s xml:id="echoid-s2326" xml:space="preserve"/>
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        <div xml:id="echoid-div121" type="section" level="1" n="52">
          <head xml:id="echoid-head55" xml:space="preserve">COROLLARIVM II.</head>
          <p>
            <s xml:id="echoid-s2327" xml:space="preserve">
              <emph style="sc">Perspicvvm</emph>
            etiam eſt, ſi G, ſit cacumen alicuius montis, nos per hoc
              <lb/>
              <note position="right" xlink:label="note-087-01" xlink:href="note-087-01a" xml:space="preserve">Altitudo mõ-
                <lb/>
              tis quo pacto
                <lb/>
              inueſtigetur.</note>
            problema 1. </s>
            <s xml:id="echoid-s2328" xml:space="preserve">eius altitudinem poſſe metiri per duas ſtationes D, E, in plano fa-
              <lb/>
            ctas: </s>
            <s xml:id="echoid-s2329" xml:space="preserve">ſi nimirum prius inueſtigetur recta D F, vel E F, ab oculo menſoris vſque
              <lb/>
            ad perpendicularem GF, quæ à cacumine G, in planum Horizontis cadit, etiãſi
              <lb/>
            eius extremum F, non videamus.</s>
            <s xml:id="echoid-s2330" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2331" xml:space="preserve">ALTITVDINEM inacceſſibilem, quando diſtantia à loco mẽ-
              <lb/>
            ſoris ad baſem altitudinis ignota eſt, per duas ſtationes in plano factas,
              <lb/>
            per quadrantem dimetiri. </s>
            <s xml:id="echoid-s2332" xml:space="preserve">Atque hinc diſtantiam quoque ipſam erue-
              <lb/>
            re, etiam ſi extremus eius terminus non cernatur.</s>
            <s xml:id="echoid-s2333" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div123" type="section" level="1" n="53">
          <head xml:id="echoid-head56" xml:space="preserve">PROBLEMA II.</head>
          <p>
            <s xml:id="echoid-s2334" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2335" xml:space="preserve">
              <emph style="sc">Sit</emph>
            inquirenda altitudo AB, ſiue ea turris ſit, ſiue mons, ſiue aliquid ali-
              <lb/>
            ud, licetnon cernatur eius perpendiculi infimus terminus B, vt in omni monte
              <lb/>
            contingit: </s>
            <s xml:id="echoid-s2336" xml:space="preserve">planum autem, cui perpendicularis eſt altitudo, ſit CB. </s>
            <s xml:id="echoid-s2337" xml:space="preserve">Statura mẽ-
              <lb/>
            ſoris D E. </s>
            <s xml:id="echoid-s2338" xml:space="preserve">Ducta autem cogitatione per E, ipſi CB, parallela GF, fiat prima ſta-
              <lb/>
            tio in D, propinquior, ſecunda vero in G, remotior, vt differentia ſtationum ſit
              <lb/>
            GE. </s>
            <s xml:id="echoid-s2339" xml:space="preserve">Deinde per radios viſuales EA, GA, ad verticem A, directos diligenter ob-
              <lb/>
            ſeruentur anguli AEF, AGF, ſiue per quadrantem pendulum, vt Num. </s>
            <s xml:id="echoid-s2340" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2341" xml:space="preserve">pro-
              <lb/>
            blematis præcedentis do cuimus, ſiue per ſtabilem, vt Num. </s>
            <s xml:id="echoid-s2342" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2343" xml:space="preserve">eiuſdem proble-
              <lb/>
            matis præcepimus. </s>
            <s xml:id="echoid-s2344" xml:space="preserve">Eodem enim ſemper modo dicti anguli obſeruantur, quan-
              <lb/>
            do è loco inferiori altitu dinis faſtigium inſpicitur. </s>
            <s xml:id="echoid-s2345" xml:space="preserve">Cogitetur quo que ducta HI,
              <lb/>
              <figure xlink:label="fig-087-01" xlink:href="fig-087-01a" number="23">
                <image file="087-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/087-01"/>
              </figure>
            ipſi G F, parallela, vt demiſſæ perpendiculares H L, I K,
              <note symbol="a" position="right" xlink:label="note-087-02" xlink:href="note-087-02a" xml:space="preserve">34. prim.</note>
            parallelogrammo LI, ſint æquales, pro ſinubus totis: </s>
            <s xml:id="echoid-s2346" xml:space="preserve">quo-
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            rum tangentes ſunt EK, GL, angulis, I, H, qui complemen-
              <lb/>
            ta ſunt angulorum obſeruationum E, G, debitæ. </s>
            <s xml:id="echoid-s2347" xml:space="preserve">Et quo-
              <lb/>
            niam angulus G A F, maior eſt angulo E A F, eſt que
              <note symbol="b" position="right" xlink:label="note-087-03" xlink:href="note-087-03a" xml:space="preserve">29. primi.</note>
            angulus G H L, & </s>
            <s xml:id="echoid-s2348" xml:space="preserve">poſteriori angulus E I K, æqualis: </s>
            <s xml:id="echoid-s2349" xml:space="preserve">erit
              <lb/>
            quo que GHL, maior quam EIK, ideo que tãgens G L, ma-
              <lb/>
            ior Tangente EK, quòd ſinus toti H L, I K, æquales ſint. </s>
            <s xml:id="echoid-s2350" xml:space="preserve">Ab-
              <lb/>
            ſcindatur LM, ipſi EK, æqualis, vt GM, ſit differẽtia Tangẽ-
              <lb/>
            tium G L, E K, Et quia eſt vt G L, ad L H, ita G F, ad F A, erit permutando,
              <note symbol="c" position="right" xlink:label="note-087-04" xlink:href="note-087-04a" xml:space="preserve">4. ſexti.</note>
            GL, ad GF, ita LH, vel IK, ad FA; </s>
            <s xml:id="echoid-s2351" xml:space="preserve"> Vtautem IK, ad F A, ita quoque eſt EK,
              <note symbol="d" position="right" xlink:label="note-087-05" xlink:href="note-087-05a" xml:space="preserve">4. ſexti &
                <lb/>
              permutando</note>
            EF. </s>
            <s xml:id="echoid-s2352" xml:space="preserve">Igitur erit, vttota GL, ad totam GF, ita EK, vel LM, ex GL, ablata, ad EF,
              <lb/>
            ex GF, ablatam: </s>
            <s xml:id="echoid-s2353" xml:space="preserve"> ac proinde erit etiam vt GM, ex GL, reliqua ad G E, ex G
              <note symbol="e" position="right" xlink:label="note-087-06" xlink:href="note-087-06a" xml:space="preserve">19. quinti</note>
            reliquam, ita tota G L, ad totam G F, hoc eſt, ita L H, ſinus totus, a d F A.</s>
            <s xml:id="echoid-s2354" xml:space="preserve">
              <note symbol="f" position="right" xlink:label="note-087-07" xlink:href="note-087-07a" xml:space="preserve">4 ſexti &
                <lb/>
              permutando.</note>
            Quamobrem ſi fiat.</s>
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          <note style="it" position="right" xml:space="preserve">
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          Vt G M, differentia Tangentium \\ G L, E K, complementorum an- \\ gulorum obſeruationum # ad G E, diffe- \\ rentiam ſt a- \\ tionum. # ita L H, \\ ſin{us} i
            <unsure/>
          o- \\ t{us}. # ad FA,
            <lb/>
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