Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div383" type="section" level="1" n="160">
          <p>
            <s xml:id="echoid-s5639" xml:space="preserve">
              <pb o="146" file="176" n="176" rhead="GEOMETR. PRACT."/>
            reperietur CB, maior diſtantia ſpeculi C, ab altitudine. </s>
            <s xml:id="echoid-s5640" xml:space="preserve">Ex qua ſi auferatur K C,
              <lb/>
            differentia poſitionum ſpeculi, nota remanebit KB, minor diſtantia ſpeculiK,
              <lb/>
            ab eadem altitudine. </s>
            <s xml:id="echoid-s5641" xml:space="preserve">Quæ etiam inuenietur, ſi fiat, vt KC, differentia prædicto-
              <lb/>
            rum angulorum, qui complementa ſunt angulorum incidentiæ in ſpeculo, ad
              <lb/>
            KB, tangentem minorem: </s>
            <s xml:id="echoid-s5642" xml:space="preserve">Ita KC, differentia poſitionum ſpeculi ad aliud, vt
              <lb/>
            perſpicuum eſt.</s>
            <s xml:id="echoid-s5643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5644" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            quia angulus AKB, in propinquiore ſpeculi poſitione
              <note symbol="a" position="left" xlink:label="note-176-01" xlink:href="note-176-01a" xml:space="preserve">22. primi.</note>
            angulis ACK, CAK, æqualis eſt, ſi angulus ACK, remotioris poſitionis detra-
              <lb/>
            hatur ex angulo AKB, poſitionis propinquioris: </s>
            <s xml:id="echoid-s5645" xml:space="preserve">remanebit angulus CAK, no-
              <lb/>
            tus. </s>
            <s xml:id="echoid-s5646" xml:space="preserve"> Si igitur
              <note symbol="b" position="left" xlink:label="note-176-02" xlink:href="note-176-02a" xml:space="preserve">10. triang.
                <lb/>
              rectil.</note>
              <note style="it" position="right" xlink:label="note-176-03" xlink:href="note-176-03a" xml:space="preserve">
                <lb/>
              Vt ſin{us} anguli C A K, \\ differentiæ angulorum \\ incidentiæ # ad K C, differen- \\ tiam poſitionum \\ ſpeculi: # Ita ſin{us} anguli AKC, com- \\ plementi anguli AKB, ad \\ duos rectos in propinquio- \\ re poſitione ſpeculi # ad C A,
                <lb/>
              </note>
            gignetur hypotenuſa CA, remotioris poſitionis ſpeculi, in partibus differentiæ
              <lb/>
            poſitionum ſpeculi KC. </s>
            <s xml:id="echoid-s5647" xml:space="preserve"> Et ſi rurſus
              <note symbol="c" position="left" xlink:label="note-176-04" xlink:href="note-176-04a" xml:space="preserve">10. triang.
                <lb/>
              rectil.</note>
              <note style="it" position="right" xlink:label="note-176-05" xlink:href="note-176-05a" xml:space="preserve">
                <lb/>
              Vt ſin{us} anguli C A K, \\ differentiæ angulorum \\ incidentiæ # ad K C, differentiam \\ poſitionum ſpeculi: # Ita ſin{us} anguli re- \\ flexionis ACK, in \\ remotiori poſitione \\ ſpeculi # ad K A,
                <lb/>
              </note>
            procreabitur quoquehypotenuſa KA, propinquioris poſitionis ſpeculi, in eiſ-
              <lb/>
            dem partibus differentiæ poſitionum ſpeculi KC.</s>
            <s xml:id="echoid-s5648" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div386" type="section" level="1" n="161">
          <head xml:id="echoid-head164" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s5649" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5650" xml:space="preserve">
              <emph style="sc">Per</emph>
            ſolos ſinus idem aſſequemur hocmodo. </s>
            <s xml:id="echoid-s5651" xml:space="preserve">Inuenta hypotenuſa CA,
              <lb/>
            vt proximè diximus, per ſinus. </s>
            <s xml:id="echoid-s5652" xml:space="preserve">
              <note symbol="d" position="left" xlink:label="note-176-06" xlink:href="note-176-06a" xml:space="preserve">10. triang.
                <lb/>
              rectil.</note>
              <note style="it" position="right" xlink:label="note-176-07" xlink:href="note-176-07a" xml:space="preserve">
                <lb/>
              Vt ſin{us} tot{us} angu- \\ lirecti B, # ad hypotenuſam \\ inuentam C A, # Ita ſin{us} anguli A C B, \\ remotioris poſitionis \\ ſpeculi # ad A B,
                <lb/>
              </note>
            Prodibit enim in Quotiente altitudo AB, nota in partibus hypotenuſæ inuen-
              <lb/>
            tæ CA. </s>
            <s xml:id="echoid-s5653" xml:space="preserve"> Quod ſirurſus
              <note symbol="e" position="left" xlink:label="note-176-08" xlink:href="note-176-08a" xml:space="preserve">10. triang.
                <lb/>
              rectil.</note>
              <note style="it" position="right" xlink:label="note-176-09" xlink:href="note-176-09a" xml:space="preserve">
                <lb/>
              Vt ſin{us} tot{us} an- \\ gulirecti B, # ad hypotenuſam in- \\ uentam C A, # Ita ſin{us} anguli B A C, comple- \\ menti anguli in remotiore poſi- \\ tione ſpeculi # ad C B,
                <lb/>
              </note>
            producetur CB, maior ſpeculi diſtantia ab altitudine. </s>
            <s xml:id="echoid-s5654" xml:space="preserve">Ex qua ſi ſubtrahatur KC,
              <lb/>
            differentia poſitionum ſpeculi, cognita etiam relinquetur diſtantia minor KB.
              <lb/>
            </s>
            <s xml:id="echoid-s5655" xml:space="preserve">Quæetiam, ſi inueſtigetur hypotenuſa KB, vt ſupra traditum eſt, reperietur: </s>
            <s xml:id="echoid-s5656" xml:space="preserve">ſi
              <lb/>
            fiat, vt ſinus totus angulirecti B, ad hypotenuſam inuentam KB, ita ſinus anguli
              <lb/>
            BAK, complementi anguli in propinquiore poſitione ſpeculi, ad aliud, vt ma-
              <lb/>
            nifeſtum eſt.</s>
            <s xml:id="echoid-s5657" xml:space="preserve"/>
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