Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s5597" xml:space="preserve">
              <pb o="144" file="174" n="174" rhead="GEOMETR. PRACT."/>
            vmbra verſa H I, quam dioptra in cacumen F, directa abſcindit, fiunt trlangula
              <lb/>
            A H I, F B A, æquiangula. </s>
            <s xml:id="echoid-s5598" xml:space="preserve"> Quamobrem ſi
              <note symbol="a" position="left" xlink:label="note-174-01" xlink:href="note-174-01a" xml:space="preserve">4. ſexti.</note>
              <note style="it" position="right" xlink:label="note-174-02" xlink:href="note-174-02a" xml:space="preserve">
                <lb/>
              Vt H I, vmbra ver- \\ ſa # ad A H, lat{us} qua- \\ drati # Ita lat{us} quadrati \\ A B, # ad B F,
                <lb/>
              </note>
            id eſt, ſi quadratus numerus 1000000. </s>
            <s xml:id="echoid-s5599" xml:space="preserve">lateris diuidatur per vmbram verſam, da-
              <lb/>
            bit Quotiens numerus longitudinem aſcenſus obliqui B F.</s>
            <s xml:id="echoid-s5600" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5601" xml:space="preserve">ALTITVDINEM, ad cuius baſem pateat acceſſus, beneficio ſpe-
              <lb/>
            culi plani, vna cum diſtantia ſpeculi à cacumine altitudinis depre-
              <lb/>
            hendere.</s>
            <s xml:id="echoid-s5602" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div377" type="section" level="1" n="157">
          <head xml:id="echoid-head160" xml:space="preserve">PROBLEMA XXXIX.</head>
          <p>
            <s xml:id="echoid-s5603" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5604" xml:space="preserve">
              <emph style="sc">Sit</emph>
            altitudo A B, à cuius baſe B, recedatur per quotuis paſſus, aut pedes,
              <lb/>
            vſque ad C, punctum, in quo ſpeculi plani centrum collocetur, & </s>
            <s xml:id="echoid-s5605" xml:space="preserve">ſecundum
              <lb/>
              <figure xlink:label="fig-174-01" xlink:href="fig-174-01a" number="107">
                <image file="174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/174-01"/>
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            rectam B C, retrocedatur, donec menſoris oculus
              <lb/>
            in E, conſtitutus cacumen A, intueri poſsit per ra-
              <lb/>
            dium reflexum E C A, ita vt D E, ſit ſtatura menſo-
              <lb/>
            ris ab oculo vſque ad planum. </s>
            <s xml:id="echoid-s5606" xml:space="preserve">Et quoniam an-
              <lb/>
            gulus incidentiæ D C E, æqualis eſt angulo refle-
              <lb/>
            xionis A C B, vt Perſpectiui docent, & </s>
            <s xml:id="echoid-s5607" xml:space="preserve">anguli D,
              <lb/>
            B, recti ſunt; </s>
            <s xml:id="echoid-s5608" xml:space="preserve">erunt triangula D C E, B C A, æquian-
              <lb/>
            gula; </s>
            <s xml:id="echoid-s5609" xml:space="preserve"> ideoque erit, vt C D, ad D E, ita C B, ad B A. </s>
            <s xml:id="echoid-s5610" xml:space="preserve">Quocirca ſi
              <note symbol="b" position="left" xlink:label="note-174-03" xlink:href="note-174-03a" xml:space="preserve">4. ſexti.</note>
              <note style="it" position="right" xlink:label="note-174-04" xlink:href="note-174-04a" xml:space="preserve">
                <lb/>
              Vt C D, diſtantia men- \\ ſoris à ſpeculo C, # ad D E, ſtaturam \\ menſoris: # Ita C B, diſtantia ſpecu- \\ li ab altitudine. # ad B A,
                <lb/>
              </note>
            producetur altitudo B A, quam quærimus, nota in partibus ſtaturæ menſo-
              <lb/>
            ris D E.</s>
            <s xml:id="echoid-s5611" xml:space="preserve"/>
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        <div xml:id="echoid-div379" type="section" level="1" n="158">
          <head xml:id="echoid-head161" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s5612" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5613" xml:space="preserve">
              <emph style="sc">Mensvretvr</emph>
            per quadrantem angulus D C E, vel B C A, (Hoc
              <lb/>
            fiet, ſi angulus rectus conſtruatur F G H, & </s>
            <s xml:id="echoid-s5614" xml:space="preserve">recta F G, tot particulas æquales con-
              <lb/>
            tineat, quot paſſus, vel pedes in C D, diſtantia continentur: </s>
            <s xml:id="echoid-s5615" xml:space="preserve">Item recta G H,
              <lb/>
            tot particulas eaſdem, quot paſſus aut pedes ſtatura menſoris D E, complecti-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s5616" xml:space="preserve">Iuncta namque recta F H, erit angulus F, angulo C, æqualis. </s>
            <s xml:id="echoid-s5617" xml:space="preserve">quem
              <note symbol="c" position="left" xlink:label="note-174-05" xlink:href="note-174-05a" xml:space="preserve">4. primi.</note>
            gulum F, nullo negotio per quadrantem aliquem in gradus diuiſum cognoſce-
              <lb/>
            mus.) </s>
            <s xml:id="echoid-s5618" xml:space="preserve">Nam ſi poſito ſinu toto C B, fiat.
              <lb/>
            </s>
            <s xml:id="echoid-s5619" xml:space="preserve">
              <note style="it" position="right" xlink:label="note-174-06" xlink:href="note-174-06a" xml:space="preserve">
                <lb/>
              Vt ſin{us} tot{us} \\ C B, # ad B A, tangentem anguli reflexio- \\ nis B C A, vel incidentiæ D C E, \\ quem proximè inuenim{us} # Ita C B, diſtan- \\ tia cognita # ad B A,
                <lb/>
              </note>
            prodibit altitudo B A, nota in partibus diſtantiæ C B. </s>
            <s xml:id="echoid-s5620" xml:space="preserve">Et ſi rurſum fiat,
              <lb/>
              <note style="it" position="right" xlink:label="note-174-07" xlink:href="note-174-07a" xml:space="preserve">
                <lb/>
              Vt ſin{us} tot{us} C B, # ad C A, ſecantem eiuſdem \\ anguli B C A, # Ita C B, diſtan- \\ tia cognita # ad C A,
                <lb/>
              </note>
            cognita etiam erit C A, diſtantia à ſpeculo C, vſque ad cacumen A, in partibus
              <lb/>
            diſtantiæ C B.</s>
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