Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s4890" xml:space="preserve">
              <pb o="125" file="155" n="155" rhead="LIBER TERTIVS."/>
            pars AK, quam parallela FK, per imaginationem ducta abſcindit: </s>
            <s xml:id="echoid-s4891" xml:space="preserve">ita vt omni-
              <lb/>
            no neceſſarium ſit altitudinem A K, inquirere. </s>
            <s xml:id="echoid-s4892" xml:space="preserve">quod per 8. </s>
            <s xml:id="echoid-s4893" xml:space="preserve">problema facilè
              <lb/>
            exequemur, ſi in vtra que ſtatione vmbra verſa ſecetur in I, N, (quod plerunque
              <lb/>
            hic continget (& </s>
            <s xml:id="echoid-s4894" xml:space="preserve">vtraque abſciſſa B I, b N, ad rectas D M, d O, reuocetur:
              <lb/>
            </s>
            <s xml:id="echoid-s4895" xml:space="preserve">Nam ſi fiat,
              <lb/>
              <figure xlink:label="fig-155-01" xlink:href="fig-155-01a" number="84">
                <image file="155-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/155-01"/>
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              <note style="it" position="right" xlink:label="note-155-01" xlink:href="note-155-01a" xml:space="preserve">
                <lb/>
              Vt L M, differentia vm- \\ brarum rectarum # ad D d, differentiam \\ ſtationum: # ita A D, \\ lat{us} # ad A K,
                <lb/>
              </note>
            inuenta erit altitudo A K, oculo poſito in eius ſummitate A; </s>
            <s xml:id="echoid-s4896" xml:space="preserve">vt in dicto pro-
              <lb/>
            blem. </s>
            <s xml:id="echoid-s4897" xml:space="preserve">8. </s>
            <s xml:id="echoid-s4898" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s4899" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4900" xml:space="preserve">diximus, &</s>
            <s xml:id="echoid-s4901" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4902" xml:space="preserve">Quætamen altitudo A K, facilius per ſcholium
              <lb/>
            problem. </s>
            <s xml:id="echoid-s4903" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4904" xml:space="preserve">reperiri poteſt.</s>
            <s xml:id="echoid-s4905" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4906" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            quia vmbra B I, per 1. </s>
            <s xml:id="echoid-s4907" xml:space="preserve">problema patefacit angulum B A I, hoc eſt,
              <lb/>
            alternum A F K, ſibi æqualem, nec non & </s>
            <s xml:id="echoid-s4908" xml:space="preserve">eius complementum F A K; </s>
            <s xml:id="echoid-s4909" xml:space="preserve">erunt in
              <lb/>
            triangulo rectangulo AKF, duo anguliacuti cogniti, vna cumlatere AK, proxi-
              <lb/>
              <note symbol="a" position="right" xlink:label="note-155-02" xlink:href="note-155-02a" xml:space="preserve">5. Triang.
                <lb/>
              rectil.</note>
            mè inuento; </s>
            <s xml:id="echoid-s4910" xml:space="preserve"> Ita que ſi
              <note style="it" position="right" xlink:label="note-155-03" xlink:href="note-155-03a" xml:space="preserve">
                <lb/>
              Vt ſin{us} to- \\ t{us} # ad lat{us} A K, in- \\ uentum: # ita A F, ſecans anguli \\ FAK, # ad A F,
                <lb/>
              </note>
            cognita fiet A F, in partibus lateris inuenti A K. </s>
            <s xml:id="echoid-s4911" xml:space="preserve">Vel inuenta parte dioptræ A I,
              <lb/>
            in partibus milleſimis lateris quadrati, vt ſupra dictum eſt prope initium huius
              <lb/>
              <note symbol="b" position="right" xlink:label="note-155-04" xlink:href="note-155-04a" xml:space="preserve">4. ſexti.</note>
            problematis, ſi
              <note style="it" position="right" xlink:label="note-155-05" xlink:href="note-155-05a" xml:space="preserve">
                <lb/>
              Vt B I, vmbra \\ verſa # ad I A, partem dioptræ \\ inuentæ: # ita K A, altitudo \\ inuenta # ad A F,
                <lb/>
              </note>
            nota rurſus efficietur diſtantia A F, in partibus rectæ AK, inuentæ.</s>
            <s xml:id="echoid-s4912" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4913" xml:space="preserve">
              <emph style="sc">Porro</emph>
            diſtantiam E F, à pede menſoris ad pun ctum F, inueniemus, vt ſupra: </s>
            <s xml:id="echoid-s4914" xml:space="preserve">propterea quo din triangulo AEF, duo latera AE, AF, nota ſunt, cum il-
              <lb/>
              <note symbol="c" position="right" xlink:label="note-155-06" xlink:href="note-155-06a" xml:space="preserve">12. triang.
                <lb/>
              rectil.</note>
            lud ſit ſtatura menſoris, hoc autem ſit proximè inuentum, angulumque conti-
              <lb/>
            nent notum FAK, vt paulò ante diximus</s>
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          <p>
            <s xml:id="echoid-s4915" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4916" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter vtra que diſtantia cognoſcetur, ſi punctum F, in Horizonte
              <lb/>
            ſit poſitum, qui Horizon per FK, intelligatur tranſire, ita vt ſtatura menſoris, vel
              <lb/>
            aliqua alia altitudo nota, ſit AK. </s>
            <s xml:id="echoid-s4917" xml:space="preserve">Nam cognita portione dioptrę A I, vt ſupra
              <lb/>
              <note symbol="d" position="right" xlink:label="note-155-07" xlink:href="note-155-07a" xml:space="preserve">4. ſexti.</note>
            traditum eſt; </s>
            <s xml:id="echoid-s4918" xml:space="preserve"> Si
              <note style="it" position="right" xlink:label="note-155-08" xlink:href="note-155-08a" xml:space="preserve">
                <lb/>
              Vt B I, vmbra \\ abſciſſa # ad I A, portionem dio- \\ ptra inuentans: # ita A K, altitudo, \\ vel ſtatura men- \\ſoris # ad A F,
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