Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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        <div xml:id="echoid-div354" type="section" level="1" n="128">
          <p>
            <s xml:id="echoid-s6018" xml:space="preserve">
              <pb o="103" file="0123" n="123" rhead="LIBER PRIMVS."/>
            gradibus 42. </s>
            <s xml:id="echoid-s6019" xml:space="preserve">Erit altitudo poli ſupra planum E F, per propoſ. </s>
            <s xml:id="echoid-s6020" xml:space="preserve">pręcedentem inuẽta grad. </s>
            <s xml:id="echoid-s6021" xml:space="preserve">40. </s>
            <s xml:id="echoid-s6022" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s6023" xml:space="preserve">3, ferè. </s>
            <s xml:id="echoid-s6024" xml:space="preserve">Arcus verò Meridiani inter idem planum, & </s>
            <s xml:id="echoid-s6025" xml:space="preserve">polum continebit grad. </s>
            <s xml:id="echoid-s6026" xml:space="preserve">48. </s>
            <s xml:id="echoid-s6027" xml:space="preserve">quantum nimirũ
              <lb/>
            eſt complementum altitudinis poli ſupra Horizontem. </s>
            <s xml:id="echoid-s6028" xml:space="preserve">Igitur ſi fiat, vt 76548. </s>
            <s xml:id="echoid-s6029" xml:space="preserve">ſinus complemen-
              <lb/>
            ti altitudinis poli ſupra planum, ad 66913. </s>
            <s xml:id="echoid-s6030" xml:space="preserve">ſinum complementi arcus Meridiani inter planum & </s>
            <s xml:id="echoid-s6031" xml:space="preserve">
              <lb/>
            polum, (quod complementum in huiuſmodi planis inclinatis eſt ipſamet poli altitudo ſupra Ho
              <lb/>
            rizontem,) ita 100000. </s>
            <s xml:id="echoid-s6032" xml:space="preserve">ſinus totus ad, aliud, rep erietur hic ferè ſinus 87413. </s>
            <s xml:id="echoid-s6033" xml:space="preserve">cuius arcus continet
              <lb/>
            gradus 60. </s>
            <s xml:id="echoid-s6034" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6035" xml:space="preserve">57. </s>
            <s xml:id="echoid-s6036" xml:space="preserve">quo detracto ex quadrante, reliquus erit arcus grad. </s>
            <s xml:id="echoid-s6037" xml:space="preserve">29. </s>
            <s xml:id="echoid-s6038" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6039" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6040" xml:space="preserve">ipſius plani,
              <lb/>
            qui inter Meridianum ipſius, & </s>
            <s xml:id="echoid-s6041" xml:space="preserve">Meridianum Horizontis interiicitut. </s>
            <s xml:id="echoid-s6042" xml:space="preserve">Quod eſt primum. </s>
            <s xml:id="echoid-s6043" xml:space="preserve">Rurſus
              <lb/>
            ſi fiat, vt 74314. </s>
            <s xml:id="echoid-s6044" xml:space="preserve">ſinus arcus Meridiani inter planum & </s>
            <s xml:id="echoid-s6045" xml:space="preserve">polum, ad 100000. </s>
            <s xml:id="echoid-s6046" xml:space="preserve">ſinũ totum, ita 48557. </s>
            <s xml:id="echoid-s6047" xml:space="preserve">
              <lb/>
            ſinus arcus inter duos Meridianos inuenti ad aliud, inuenietur hic ferè ſinus 65340. </s>
            <s xml:id="echoid-s6048" xml:space="preserve">cuius arcus
              <lb/>
              <note position="left" xlink:label="note-0123-01" xlink:href="note-0123-01a" xml:space="preserve">10</note>
            complectitur grad. </s>
            <s xml:id="echoid-s6049" xml:space="preserve">40. </s>
            <s xml:id="echoid-s6050" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6051" xml:space="preserve">48. </s>
            <s xml:id="echoid-s6052" xml:space="preserve">Tanta eſt inclinatio Meridiani ipſius plani ad Meridianum Hori-
              <lb/>
            zontis. </s>
            <s xml:id="echoid-s6053" xml:space="preserve">quod eſt ſecundum.</s>
            <s xml:id="echoid-s6054" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6055" xml:space="preserve">PRO figura autem tertia hoc ſume exemplum. </s>
            <s xml:id="echoid-s6056" xml:space="preserve">Ponatur planum E F, declinare à Meridiano
              <lb/>
              <note position="right" xlink:label="note-0123-02" xlink:href="note-0123-02a" xml:space="preserve">Exemplum ter-
                <lb/>
              tium.</note>
            grad. </s>
            <s xml:id="echoid-s6057" xml:space="preserve">60. </s>
            <s xml:id="echoid-s6058" xml:space="preserve">& </s>
            <s xml:id="echoid-s6059" xml:space="preserve">idcirco ab Horizonte grad. </s>
            <s xml:id="echoid-s6060" xml:space="preserve">30. </s>
            <s xml:id="echoid-s6061" xml:space="preserve">Erit altitudo poli ſupra ipſum (nempe arcus H I,) per
              <lb/>
            pręcedentem propoſ. </s>
            <s xml:id="echoid-s6062" xml:space="preserve">inuenta, grad. </s>
            <s xml:id="echoid-s6063" xml:space="preserve">35. </s>
            <s xml:id="echoid-s6064" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6065" xml:space="preserve">25. </s>
            <s xml:id="echoid-s6066" xml:space="preserve">Itaque ſi fiat, vt 81495. </s>
            <s xml:id="echoid-s6067" xml:space="preserve">ſinus complementi altitu
              <lb/>
            dinis poli ſupra planum, ad 74314. </s>
            <s xml:id="echoid-s6068" xml:space="preserve">ſinum complementi arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s6069" xml:space="preserve">polũ,
              <lb/>
            hoc eſt, ad ſinum complementi altitudinis poli ſupra Horizontem in hoc exemplo, ita 100000. </s>
            <s xml:id="echoid-s6070" xml:space="preserve">ſi-
              <lb/>
            nus totus ad aliud, reperietur hic ferè ſinus 91188. </s>
            <s xml:id="echoid-s6071" xml:space="preserve">cuius arcus continet gradus 65. </s>
            <s xml:id="echoid-s6072" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6073" xml:space="preserve">46. </s>
            <s xml:id="echoid-s6074" xml:space="preserve">quo
              <lb/>
            detracto ex quadrante, reliquus erit arcus grad. </s>
            <s xml:id="echoid-s6075" xml:space="preserve">24. </s>
            <s xml:id="echoid-s6076" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6077" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6078" xml:space="preserve">ipſius plani inter Meridianum ipſius,
              <lb/>
            & </s>
            <s xml:id="echoid-s6079" xml:space="preserve">Meridianum Horizontis interiecti, nempe arcus G I. </s>
            <s xml:id="echoid-s6080" xml:space="preserve">Quod eſt primũ. </s>
            <s xml:id="echoid-s6081" xml:space="preserve">Rurſus ſi fiat, vt 66913.
              <lb/>
            </s>
            <s xml:id="echoid-s6082" xml:space="preserve">
              <note position="left" xlink:label="note-0123-03" xlink:href="note-0123-03a" xml:space="preserve">20</note>
            ſinus arcus Meridiani inter planum & </s>
            <s xml:id="echoid-s6083" xml:space="preserve">polum, nempe in hoc exemplo, vt ſinus altitudinis poli ſu-
              <lb/>
            pra Horizontem, ad 100000. </s>
            <s xml:id="echoid-s6084" xml:space="preserve">ſinum totum, ita 41045. </s>
            <s xml:id="echoid-s6085" xml:space="preserve">ſinus arcus G I, inter duos Meridianos in-
              <lb/>
            uenti ad aliud, inuenietur hic fere ſinus 61341. </s>
            <s xml:id="echoid-s6086" xml:space="preserve">cuius arcus complectitur grad. </s>
            <s xml:id="echoid-s6087" xml:space="preserve">37. </s>
            <s xml:id="echoid-s6088" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6089" xml:space="preserve">50. </s>
            <s xml:id="echoid-s6090" xml:space="preserve">Tan-
              <lb/>
            ta eſt inclinatio Meridiani ipſius plani ad Meridianum Horizontis, hoc eſt, tantus eſt angulus
              <lb/>
            G H I, ſeu arcus Aequatoris inter duos Meridianos poſitus. </s>
            <s xml:id="echoid-s6091" xml:space="preserve">Quod eſt ſecundum.</s>
            <s xml:id="echoid-s6092" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6093" xml:space="preserve">SI planum inclinatum per polum trãſeat, nullus erit arcus ipſius interpoſitus inter Meridianũ
              <lb/>
              <note position="right" xlink:label="note-0123-04" xlink:href="note-0123-04a" xml:space="preserve">Quando plan@
                <lb/>
              inclinarum per
                <lb/>
              polos mundi
                <lb/>
              tranſit.</note>
            Horizontis, & </s>
            <s xml:id="echoid-s6094" xml:space="preserve">Meridianum plani inclinati; </s>
            <s xml:id="echoid-s6095" xml:space="preserve">& </s>
            <s xml:id="echoid-s6096" xml:space="preserve">cõplementum inclinationis plani ad Meridianum,
              <lb/>
            erit inclinatio Meridiani ipſius ad Horizontis Meridianum, vt patet in ſphæra materiali. </s>
            <s xml:id="echoid-s6097" xml:space="preserve">Dato
              <lb/>
            igitur plano ad Meridianum inclinato, quantus ſit interceptus arcus, &</s>
            <s xml:id="echoid-s6098" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6099" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s6100" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div363" type="section" level="1" n="129">
          <head xml:id="echoid-head132" xml:space="preserve">PROBLEMA 10. PROPOSITIO 31.</head>
          <p>
            <s xml:id="echoid-s6101" xml:space="preserve">DATO plano ad Meridianum inclinato, quantus ſit arcus ipſius in-
              <lb/>
            terceptus inter circulum maximum, qui per polos ipſius, & </s>
            <s xml:id="echoid-s6102" xml:space="preserve">polos Hori-
              <lb/>
            zontis tranſit, metiturq́; </s>
            <s xml:id="echoid-s6103" xml:space="preserve">eius inclinationem ad Horizontem, & </s>
            <s xml:id="echoid-s6104" xml:space="preserve">tam Me
              <lb/>
            ridianum proprium ipſius, (nempe circulum maximum, qui per eius
              <lb/>
            polos, & </s>
            <s xml:id="echoid-s6105" xml:space="preserve">polos mundi ducitur, altitudinemq́; </s>
            <s xml:id="echoid-s6106" xml:space="preserve">poli ſupra ipſum dimeti-
              <lb/>
              <note position="left" xlink:label="note-0123-06" xlink:href="note-0123-06a" xml:space="preserve">40</note>
            tur, inſtar proprij Meridiani) quàm Meridianum Horizontis, reperire.</s>
            <s xml:id="echoid-s6107" xml:space="preserve"/>
          </p>
          <figure number="89">
            <image file="0123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123-01"/>
          </figure>
          <note position="left" xml:space="preserve">50</note>
          <note position="right" xml:space="preserve">Arcus plani in-
            <lb/>
          clinati inter
            <lb/>
          maximum cir-
            <lb/>
          culum per eius
            <lb/>
          polos, & per po-
            <lb/>
          los Horizontis
            <lb/>
          ductum, & Me-
            <lb/>
          ridianum eius
            <lb/>
          proprium in-
            <lb/>
          teriectus, qua
            <lb/>
          uia cognoſca-
            <lb/>
          tur.</note>
          <p>
            <s xml:id="echoid-s6108" xml:space="preserve">SIT Horizon A B C D; </s>
            <s xml:id="echoid-s6109" xml:space="preserve">Meridianus A C; </s>
            <s xml:id="echoid-s6110" xml:space="preserve">Verticalis k L; </s>
            <s xml:id="echoid-s6111" xml:space="preserve">planum inclinatum E F, ſecans Me-
              <lb/>
            ridianum in G; </s>
            <s xml:id="echoid-s6112" xml:space="preserve">eius Meridianus B D, per eius polum P, & </s>
            <s xml:id="echoid-s6113" xml:space="preserve">per polum mundi H, tranſiens; </s>
            <s xml:id="echoid-s6114" xml:space="preserve">Cir-
              <lb/>
            culus maximus inclinationem plani ad Horizontem metiens, hoc eſt, per verticem M, ſeu polum
              <lb/>
            Horizontis, & </s>
            <s xml:id="echoid-s6115" xml:space="preserve">per P, polum plani inclinati deſcriptus N O, ſecans planum inclinatum in Q; </s>
            <s xml:id="echoid-s6116" xml:space="preserve">opor-
              <lb/>
            teatq́; </s>
            <s xml:id="echoid-s6117" xml:space="preserve">inuenire tam arcum I Q, quàm arcum G Q. </s>
            <s xml:id="echoid-s6118" xml:space="preserve">Quoniam arcus M N, P Q, quadrantes </s>
          </p>
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