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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          <pb o="134" file="0154" n="154" rhead="GNOMONICES"/>
          <p>
            <s xml:id="echoid-s8476" xml:space="preserve">POSTREMO exiſtat Sol in parallelo quocunq; </s>
            <s xml:id="echoid-s8477" xml:space="preserve">auſtrali, vt in principio ♑, habeatq́; </s>
            <s xml:id="echoid-s8478" xml:space="preserve">díſtan-
              <lb/>
              <note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">Exemplũ quar-
                <lb/>
              tum.</note>
            tiam à meridie hor. </s>
            <s xml:id="echoid-s8479" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8480" xml:space="preserve">hoc eſt, grad. </s>
            <s xml:id="echoid-s8481" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8482" xml:space="preserve">Fiat vt 100000. </s>
            <s xml:id="echoid-s8483" xml:space="preserve">ad 50000. </s>
            <s xml:id="echoid-s8484" xml:space="preserve">ſinum diſtantiæ Solis à meri-
              <lb/>
            die, ita 91706. </s>
            <s xml:id="echoid-s8485" xml:space="preserve">ſinus complementi declinationis ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s8486" xml:space="preserve">hic ſinus 45853. </s>
            <s xml:id="echoid-s8487" xml:space="preserve">cuius ar
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s8488" xml:space="preserve">27. </s>
            <s xml:id="echoid-s8489" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8490" xml:space="preserve">18. </s>
            <s xml:id="echoid-s8491" xml:space="preserve">ablatus ex quadrante relinquet arcũ grad. </s>
            <s xml:id="echoid-s8492" xml:space="preserve">62. </s>
            <s xml:id="echoid-s8493" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8494" xml:space="preserve">42. </s>
            <s xml:id="echoid-s8495" xml:space="preserve">pro Inuẽto primo.</s>
            <s xml:id="echoid-s8496" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8497" xml:space="preserve">DEINDE fiat, vt 88861. </s>
            <s xml:id="echoid-s8498" xml:space="preserve">ſinus Inuenti primi ad 39874. </s>
            <s xml:id="echoid-s8499" xml:space="preserve">ſinum declinationis, ita 100000.
              <lb/>
            </s>
            <s xml:id="echoid-s8500" xml:space="preserve">ſinus totus ad aliud, habebiturq́; </s>
            <s xml:id="echoid-s8501" xml:space="preserve">ferè ſinus hic 44872. </s>
            <s xml:id="echoid-s8502" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s8503" xml:space="preserve">26. </s>
            <s xml:id="echoid-s8504" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8505" xml:space="preserve">40. </s>
            <s xml:id="echoid-s8506" xml:space="preserve">ſublatus
              <lb/>
            ex complemento altitudinis poli grad. </s>
            <s xml:id="echoid-s8507" xml:space="preserve">48. </s>
            <s xml:id="echoid-s8508" xml:space="preserve">quia ſol auſtralis eſt, relinquet arcum grad. </s>
            <s xml:id="echoid-s8509" xml:space="preserve">21. </s>
            <s xml:id="echoid-s8510" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8511" xml:space="preserve">
              <lb/>
            20. </s>
            <s xml:id="echoid-s8512" xml:space="preserve">pro Inuento ſecundo.</s>
            <s xml:id="echoid-s8513" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8514" xml:space="preserve">FIAT tandem, vt 100000. </s>
            <s xml:id="echoid-s8515" xml:space="preserve">ſinus totus ad 88861. </s>
            <s xml:id="echoid-s8516" xml:space="preserve">ſinum Inuenti primi, ita 36379. </s>
            <s xml:id="echoid-s8517" xml:space="preserve">ſinus In-
              <lb/>
            uenti ſecundi ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s8518" xml:space="preserve">hic propemodum ſinus 32327. </s>
            <s xml:id="echoid-s8519" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s8520" xml:space="preserve">18. </s>
            <s xml:id="echoid-s8521" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s8522" xml:space="preserve">
              <note position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">10</note>
            52. </s>
            <s xml:id="echoid-s8523" xml:space="preserve">exhibebit quæſitam Solis altitudinem.</s>
            <s xml:id="echoid-s8524" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8525" xml:space="preserve">SOLE exiſtente in Verticali circulo, vt in puncto K, veluti in figura quinta apparet, multo
              <lb/>
              <note position="left" xlink:label="note-0154-03" xlink:href="note-0154-03a" xml:space="preserve">Altitudo Solis
                <lb/>
              in circulo Ver-
                <lb/>
              ticali quomodo
                <lb/>
              ex data hora p
                <lb/>
              triangula ſphæ
                <lb/>
              tica ſupputetur.</note>
              <figure xlink:label="fig-0154-01" xlink:href="fig-0154-01a" number="112">
                <image file="0154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0154-01"/>
              </figure>
              <note position="left" xlink:label="note-0154-04" xlink:href="note-0154-04a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0154-05" xlink:href="note-0154-05a" xml:space="preserve">30</note>
            expeditius ex diſtantia Solis à meridie cognita altitudinem per ſphęrica triangula venabimur,
              <lb/>
            hac ratione. </s>
            <s xml:id="echoid-s8526" xml:space="preserve">Quoniam in triangulo ſphærico A k M, angulus M, rectus eſt, erit per propoſ. </s>
            <s xml:id="echoid-s8527" xml:space="preserve">19.
              <lb/>
            </s>
            <s xml:id="echoid-s8528" xml:space="preserve">
              <note position="left" xlink:label="note-0154-06" xlink:href="note-0154-06a" xml:space="preserve">40</note>
            lib. </s>
            <s xml:id="echoid-s8529" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8530" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8531" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8532" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s8533" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8534" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8535" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8536" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s8537" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8538" xml:space="preserve">noſtrorũ
              <lb/>
            triangulorum ſphæricorum, vt ſinus complementi arcus A M, hoc eſt, vt ſinus diſtantiæ Solis à
              <lb/>
            meridie, id eſt, vt ſinus arcus F M, ad ſinum totum, ita ſinus complementi arcus A
              <emph style="sc">K</emph>
            , ad ſinum
              <lb/>
            complementi arcus K M, hoc eſt, ad ſinum complementi declinationis. </s>
            <s xml:id="echoid-s8539" xml:space="preserve">Conuertendo ergo erit
              <lb/>
            quoque, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complementi declinationis pa-
              <lb/>
            ralleli propoſiti ad ſinum complementi arcus A K, vnde ex prioribus tribus cognitis cognoſce-
              <lb/>
            @ur & </s>
            <s xml:id="echoid-s8540" xml:space="preserve">quartum, nempe complementum arcus A K, atque adeò & </s>
            <s xml:id="echoid-s8541" xml:space="preserve">ipſemet arcus A
              <emph style="sc">K</emph>
            , altitudinem
              <lb/>
            Solis metiens. </s>
            <s xml:id="echoid-s8542" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s8543" xml:space="preserve">Sole in Verticali circulo exiſtente, ſi fiat vt ſinus totus ad ſinum diſtantiæ Solis
              <lb/>
            à meridie, ita ſinus complementi declinationis ad aliud, inuenietur ſinus complementi altitudinis
              <lb/>
            Solis, ac proinde & </s>
            <s xml:id="echoid-s8544" xml:space="preserve">ipſa altitudo manifeſta erit.</s>
            <s xml:id="echoid-s8545" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s8546" xml:space="preserve">SED ſi diſtantia Solis à meridie ignota fuerit, inueniemus nihilominus altitudinem Solis in
              <lb/>
              <note position="left" xlink:label="note-0154-08" xlink:href="note-0154-08a" xml:space="preserve">Altitudo Solis
                <lb/>
              in Verticali quo
                <lb/>
              modo ſuppute-
                <lb/>
              tur per ſphæti-
                <lb/>
              ca triangula,
                <lb/>
              etiãſi hora igno
                <lb/>
              retur.</note>
            Verticali exiſtentis hoc modo. </s>
            <s xml:id="echoid-s8547" xml:space="preserve">Quoniam in triangulo ſphærico E K N, angulus E, rectus eſt; </s>
            <s xml:id="echoid-s8548" xml:space="preserve">erit
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s8549" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8550" xml:space="preserve">l b. </s>
            <s xml:id="echoid-s8551" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8552" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8553" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8554" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s8555" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8556" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8557" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8558" xml:space="preserve">Gebri, vel per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s8559" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8560" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus complementi arcus E N, hoc eſt, vt ſi-
              <lb/>
            nus arcus E F, altitudinis poli, ad ſinum totum, ita ſinus complementi arcus N k, id eſt, ita ſinus
              <lb/>
            arcus K M, declinationis paralleli propoſiti, ad ſinum complementi arcus E K, hoc eſt, ad ſinum
              <lb/>
            arcus A K, altitudinis Solis. </s>
            <s xml:id="echoid-s8561" xml:space="preserve">Igitur ſi fiat, vt ſinus altitudinis poli ad ſinum totum, ita ſinus decli-
              <lb/>
            nationis ad aliud, inuenietur ſinus altitudinis Solis. </s>
            <s xml:id="echoid-s8562" xml:space="preserve">Quod etiam clarius ita poterit demonſtrari.
              <lb/>
            </s>
            <s xml:id="echoid-s8563" xml:space="preserve">Quoniam in triangulo ſphærico A K M, eiuſdem figuræ quintę angulus M, rectus eſt, erit per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s8564" xml:space="preserve">16. </s>
            <s xml:id="echoid-s8565" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8566" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8567" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8568" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8569" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s8570" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8571" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8572" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8573" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s8574" xml:space="preserve">41. </s>
            <s xml:id="echoid-s8575" xml:space="preserve">
              <lb/>
            noſtrorum triangulorum ſphæricorum, vt ſinus anguli A, altitudinis poli, (eſt enim E F, & </s>
            <s xml:id="echoid-s8576" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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