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-div426" type="section" level="1" n="138">
          <p>
            <s xml:id="echoid-s8694" xml:space="preserve">
              <pb o="136" file="0156" n="156" rhead="GNOMONICES"/>
            tur ſinus arcus cuiuſdam, qui ex quadrante ſublatus dabit arcum, quem vocabimus Inuen-
              <lb/>
            tum primum.</s>
            <s xml:id="echoid-s8695" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8696" xml:space="preserve">DEINDE ſi fiat, vt ſinus illius arcus, quem Inuentum primum diximus, ad ſinum altitudinis
              <lb/>
            poli, ita ſinus totus ad aliud, reperietur ſinus arcus alterius, ex quo, ſi Sol fuerit borealis, habueritq́
              <lb/>
            diſtantiam à meridie maiorem, quàm hor. </s>
            <s xml:id="echoid-s8697" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8698" xml:space="preserve">ſubtractus arcus complementi declinationis dabit
              <lb/>
              <note position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">Inuen@@ ſe-
                <lb/>
              cundum.</note>
            arcum quendam, quem Inuentum ſecundum appellabimus. </s>
            <s xml:id="echoid-s8699" xml:space="preserve">Quòd ſi diſtantia Solis à meridie
              <lb/>
            minor fuerit quàm hor. </s>
            <s xml:id="echoid-s8700" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8701" xml:space="preserve">in quocunque parallelo extiterit Sol, detrahendus erit arcus per Inuen-
              <lb/>
            tum primum compertus ex ſemicirculo, & </s>
            <s xml:id="echoid-s8702" xml:space="preserve">ex reliquo arcu, ſi Sol eſt borealis, ſubtrahendus rur-
              <lb/>
            ſus arcus complementi declinationis, vel ſi auſtralis Sol eſt, auferendus arcus compoſitus ex qua-
              <lb/>
            drante, & </s>
            <s xml:id="echoid-s8703" xml:space="preserve">arcu declinationis, vt arcus inueniatur, quem Inuentum ſecundum vocemus.</s>
            <s xml:id="echoid-s8704" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s8705" xml:space="preserve">POSTREMO ſi fiat, vt ſinus totus ad ſinumarcus, quem ſecundum Inuentum nominaui-
              <lb/>
            mus, ita ſinus arcus, quem diximus Inuentum primum, ad aliud, inuentus erit ſinus altitudinis
              <lb/>
            Solis quæſitæ. </s>
            <s xml:id="echoid-s8706" xml:space="preserve">Quod vt planius fiat, duobus exemplis rem totam explicabimus.</s>
            <s xml:id="echoid-s8707" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8708" xml:space="preserve">PONATVR Sol in principio ♋, habere diſtantiam à meridie hor. </s>
            <s xml:id="echoid-s8709" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8710" xml:space="preserve">hoc eſt, grad. </s>
            <s xml:id="echoid-s8711" xml:space="preserve">105. </s>
            <s xml:id="echoid-s8712" xml:space="preserve">ita
              <lb/>
              <note position="left" xlink:label="note-0156-03" xlink:href="note-0156-03a" xml:space="preserve">Exemplum pri-
                <lb/>
              num.</note>
            vt angulus BNQ, totidem gradus complectatur, atque adeo reliquus ex duobus rectis DNQ,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8713" xml:space="preserve">75. </s>
            <s xml:id="echoid-s8714" xml:space="preserve">Fiat ergo, vt 100000. </s>
            <s xml:id="echoid-s8715" xml:space="preserve">ſinus totus ad 96592. </s>
            <s xml:id="echoid-s8716" xml:space="preserve">ſinum anguli DNQ, ita 74314. </s>
            <s xml:id="echoid-s8717" xml:space="preserve">ſinus cõ-
              <lb/>
            plementi altitudinis poli ad aliud, inueniemusq́; </s>
            <s xml:id="echoid-s8718" xml:space="preserve">hunc propemodum ſinum 71781. </s>
            <s xml:id="echoid-s8719" xml:space="preserve">cuius arcus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8720" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8721" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8722" xml:space="preserve">52. </s>
            <s xml:id="echoid-s8723" xml:space="preserve">ex quadrante detractus relinquet arcum grad. </s>
            <s xml:id="echoid-s8724" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8725" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8726" xml:space="preserve">8. </s>
            <s xml:id="echoid-s8727" xml:space="preserve">pro Inuento primo.</s>
            <s xml:id="echoid-s8728" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8729" xml:space="preserve">RVRSVS fiat, vt 69633. </s>
            <s xml:id="echoid-s8730" xml:space="preserve">ſinus arcus Primi Inuenti ad 66913. </s>
            <s xml:id="echoid-s8731" xml:space="preserve">ſinum altitudinis poli, ita
              <lb/>
            100000. </s>
            <s xml:id="echoid-s8732" xml:space="preserve">ſinus totus ad aliud, reperiemus q́; </s>
            <s xml:id="echoid-s8733" xml:space="preserve">fere hunc ſinum 96093. </s>
            <s xml:id="echoid-s8734" xml:space="preserve">ex cuius arcu grad. </s>
            <s xml:id="echoid-s8735" xml:space="preserve">73. </s>
            <s xml:id="echoid-s8736" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s8737" xml:space="preserve">
              <note position="left" xlink:label="note-0156-04" xlink:href="note-0156-04a" xml:space="preserve">20</note>
            56. </s>
            <s xml:id="echoid-s8738" xml:space="preserve">(quoniam Sol borealis ponitur, eiuſq́; </s>
            <s xml:id="echoid-s8739" xml:space="preserve">diſtantia à meridie maior, quàm hor. </s>
            <s xml:id="echoid-s8740" xml:space="preserve">6.) </s>
            <s xml:id="echoid-s8741" xml:space="preserve">ſi detrahatur
              <lb/>
            complementum declinationis paralleli ♋, nempe grad. </s>
            <s xml:id="echoid-s8742" xml:space="preserve">66. </s>
            <s xml:id="echoid-s8743" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8744" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8745" xml:space="preserve">relinquetur arcus grad. </s>
            <s xml:id="echoid-s8746" xml:space="preserve">7.
              <lb/>
            </s>
            <s xml:id="echoid-s8747" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8748" xml:space="preserve">26. </s>
            <s xml:id="echoid-s8749" xml:space="preserve">pro Inuento ſecundo.</s>
            <s xml:id="echoid-s8750" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8751" xml:space="preserve">TANDEM fiat, vt 100000. </s>
            <s xml:id="echoid-s8752" xml:space="preserve">ſinus totus ad 12937. </s>
            <s xml:id="echoid-s8753" xml:space="preserve">ſinum arcus Inuenti ſecundi, ita 69633.
              <lb/>
            </s>
            <s xml:id="echoid-s8754" xml:space="preserve">ſinus arcus Inuenti primi ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s8755" xml:space="preserve">hic ferme ſinus 9008. </s>
            <s xml:id="echoid-s8756" xml:space="preserve">altitudinis Solis. </s>
            <s xml:id="echoid-s8757" xml:space="preserve">Quare
              <lb/>
            altitudo Solis comprehendet grad. </s>
            <s xml:id="echoid-s8758" xml:space="preserve">5. </s>
            <s xml:id="echoid-s8759" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8760" xml:space="preserve">10.</s>
            <s xml:id="echoid-s8761" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8762" xml:space="preserve">STATVATVR rurſus Sol in principio ♑, & </s>
            <s xml:id="echoid-s8763" xml:space="preserve">diſtantia eius à meridie hor. </s>
            <s xml:id="echoid-s8764" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8765" xml:space="preserve">hoc eſt, grad.
              <lb/>
            </s>
            <s xml:id="echoid-s8766" xml:space="preserve">
              <note position="left" xlink:label="note-0156-05" xlink:href="note-0156-05a" xml:space="preserve">Exemplum ſe-
                <lb/>
              cundum.</note>
            30. </s>
            <s xml:id="echoid-s8767" xml:space="preserve">ita vt angulus BNQ, totidem gradus cõtineat, ac proinde reliquus ex duobus rectis DNQ,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8768" xml:space="preserve">150. </s>
            <s xml:id="echoid-s8769" xml:space="preserve">Fiat igitur, vt 100000. </s>
            <s xml:id="echoid-s8770" xml:space="preserve">ſinus totus ad 50000. </s>
            <s xml:id="echoid-s8771" xml:space="preserve">ſinum anguli DNQ, (eſt enim idem ſi-
              <lb/>
            nus arcus grad. </s>
            <s xml:id="echoid-s8772" xml:space="preserve">150. </s>
            <s xml:id="echoid-s8773" xml:space="preserve">& </s>
            <s xml:id="echoid-s8774" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s8775" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8776" xml:space="preserve">qui cum illo ſemicirculum conficit, vt in tractatu ſinuum
              <lb/>
              <note position="left" xlink:label="note-0156-06" xlink:href="note-0156-06a" xml:space="preserve">30</note>
            docuimus) ita 74314. </s>
            <s xml:id="echoid-s8777" xml:space="preserve">ſinus complementi altitudinis poliad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s8778" xml:space="preserve">ferme ſinus hic,
              <lb/>
            37157. </s>
            <s xml:id="echoid-s8779" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s8780" xml:space="preserve">21. </s>
            <s xml:id="echoid-s8781" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8782" xml:space="preserve">49. </s>
            <s xml:id="echoid-s8783" xml:space="preserve">ex quadrante detractus relinquet pro Inuento primo arcum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8784" xml:space="preserve">68. </s>
            <s xml:id="echoid-s8785" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8786" xml:space="preserve">11.</s>
            <s xml:id="echoid-s8787" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8788" xml:space="preserve">DEINDE fiat, vt 92837. </s>
            <s xml:id="echoid-s8789" xml:space="preserve">ſinus arcus Primi Inuenti, ad 66913. </s>
            <s xml:id="echoid-s8790" xml:space="preserve">ſinum altitudinis poli, ita
              <lb/>
            100000. </s>
            <s xml:id="echoid-s8791" xml:space="preserve">ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s8792" xml:space="preserve">hic quaſi ſinus 72075. </s>
            <s xml:id="echoid-s8793" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s8794" xml:space="preserve">46. </s>
            <s xml:id="echoid-s8795" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8796" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8797" xml:space="preserve">ex ſemicirculo
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8798" xml:space="preserve">180. </s>
            <s xml:id="echoid-s8799" xml:space="preserve">deductus (quoniam diſtantia Solis à meridie ad hor. </s>
            <s xml:id="echoid-s8800" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8801" xml:space="preserve">non peruenit) dabit arcum NQ,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8802" xml:space="preserve">133. </s>
            <s xml:id="echoid-s8803" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8804" xml:space="preserve">53. </s>
            <s xml:id="echoid-s8805" xml:space="preserve">ex quo, quia Sol auſtralis ponitur, ſi detrahatur arcus NL, compoſitus ex ſinu
              <lb/>
            toto, & </s>
            <s xml:id="echoid-s8806" xml:space="preserve">ſinu declinationis, nempe grad. </s>
            <s xml:id="echoid-s8807" xml:space="preserve">113. </s>
            <s xml:id="echoid-s8808" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8809" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8810" xml:space="preserve">relinquetur pro Inuento ſecundo arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s8811" xml:space="preserve">20. </s>
            <s xml:id="echoid-s8812" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8813" xml:space="preserve">23.</s>
            <s xml:id="echoid-s8814" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8815" xml:space="preserve">POSTREMO fiat, vt 100000. </s>
            <s xml:id="echoid-s8816" xml:space="preserve">ſinus totus ad 34829. </s>
            <s xml:id="echoid-s8817" xml:space="preserve">ſinum arcus Inuenti ſecundi, ita
              <lb/>
              <note position="left" xlink:label="note-0156-07" xlink:href="note-0156-07a" xml:space="preserve">40</note>
            92837. </s>
            <s xml:id="echoid-s8818" xml:space="preserve">ſinus Inuenti primi ad aliud, reperieturq́; </s>
            <s xml:id="echoid-s8819" xml:space="preserve">hic fere ſinus 32334. </s>
            <s xml:id="echoid-s8820" xml:space="preserve">altitudinis Solis, atq; </s>
            <s xml:id="echoid-s8821" xml:space="preserve">adeo
              <lb/>
            altitudo ipſa Solis complectetur grad. </s>
            <s xml:id="echoid-s8822" xml:space="preserve">18. </s>
            <s xml:id="echoid-s8823" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8824" xml:space="preserve">52.</s>
            <s xml:id="echoid-s8825" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8826" xml:space="preserve">PORRO quando Sol exiſtit in Verticali circulo, vel abeſt à meridie horis ſex, aut denique in
              <lb/>
            Aequatore conſtitutus eſt, expediemus rem, vt paulo ante tradidimus.</s>
            <s xml:id="echoid-s8827" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8828" xml:space="preserve">AD extremum abſoluemus idem hoc proble-
              <lb/>
              <note position="left" xlink:label="note-0156-08" xlink:href="note-0156-08a" xml:space="preserve">Altitudo Solis
                <lb/>
              in ęquinoctiis,
                <lb/>
              quomodo in
                <lb/>
              ſphęra recta ex
                <lb/>
              data hora depre
                <lb/>
              hendatur.</note>
              <figure xlink:label="fig-0156-01" xlink:href="fig-0156-01a" number="113">
                <image file="0156-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0156-01"/>
              </figure>
            ma per triangula ſphærica in ſphæra recta, hac ra-
              <lb/>
            tione. </s>
            <s xml:id="echoid-s8829" xml:space="preserve">Sole Aequatorem percurrente, erit comple
              <lb/>
            mentum diſtantiæ ipſius à meridie, altitudo Solis
              <lb/>
            ſupra Horizontem: </s>
            <s xml:id="echoid-s8830" xml:space="preserve">quia in ſphæra recta Aequator
              <lb/>
            idem eſt, quod Verticalis circulus per centrum Solis
              <lb/>
              <note position="left" xlink:label="note-0156-09" xlink:href="note-0156-09a" xml:space="preserve">50</note>
            tranſiens. </s>
            <s xml:id="echoid-s8831" xml:space="preserve">Vt in ſubiecta figura, ſi poli mundi intelli
              <lb/>
            gantur B, D, erit Verticalis AEC, & </s>
            <s xml:id="echoid-s8832" xml:space="preserve">idẽ ipſe Aequa
              <lb/>
            tor. </s>
            <s xml:id="echoid-s8833" xml:space="preserve">Poſito ergo Sole in I, erit arcus AI, complemen
              <lb/>
            ti diſtantiæ Solis à meridie, arcus etiam altitudinis
              <lb/>
            Solis, vt perſpicuum eſt.</s>
            <s xml:id="echoid-s8834" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8835" xml:space="preserve">SOLE autem occupante quemcunque paral-
              <lb/>
              <note position="left" xlink:label="note-0156-10" xlink:href="note-0156-10a" xml:space="preserve">Altitudo Solis
                <lb/>
              in quocunque
                <lb/>
              parallelo exiſtẽ-
                <lb/>
              tis, quo pacto
                <lb/>
              per triangula
                <lb/>
              ſphęrica in ſphę
                <lb/>
              ra recta ex data
                <lb/>
              hora colligatur.</note>
            lelum FG, ſiue borealem, ſiue auſtralem, ita rem
              <lb/>
            exequemur. </s>
            <s xml:id="echoid-s8836" xml:space="preserve">Ponatur Sol in k, ducaturq́ Vertica-
              <lb/>
            lis EL, ex E, vertice per centrum Solis k: </s>
            <s xml:id="echoid-s8837" xml:space="preserve">Item
              <lb/>
            circulus declinationis D
              <emph style="sc">K</emph>
            B, per polos mundi, & </s>
            <s xml:id="echoid-s8838" xml:space="preserve">
              <lb/>
            per centrum Solis ductus ſit, ſecans </s>
          </p>
        </div>
      </text>
    </echo>
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