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-div1608" type="section" level="1" n="408">
          <p>
            <s xml:id="echoid-s31073" xml:space="preserve">
              <pb o="486" file="0502" n="502" rhead="GNOMONICES"/>
            includitur, complementumq́ue eſt declinationis L M.) </s>
            <s xml:id="echoid-s31074" xml:space="preserve">ad ſinum anguli N E L; </s>
            <s xml:id="echoid-s31075" xml:space="preserve">Si fiat vt ſinus
              <lb/>
            complementi altitudinis Solis ad ſinum diſtantiæ Solis à Meridiano propoſiti circuli, i
              <unsure/>
            ta ſinus
              <lb/>
            complementi declinationis ad aliud, inuenietur ſinus anguli N E L, ſiue arcns D O, cuius comple-
              <lb/>
            mentũ eſt A O, arcus quæſitus, quem ita ex arcu D O, inueſtigabimus. </s>
            <s xml:id="echoid-s31076" xml:space="preserve">Si Sol vltra Verticalẽ pro-
              <lb/>
            prium verſus polum occultũ extiterit, vt in primo, & </s>
            <s xml:id="echoid-s31077" xml:space="preserve">quarto circulo, (quod qua ratione cogno-
              <lb/>
            ſcatur, paulo poſt in ſcholio explicabitur) auferemus arcũ B O, ſinui inuento anguli B E O, debitũ
              <lb/>
            (Habet enim angulus hic, vel arcus B O, eundem ſinum, quem angulus N E L, vel arcus D O,
              <lb/>
              <figure xlink:label="fig-0502-01" xlink:href="fig-0502-01a" number="314">
                <image file="0502-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0502-01"/>
              </figure>
              <note position="left" xlink:label="note-0502-01" xlink:href="note-0502-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0502-02" xlink:href="note-0502-02a" xml:space="preserve">20</note>
            cùm duo illi anguli ſint duobus rectis æquales, & </s>
            <s xml:id="echoid-s31078" xml:space="preserve">dicti duo arcus ſemicirculũ conficiant) ex qua-
              <lb/>
            drãte A B, remanebitq́ue arcus quæſitus A O, verſus polum occultum notus. </s>
            <s xml:id="echoid-s31079" xml:space="preserve">Si vero Sol citra Ver-
              <lb/>
            ticalem proprie dictum verſus polum conſpicuum fuerit inuentus, vt in ſecundo, tertio, & </s>
            <s xml:id="echoid-s31080" xml:space="preserve">ſexto
              <lb/>
            circulo, detrahemus arcũ D O, ſinui inuento anguli N E L, reſpondentem ex quadrante A D, re-
              <lb/>
            linqueturq́ue arcus quæſitus A O, verſus polum conſpicuum.</s>
            <s xml:id="echoid-s31081" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s31082" xml:space="preserve">FACILIVS autem redditur problema, Sole exiſtente in Æquatore, propterea quod tunc
              <lb/>
              <note position="left" xlink:label="note-0502-03" xlink:href="note-0502-03a" xml:space="preserve">Idem arcus faci
                <lb/>
              l@us inueſt@ga@
                <lb/>
              tur @ẽpore æqui
                <lb/>
              noctiorum.</note>
            multiplicatio fit per ſin ũ totum. </s>
            <s xml:id="echoid-s31083" xml:space="preserve">Si enim in primo circulo concipiatur parallelus G H I, eſſe Æ-
              <lb/>
            quator, ita vt Verticalis proprie dictus tranſeat per G, & </s>
            <s xml:id="echoid-s31084" xml:space="preserve">I, & </s>
            <s xml:id="echoid-s31085" xml:space="preserve">arcus, qui quęritur, ſit G O, erit
              <lb/>
            arcus N L, quadrans, cui reſpondet ſinus totus, non autem ſinus complementi declinationis, vt
              <lb/>
              <note position="left" xlink:label="note-0502-04" xlink:href="note-0502-04a" xml:space="preserve">30</note>
            prius. </s>
            <s xml:id="echoid-s31086" xml:space="preserve">Vnde ſi fiat, vt ſinus arcus E L, complementi altitudinis Solis ad ſinum anguli E N L, di-
              <lb/>
            ſtantiæ Solis à Meridiano propoſiti circuli, ita ſinus totus quadrantis N L, ad aliud, inuenietur ſi-
              <lb/>
            nus anguli N E L, ſeu B E O, cuius arcus B O, ex quadrante B G, ſublatus relinquet arcum quæ-
              <lb/>
            ſitum G O, &</s>
            <s xml:id="echoid-s31087" xml:space="preserve">c.</s>
            <s xml:id="echoid-s31088" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quando dictus
            <lb/>
          ar
            <unsure/>
          cus aut nihil
            <lb/>
          eſt, aut
            <unsure/>
          quadrã
            <lb/>
          ti æqualis.</note>
          <p>
            <s xml:id="echoid-s31089" xml:space="preserve">HIC arcus nihil eſt, Sole exiſtente in Verticali proprie dicto circuli propoſiti: </s>
            <s xml:id="echoid-s31090" xml:space="preserve">quadranti autẽ
              <lb/>
            æqualis eſt, eodem conſtituto in Meridiano eiuſdem circuli propoſiti, vt perſpicuum eſt.</s>
            <s xml:id="echoid-s31091" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s31092" xml:space="preserve">EVNDEM arcũ in Meridiano Horizõtis hac ratione inueniemus. </s>
            <s xml:id="echoid-s31093" xml:space="preserve">Repetatur figura propoſ. </s>
            <s xml:id="echoid-s31094" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s31095" xml:space="preserve">huius libri, in qua dictus arcus eſt
              <lb/>
              <note position="left" xlink:label="note-0502-06" xlink:href="note-0502-06a" xml:space="preserve">Quo pacto idẽ
                <lb/>
              arcus in Meri-
                <lb/>
              diano Horizon
                <lb/>
              ti
                <unsure/>
              s
                <unsure/>
              inueniatur.</note>
              <figure xlink:label="fig-0502-02" xlink:href="fig-0502-02a" number="315">
                <image file="0502-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0502-02"/>
              </figure>
            E I; </s>
            <s xml:id="echoid-s31096" xml:space="preserve">cum Æquator B E D, ſit Vertica
              <lb/>
            lis proprie dictus Meridiani Hori-
              <lb/>
              <note position="left" xlink:label="note-0502-07" xlink:href="note-0502-07a" xml:space="preserve">40</note>
            zontis, & </s>
            <s xml:id="echoid-s31097" xml:space="preserve">B H I, Verticalis per B, po
              <lb/>
            lum Meridiani, & </s>
            <s xml:id="echoid-s31098" xml:space="preserve">H, locum Solis
              <lb/>
            ductus. </s>
            <s xml:id="echoid-s31099" xml:space="preserve">Quia vero in triangulo ſphę
              <lb/>
            rico B H K, angulus K, rectus eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s31100" xml:space="preserve">erit per propoſ. </s>
            <s xml:id="echoid-s31101" xml:space="preserve">16. </s>
            <s xml:id="echoid-s31102" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s31103" xml:space="preserve">4. </s>
            <s xml:id="echoid-s31104" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s31105" xml:space="preserve">Re-
              <lb/>
            giom. </s>
            <s xml:id="echoid-s31106" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s31107" xml:space="preserve">
              <lb/>
            13. </s>
            <s xml:id="echoid-s31108" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s31109" xml:space="preserve">1. </s>
            <s xml:id="echoid-s31110" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s31111" xml:space="preserve">41. </s>
            <s xml:id="echoid-s31112" xml:space="preserve">
              <lb/>
            noſtrorum triangulorum ſphærico-
              <lb/>
            rum, vt ſinus arcus B H, complemen
              <lb/>
            ti altitudinis Solis ſupra Meridianũ
              <lb/>
              <note position="left" xlink:label="note-0502-08" xlink:href="note-0502-08a" xml:space="preserve">50</note>
            Horizontis, ad ſinum totum anguli
              <lb/>
            recti K, ita ſinus arcus H K, declina-
              <lb/>
            tionis ad ſinum anguli H B K, ſeu
              <lb/>
            arcus E I, quæſiti. </s>
            <s xml:id="echoid-s31113" xml:space="preserve">Si igitur fiat, vt ſi-
              <lb/>
            nus complementi altitudininis So-
              <lb/>
            lis ſupra Meridianum ad ſinum to-
              <lb/>
            tum, ita ſinus declinationis ad aliud,
              <lb/>
            reperietur ſinus arcus Meridiani in-
              <lb/>
            ter duos Verticales incluſus, qui
              <lb/>
            quæritur.</s>
            <s xml:id="echoid-s31114" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s31115" xml:space="preserve">POSTREMO arcum quoque eundem in Horizonte recto, circulove horæ 6. </s>
            <s xml:id="echoid-s31116" xml:space="preserve">à </s>
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