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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          <p>
            <s xml:id="echoid-s17434" xml:space="preserve">
              <pb o="257" file="0273" n="273" rhead="LIBER SECVNDVS."/>
            circulo ſextæ horæ à meridie, vel media nocte, qui per polos mundi
              <lb/>
            ducitur, rectusq́; </s>
            <s xml:id="echoid-s17435" xml:space="preserve">eſt ad Meridianum, deſcribere.</s>
            <s xml:id="echoid-s17436" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17437" xml:space="preserve">NON differt hoc horologium à Meridiano horologio, excepto numero horarum, & </s>
            <s xml:id="echoid-s17438" xml:space="preserve">ordine.
              <lb/>
            </s>
            <s xml:id="echoid-s17439" xml:space="preserve">
              <note position="right" xlink:label="note-0273-01" xlink:href="note-0273-01a" xml:space="preserve">Quomodo dif
                <unsure/>
              -
                <lb/>
              ferat polare ho
                <lb/>
              rologium Aſtro
                <lb/>
              nomicum a Me
                <lb/>
              ridiano.</note>
            In hoc enim ex vtraque parte rectæ D E, ſumendæ ſunt omnes horę, quę in planum horologii ca-
              <lb/>
            dere poſſunt, & </s>
            <s xml:id="echoid-s17440" xml:space="preserve">recta D E, non monſtrat amplius horam 6. </s>
            <s xml:id="echoid-s17441" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s17442" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s17443" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s17444" xml:space="preserve">vt ibi, ſed 12. </s>
            <s xml:id="echoid-s17445" xml:space="preserve">& </s>
            <s xml:id="echoid-s17446" xml:space="preserve">
              <lb/>
            linee, quę ab ea
              <lb/>
              <figure xlink:label="fig-0273-01" xlink:href="fig-0273-01a" number="190">
                <image file="0273-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0273-01"/>
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            recedũt verſus or
              <lb/>
            tum, horas indi-
              <lb/>
              <note position="left" xlink:label="note-0273-02" xlink:href="note-0273-02a" xml:space="preserve">10</note>
            cant à mer. </s>
            <s xml:id="echoid-s17447" xml:space="preserve">quæ
              <lb/>
            verò verſus occa-
              <lb/>
            ſum ſunt poſitę,
              <lb/>
            horas à med. </s>
            <s xml:id="echoid-s17448" xml:space="preserve">noc.
              <lb/>
            </s>
            <s xml:id="echoid-s17449" xml:space="preserve">monſtrant, vt in
              <lb/>
            appoſito horolo-
              <lb/>
              <note position="right" xlink:label="note-0273-03" xlink:href="note-0273-03a" xml:space="preserve">Quomodo pol
                <unsure/>
              a
                <lb/>
              re horologium
                <lb/>
              in proprio ſitu
                <lb/>
              collocandũ ſit.</note>
            gio apparet. </s>
            <s xml:id="echoid-s17450" xml:space="preserve">Nam
              <lb/>
            ſi horologiũ hoc
              <lb/>
            ita collocetur, vt
              <lb/>
            recta C S, Hori-
              <lb/>
              <note position="left" xlink:label="note-0273-04" xlink:href="note-0273-04a" xml:space="preserve">20</note>
            zonti ęquidiſtet,
              <lb/>
            rectaq́ue D E, in
              <lb/>
            plano Meridiani
              <lb/>
            circuli ſita ſit, pun
              <lb/>
            ctumq́ue E ad au-
              <lb/>
            ſtrum, & </s>
            <s xml:id="echoid-s17451" xml:space="preserve">D, ad boream vergat, punctum denique D, ex parte Septentrionis eleuetur ſecundum al-
              <lb/>
            titudinem poli, hoc eſt, recta D E, cum meridiana linea in plano, quod parallelum ſit Horizonti,
              <lb/>
            conſtituat ad partes puncti D, angulum altitudinis poli, indicabit ſtylus A E, in A, ad angulos re-
              <lb/>
            ctos inſiſtens plano horologii, ita vt ſit communis ſectio Æ quatoris, ac Meridiani, vel certe recta
              <lb/>
            O P, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s17452" xml:space="preserve">25. </s>
            <s xml:id="echoid-s17453" xml:space="preserve">huius libri docuimus, horas à mer. </s>
            <s xml:id="echoid-s17454" xml:space="preserve">& </s>
            <s xml:id="echoid-s17455" xml:space="preserve">med. </s>
            <s xml:id="echoid-s17456" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s17457" xml:space="preserve">ita vt lineæ, quę orien
              <lb/>
              <note position="left" xlink:label="note-0273-05" xlink:href="note-0273-05a" xml:space="preserve">30</note>
            taliores ſunt, quàm D E, cuiuſmodi ſunt lineę verſus punctum S, dent horas à mer. </s>
            <s xml:id="echoid-s17458" xml:space="preserve">quę verò ſunt
              <lb/>
            occidentaliores, quales ſunt lineę verſus punctum C, pertineant ad horas à med. </s>
            <s xml:id="echoid-s17459" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s17460" xml:space="preserve">vt in fi-
              <lb/>
            gura apparet.</s>
            <s xml:id="echoid-s17461" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17462" xml:space="preserve">ITAQVE ſi deſcribendum ſit horologium polare Aſtronomicum, ducendę erunt in plano
              <lb/>
              <note position="right" xlink:label="note-0273-06" xlink:href="note-0273-06a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii polaris
                <lb/>
              Aſtronomici
                <lb/>
              Superioris.</note>
            aliquo duæ rectę lineę C S, D E, ſeſe ad angulos rectos ſecantes in A, & </s>
            <s xml:id="echoid-s17463" xml:space="preserve">in recta D E, ſumenda re-
              <lb/>
            cta A E, ſtylo propoſito æqualis. </s>
            <s xml:id="echoid-s17464" xml:space="preserve">Deinde ex E, deſcripto circulo cuiuſcunque magnitudinis, eoq́
              <lb/>
            diuiſo in partes 24. </s>
            <s xml:id="echoid-s17465" xml:space="preserve">æquales, reliqua perficienda, vt in Meridiano horologio, &</s>
            <s xml:id="echoid-s17466" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17467" xml:space="preserve">Quòd autem
              <lb/>
            horologium Meridianum ſit polare, ſi fiat illa permutatio numerorum horarum, vt diximus, fa-
              <lb/>
            cile hoc modo intelligi poterit. </s>
            <s xml:id="echoid-s17468" xml:space="preserve">Quoniam tam circulus horæ 6. </s>
            <s xml:id="echoid-s17469" xml:space="preserve">à meridie, vel media nocte, cui
              <lb/>
            planum horologii polaris æquidiſtat, quàm Meridianus, cui æquidiſtat horologium Meridianũ,
              <lb/>
              <note position="left" xlink:label="note-0273-07" xlink:href="note-0273-07a" xml:space="preserve">40</note>
            per polos mundi ducitur, fit, vt circuli horarum à meridie, vel media nocte eodem modo vtriuſ-
              <lb/>
            que horologii planum ſecent, cum eodem modo ſe ſe habeant reſpectu vtriuſque, mutato ſolum
              <lb/>
            ordine, & </s>
            <s xml:id="echoid-s17470" xml:space="preserve">numero horarum. </s>
            <s xml:id="echoid-s17471" xml:space="preserve">Nam vt ſe habet circulus horæ 6. </s>
            <s xml:id="echoid-s17472" xml:space="preserve">reſpectu Meridiani, ſecans nimi-
              <lb/>
            rum ipſum ad rectos angalos, ita quoque viciſſim ſe habet Meridianus reſpectu circuli horæ 6.
              <lb/>
            </s>
            <s xml:id="echoid-s17473" xml:space="preserve">
              <note position="right" xlink:label="note-0273-08" xlink:href="note-0273-08a" xml:space="preserve">Demonſtratio
                <lb/>
              conſtru ctionis
                <lb/>
              horologii pola-
                <lb/>
              ris Aſtronomi-
                <lb/>
              ci.</note>
            ac proinde linea, quæ in Meridiano horologio dat horam 6. </s>
            <s xml:id="echoid-s17474" xml:space="preserve">dabit horam 12. </s>
            <s xml:id="echoid-s17475" xml:space="preserve">in horologio pola-
              <lb/>
            ri, &</s>
            <s xml:id="echoid-s17476" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17477" xml:space="preserve">Verum geometricè quoque conſtructionem horologii polaris, quam proxime expoſuimus,
              <lb/>
            ita demonſtrabimus. </s>
            <s xml:id="echoid-s17478" xml:space="preserve">Quia plana Meridiani, & </s>
            <s xml:id="echoid-s17479" xml:space="preserve">circuli horæ 6. </s>
            <s xml:id="echoid-s17480" xml:space="preserve">ad planum Æ quatoris recta ſunt,
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s17481" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17482" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s17483" xml:space="preserve">1. </s>
            <s xml:id="echoid-s17484" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s17485" xml:space="preserve">cum per eius polos tranſeant; </s>
            <s xml:id="echoid-s17486" xml:space="preserve">erit communis eorum ſectio ad idem
              <lb/>
              <note position="right" xlink:label="note-0273-09" xlink:href="note-0273-09a" xml:space="preserve">19. vndec.</note>
            planum Æ quatoris recta. </s>
            <s xml:id="echoid-s17487" xml:space="preserve">Cum ergo huic ſectioni parallela ſit ſectio, quam Meridianus in plano
              <lb/>
              <note position="right" xlink:label="note-0273-10" xlink:href="note-0273-10a" xml:space="preserve">16. vndec.</note>
            horologii polaris efficit, nempe linea meridiana; </s>
            <s xml:id="echoid-s17488" xml:space="preserve">erit quoque linea meridiana horologii ad planũ
              <lb/>
              <note position="left" xlink:label="note-0273-11" xlink:href="note-0273-11a" xml:space="preserve">50</note>
              <note position="right" xlink:label="note-0273-12" xlink:href="note-0273-12a" xml:space="preserve">8. vndec.</note>
            Æquatoris recta; </s>
            <s xml:id="echoid-s17489" xml:space="preserve">atque adeo per defin. </s>
            <s xml:id="echoid-s17490" xml:space="preserve">3. </s>
            <s xml:id="echoid-s17491" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s17492" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17493" xml:space="preserve">Euclid & </s>
            <s xml:id="echoid-s17494" xml:space="preserve">ad communem ſectionem plani horo-
              <lb/>
            logii, & </s>
            <s xml:id="echoid-s17495" xml:space="preserve">Æ quatoris, nempe ad lineam æquinoctialem horologii in plano Æ quatoris exiſtentem,
              <lb/>
            perpendicularis erit. </s>
            <s xml:id="echoid-s17496" xml:space="preserve">Quocirca ſi recta C S, ponatur linea æquinoctialis, erit recta D E, linea meri
              <lb/>
            diana in horologio polari, quandoquidem recta D E, ad C S, per conſtructionem, perpendicula-
              <lb/>
            ris eſt. </s>
            <s xml:id="echoid-s17497" xml:space="preserve">Igitur ſi circa rectam C S, quieſcentem intelligatur moueri planum circuli ex E, deſcripti,
              <lb/>
            donec cum plano Æ quatoris, & </s>
            <s xml:id="echoid-s17498" xml:space="preserve">E, vertex ſtyli aſſumpti A E, cum centro mundi coniungatur, erit
              <lb/>
            circulus ipſe Æ quatori concentricus, & </s>
            <s xml:id="echoid-s17499" xml:space="preserve">rectæ per E, & </s>
            <s xml:id="echoid-s17500" xml:space="preserve">puncta diuiſionum circuli emiſſæ, commu-
              <lb/>
            nes ſectiones circulorum horariorum à meridie vel media nocte, & </s>
            <s xml:id="echoid-s17501" xml:space="preserve">Æ quatoris; </s>
            <s xml:id="echoid-s17502" xml:space="preserve">cum Æ quator & </s>
            <s xml:id="echoid-s17503" xml:space="preserve">
              <lb/>
            circulus ex E, deſcriptus circa idem centrum E, deſcripti in arcus ſimiles à dictis rectis ſecentur,
              <lb/>
            vt ad finem cap. </s>
            <s xml:id="echoid-s17504" xml:space="preserve">1. </s>
            <s xml:id="echoid-s17505" xml:space="preserve">in ſphæram dem onſtrauimus; </s>
            <s xml:id="echoid-s17506" xml:space="preserve">nempe diameter circuli ex E, deſcripti ad C S,
              <lb/>
            perpendicularis, communis ſectio Æ quatoris, & </s>
            <s xml:id="echoid-s17507" xml:space="preserve">circuli horæ 12. </s>
            <s xml:id="echoid-s17508" xml:space="preserve">ſeu Meridiani, &</s>
            <s xml:id="echoid-s17509" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17510" xml:space="preserve">vt </s>
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