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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            <s xml:id="echoid-s13736" xml:space="preserve">
              <pb o="202" file="0222" n="222" rhead="GNOMONICES"/>
            bri manifeſtum eſt. </s>
            <s xml:id="echoid-s13737" xml:space="preserve">Eadem enim demõſtratio huc afferri poteſt; </s>
            <s xml:id="echoid-s13738" xml:space="preserve">quia eodem modo oſtendemus,
              <lb/>
            circulum per polos mundi, & </s>
            <s xml:id="echoid-s13739" xml:space="preserve">horam 12. </s>
            <s xml:id="echoid-s13740" xml:space="preserve">inæqualem in tropico ♋. </s>
            <s xml:id="echoid-s13741" xml:space="preserve">ductum tranſire per punctum
              <lb/>
            b, cùm idem punctum in tropico ♋, ſit horæ 12. </s>
            <s xml:id="echoid-s13742" xml:space="preserve">inæqualis, & </s>
            <s xml:id="echoid-s13743" xml:space="preserve">horæ 24. </s>
            <s xml:id="echoid-s13744" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s13745" xml:space="preserve">Hinc rurſus oſten
              <lb/>
            demus (cum arcus inter b, & </s>
            <s xml:id="echoid-s13746" xml:space="preserve">proximum punctum diuiſionis verſus N, ſimilis ſit arcui tropici ♋,
              <lb/>
              <figure xlink:label="fig-0222-01" xlink:href="fig-0222-01a" number="154">
                <image file="0222-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0222-01"/>
              </figure>
              <note position="left" xlink:label="note-0222-01" xlink:href="note-0222-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0222-02" xlink:href="note-0222-02a" xml:space="preserve">20</note>
            inter duos maximos circulos per polos mundi ductos interiecto, quorum vnus per horam 12. </s>
            <s xml:id="echoid-s13747" xml:space="preserve">in-
              <lb/>
              <note position="left" xlink:label="note-0222-03" xlink:href="note-0222-03a" xml:space="preserve">30</note>
            æqualem, alter vero per horam 11. </s>
            <s xml:id="echoid-s13748" xml:space="preserve">inæqualem in tropico ♋, ducitur; </s>
            <s xml:id="echoid-s13749" xml:space="preserve">quòd vterque arcus duode-
              <lb/>
            cima pars ſit arcus ſemidiurni tropici ♋, in ſuo circulo) circulum maximum per polos mundi, & </s>
            <s xml:id="echoid-s13750" xml:space="preserve">
              <lb/>
            horam 11. </s>
            <s xml:id="echoid-s13751" xml:space="preserve">inæqualem in tropico ♋, ductum tranſire per proximum punctum diuiſionis à b, ver-
              <lb/>
            ſus N, & </s>
            <s xml:id="echoid-s13752" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s13753" xml:space="preserve">Si igitur per puncta diuiſionum, & </s>
            <s xml:id="echoid-s13754" xml:space="preserve">centrum E, rectæ ducantur ſecantes
              <lb/>
            æquinoctialem lineam in punctis, per quæ rurſus ex H, centro horologii emittantur rectæ, repe-
              <lb/>
            rientur in tropicis ♋, & </s>
            <s xml:id="echoid-s13755" xml:space="preserve">♑, puncta horarum inæqualium, non ſecus ac propoſ. </s>
            <s xml:id="echoid-s13756" xml:space="preserve">10. </s>
            <s xml:id="echoid-s13757" xml:space="preserve">& </s>
            <s xml:id="echoid-s13758" xml:space="preserve">11. </s>
            <s xml:id="echoid-s13759" xml:space="preserve">huius lib.
              <lb/>
            </s>
            <s xml:id="echoid-s13760" xml:space="preserve">in eiſdem puncta inuenimus horarum ab occaſu, & </s>
            <s xml:id="echoid-s13761" xml:space="preserve">ortu. </s>
            <s xml:id="echoid-s13762" xml:space="preserve">Vnde ſi reſpondentia puncta lineis re-
              <lb/>
            ctis iungantur, deſcriptum erit horologium Antiquum. </s>
            <s xml:id="echoid-s13763" xml:space="preserve">Tranſibunt autem omnes lineæ horarum
              <lb/>
            inæqualium per horas à meridie, vel media nocte in linea æquinoctiali, vt conſtat ex tabula 13. </s>
            <s xml:id="echoid-s13764" xml:space="preserve">
              <lb/>
            ſcholii propoſ. </s>
            <s xml:id="echoid-s13765" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13766" xml:space="preserve">præcedentis libri. </s>
            <s xml:id="echoid-s13767" xml:space="preserve">Sed accipe huiuſce deſcriptionis vnum, aut alterum exem-
              <lb/>
              <note position="left" xlink:label="note-0222-04" xlink:href="note-0222-04a" xml:space="preserve">40</note>
            plum. </s>
            <s xml:id="echoid-s13768" xml:space="preserve">Ex f, puncto horæ 3. </s>
            <s xml:id="echoid-s13769" xml:space="preserve">inæqualis in tropico ♑, per E, ducta recta ſecat æquinoctialem lineã
              <lb/>
            in g; </s>
            <s xml:id="echoid-s13770" xml:space="preserve">recta autem ex H, per g, emiſſa ſecat tropicum ♑, in h, puncto horæ tertiæ inæqualis. </s>
            <s xml:id="echoid-s13771" xml:space="preserve">Rurſus
              <lb/>
            ex puncto m, quod opponitur horæ vndecimæ inæquali in tropico ♋, recta emiſſa per E, ſecat li-
              <lb/>
            neam æquinoctialem in n, at recta H n, ſecat tropicum ♋, in puncto p, quod ſemicirculo maximi
              <lb/>
            circuli per punctum m, ducto debetur: </s>
            <s xml:id="echoid-s13772" xml:space="preserve">producta autem n H, vltra centrum ſecat eundem tropi-
              <lb/>
            cum ♋, in q, puncto horæ vndecimæ inæqualis, & </s>
            <s xml:id="echoid-s13773" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13774" xml:space="preserve">Quæ omnia ex demonſtratis propoſ. </s>
            <s xml:id="echoid-s13775" xml:space="preserve">10. </s>
            <s xml:id="echoid-s13776" xml:space="preserve">huius
              <lb/>
            libri perſpicua ſunt.</s>
            <s xml:id="echoid-s13777" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13778" xml:space="preserve">HIC quoque, vt in propoſ. </s>
            <s xml:id="echoid-s13779" xml:space="preserve">10. </s>
            <s xml:id="echoid-s13780" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s13781" xml:space="preserve">reperiemus in circulo M a N b, arcum diurnum no-
              <lb/>
            cturnumq́; </s>
            <s xml:id="echoid-s13782" xml:space="preserve">tropici ♋, vel ♑, aliter, quàm per ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s13783" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13784" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s13785" xml:space="preserve">ſcripſi-
              <lb/>
            mus; </s>
            <s xml:id="echoid-s13786" xml:space="preserve">ſi nimirum à puncto N, vtrinque ſupputemus arcum ſemidiurnum tropici ♋, vſque ad a,
              <lb/>
              <note position="left" xlink:label="note-0222-05" xlink:href="note-0222-05a" xml:space="preserve">50</note>
            & </s>
            <s xml:id="echoid-s13787" xml:space="preserve">b, vel tropici ♑, vſque ad d, & </s>
            <s xml:id="echoid-s13788" xml:space="preserve">e.</s>
            <s xml:id="echoid-s13789" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13790" xml:space="preserve">IMMO etiamſi dictum circulum non diuidamus in dictos arcus, reperiemus in eo punctum
              <lb/>
            cuiuſuis horæ inæqualis, Sole in quocunque parallelo exiſtente, hac ratione. </s>
            <s xml:id="echoid-s13791" xml:space="preserve">Diuidatur ar-
              <lb/>
            cus diurnus dati paralleli per 12. </s>
            <s xml:id="echoid-s13792" xml:space="preserve">vt in numero quotiente habeamus quantitatem vnius ho-
              <lb/>
            ræ inæqualis in dato parallelo; </s>
            <s xml:id="echoid-s13793" xml:space="preserve">atque adeo in eodem numero duplicato magnitudinem dua-
              <lb/>
            rum horarum, & </s>
            <s xml:id="echoid-s13794" xml:space="preserve">in triplicato trium, &</s>
            <s xml:id="echoid-s13795" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13796" xml:space="preserve">Deinde conſideretur, quantum diſter hora inæqua-
              <lb/>
            lis propoſita à Meridiano circulo ante meridiem, ſiue poſt. </s>
            <s xml:id="echoid-s13797" xml:space="preserve">Si enim hæc diſtantia in circulo
              <lb/>
            M a N b, numeretur à puncto N, verſus a, ſi hora data fuerit antemeridiana, aut verſus b,
              <lb/>
            ſi pomeridiana, offendemus punctum datæ horæ inæqualis. </s>
            <s xml:id="echoid-s13798" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s13799" xml:space="preserve">Arcus diurnus tro-
              <lb/>
            pici ♋, continet horas 15. </s>
            <s xml:id="echoid-s13800" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s13801" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13802" xml:space="preserve">hoc eſt, Gradus 226. </s>
            <s xml:id="echoid-s13803" xml:space="preserve">quibus gradibus diuiſis per 12. </s>
            <s xml:id="echoid-s13804" xml:space="preserve">pro-
              <lb/>
            dibunt grad. </s>
            <s xml:id="echoid-s13805" xml:space="preserve">18. </s>
            <s xml:id="echoid-s13806" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s13807" xml:space="preserve">50. </s>
            <s xml:id="echoid-s13808" xml:space="preserve">pro magnitudine vnius horæ inæqualis in tropico ♋. </s>
            <s xml:id="echoid-s13809" xml:space="preserve">Vnde </s>
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