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-s12799" xml:space="preserve">
              <pb o="194" file="0214" n="214" rhead="GNOMONICES"/>
            cuntur, antequam æquinoctiali lineæ occurrant, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s12800" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12801" xml:space="preserve">huius libri diximus: </s>
            <s xml:id="echoid-s12802" xml:space="preserve">cu-
              <lb/>
            iuſmodi ſunt ſolum illæ horæ, quæ in ſemicirculo t N u, reperiuntur, vt patet. </s>
            <s xml:id="echoid-s12803" xml:space="preserve">Vnde pro reliquis
              <lb/>
            horis, cuiuſmodi in noſtro exemplo ſunt 9. </s>
            <s xml:id="echoid-s12804" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12805" xml:space="preserve">& </s>
            <s xml:id="echoid-s12806" xml:space="preserve">23. </s>
            <s xml:id="echoid-s12807" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s12808" xml:space="preserve">vt in figura cernitur, inueniemus pun
              <lb/>
            cta in tropico ♋, hoc modo. </s>
            <s xml:id="echoid-s12809" xml:space="preserve">Ex horis quæ per diametrum opponuntur iſtis horis in circulo
              <lb/>
              <figure xlink:label="fig-0214-01" xlink:href="fig-0214-01a" number="151">
                <image file="0214-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0214-01"/>
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              <note position="left" xlink:label="note-0214-01" xlink:href="note-0214-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0214-02" xlink:href="note-0214-02a" xml:space="preserve">20</note>
            M a N b, (habentur autem horæ oppoſitæ ex additione horarum 12. </s>
            <s xml:id="echoid-s12810" xml:space="preserve">ad horas illas, reiectis tamen
              <lb/>
              <note position="left" xlink:label="note-0214-03" xlink:href="note-0214-03a" xml:space="preserve">30</note>
            24. </s>
            <s xml:id="echoid-s12811" xml:space="preserve">ſi numerus ex additione collectus maior fuerit, quàm 24. </s>
            <s xml:id="echoid-s12812" xml:space="preserve">Vt horæ 9. </s>
            <s xml:id="echoid-s12813" xml:space="preserve">opponitur hora 21. </s>
            <s xml:id="echoid-s12814" xml:space="preserve">quia
              <lb/>
            ex 9. </s>
            <s xml:id="echoid-s12815" xml:space="preserve">& </s>
            <s xml:id="echoid-s12816" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12817" xml:space="preserve">fiunt 21. </s>
            <s xml:id="echoid-s12818" xml:space="preserve">Ita etiam horæ 23. </s>
            <s xml:id="echoid-s12819" xml:space="preserve">opponitur hora 11. </s>
            <s xml:id="echoid-s12820" xml:space="preserve">quia ex 23. </s>
            <s xml:id="echoid-s12821" xml:space="preserve">& </s>
            <s xml:id="echoid-s12822" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12823" xml:space="preserve">fiunt 35. </s>
            <s xml:id="echoid-s12824" xml:space="preserve">& </s>
            <s xml:id="echoid-s12825" xml:space="preserve">abiectis
              <lb/>
            24. </s>
            <s xml:id="echoid-s12826" xml:space="preserve">remanent 11. </s>
            <s xml:id="echoid-s12827" xml:space="preserve">&</s>
            <s xml:id="echoid-s12828" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s12829" xml:space="preserve">ducemus per centrum E, rectas ſecantes æquinoctialem lineam in punctis,
              <lb/>
            per quæ ſi ex H, ducantur rectæ, ſecabitur quidem tropicus ♋, in punctis, quæ horis illis oppoſitis
              <lb/>
            reſpondent, vt demonſtratum eſt: </s>
            <s xml:id="echoid-s12830" xml:space="preserve">Si verò illæ rectæ vltra centrum H, producantur, ſecabitur tro-
              <lb/>
            picus ♋, in punctis, quæ illis aliis horis reſpondent, quæ in ſemicirculo t N u, non continentur, & </s>
            <s xml:id="echoid-s12831" xml:space="preserve">
              <lb/>
            quarum oppoſitæ acceptæ ſunt. </s>
            <s xml:id="echoid-s12832" xml:space="preserve">Vt ex m, puncto horæ 11. </s>
            <s xml:id="echoid-s12833" xml:space="preserve">quæ per diametrum opponitur horæ
              <lb/>
            23. </s>
            <s xml:id="echoid-s12834" xml:space="preserve">ducta recta per centrum E, ſecat æquinoctialem lineam in n: </s>
            <s xml:id="echoid-s12835" xml:space="preserve">ducta autem recta H n, ſecat tro-
              <lb/>
            picum ♋, in q, puncto horæ 11. </s>
            <s xml:id="echoid-s12836" xml:space="preserve">producta denique recta n H, vltra centrum ſecat tropicum ♋, in
              <lb/>
            puncto p, quod dico horæ 23. </s>
            <s xml:id="echoid-s12837" xml:space="preserve">deberi. </s>
            <s xml:id="echoid-s12838" xml:space="preserve">Quoniã enim circulus maximus per polos mundi ductus,
              <lb/>
              <note position="left" xlink:label="note-0214-04" xlink:href="note-0214-04a" xml:space="preserve">40</note>
            & </s>
            <s xml:id="echoid-s12839" xml:space="preserve">per horam vndecimam tropici ♋, ſecat, per propoſ. </s>
            <s xml:id="echoid-s12840" xml:space="preserve">15. </s>
            <s xml:id="echoid-s12841" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12842" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12843" xml:space="preserve">Theodoſii, tropicum ♋, atque
              <lb/>
            adeo & </s>
            <s xml:id="echoid-s12844" xml:space="preserve">Aequatorem, ſiue circulum M a N b, bifariam, tranſibit omnino per horam 23. </s>
            <s xml:id="echoid-s12845" xml:space="preserve">quæ inte-
              <lb/>
            gro ſemicirculo, hoc eſt, horis 12. </s>
            <s xml:id="echoid-s12846" xml:space="preserve">abeſt ab hora vndecima, adeò vt vnus ſemicirculus eius monſtret
              <lb/>
            horam vndecimam, & </s>
            <s xml:id="echoid-s12847" xml:space="preserve">alter 23. </s>
            <s xml:id="echoid-s12848" xml:space="preserve">Eſt ergo recta m E n, communis ſectio Aequatoris, & </s>
            <s xml:id="echoid-s12849" xml:space="preserve">circuli ma
              <lb/>
            ximi per polos mundi, & </s>
            <s xml:id="echoid-s12850" xml:space="preserve">horam vndecimam, & </s>
            <s xml:id="echoid-s12851" xml:space="preserve">23. </s>
            <s xml:id="echoid-s12852" xml:space="preserve">tropici ♋, ducti. </s>
            <s xml:id="echoid-s12853" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s12854" xml:space="preserve">recta n H p, com-
              <lb/>
            munis ſectio eſt eiuſdem circuli maximi & </s>
            <s xml:id="echoid-s12855" xml:space="preserve">plani horologij, quandoquidem dictus circulus plano
              <lb/>
            horologii occurrit in punctis n, & </s>
            <s xml:id="echoid-s12856" xml:space="preserve">H; </s>
            <s xml:id="echoid-s12857" xml:space="preserve">hac tamen lege, vt portio H n, æquinoctialem lineam ſecans
              <lb/>
            referat ſemicirculum illius circuli maximi per horam vndecimam in tropico ♋, tranſeuntem, cu-
              <lb/>
            ius videlicet ſectio m E, per centrum E, ducitur, antequam lineæ æquinoctiali occurrat, vt in ſcho
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s12858" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12859" xml:space="preserve">huius libri ſcripſimus. </s>
            <s xml:id="echoid-s12860" xml:space="preserve">Ex quo fit, vt reliqua portio H p, vltra centrum horolo-
              <lb/>
              <note position="left" xlink:label="note-0214-05" xlink:href="note-0214-05a" xml:space="preserve">50</note>
            gii producta, & </s>
            <s xml:id="echoid-s12861" xml:space="preserve">æquinoctialem lineam non ſecans, referat alterum ſemicirculum per ho-
              <lb/>
            ram 23. </s>
            <s xml:id="echoid-s12862" xml:space="preserve">ductum, veluti in eodem ſcholio docuimus. </s>
            <s xml:id="echoid-s12863" xml:space="preserve">Nam & </s>
            <s xml:id="echoid-s12864" xml:space="preserve">ibi oſtendimus, lineam horariam,
              <lb/>
            quæ æquinoctialem lineam ſecat, indicare horam vnius ſemicirculi, portionem verò eius vltra cẽ-
              <lb/>
            trum productam, quæ lineam æquinoctialem non ſecat, monſtrare horam alterius ſemicirculi op-
              <lb/>
            poſiti; </s>
            <s xml:id="echoid-s12865" xml:space="preserve">ita vt duæ illæ horæ integro ſemicirculo, ſeu 12. </s>
            <s xml:id="echoid-s12866" xml:space="preserve">horis in Aequatore inter ſe diſtent, vt & </s>
            <s xml:id="echoid-s12867" xml:space="preserve">
              <lb/>
            hic contingit. </s>
            <s xml:id="echoid-s12868" xml:space="preserve">Quare per punctum p, ducenda eſt linea horæ 23. </s>
            <s xml:id="echoid-s12869" xml:space="preserve">Idem de cæteris iudicium ha-
              <lb/>
            beatur. </s>
            <s xml:id="echoid-s12870" xml:space="preserve">Nam ita inueſtigabimus puncta in eodem tropico ♋, pro horis 9. </s>
            <s xml:id="echoid-s12871" xml:space="preserve">& </s>
            <s xml:id="echoid-s12872" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12873" xml:space="preserve">ſi ex horis 21. </s>
            <s xml:id="echoid-s12874" xml:space="preserve">& </s>
            <s xml:id="echoid-s12875" xml:space="preserve">
              <lb/>
            22. </s>
            <s xml:id="echoid-s12876" xml:space="preserve">quæ illis opponuntur, per centrum E, rectas educamus, &</s>
            <s xml:id="echoid-s12877" xml:space="preserve">c.</s>
            <s xml:id="echoid-s12878" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12879" xml:space="preserve">EODEM modo, ſi circulum ex E, deſcriptum ſecemus in duas portiones, quarum d N e, ſi-
              <lb/>
            milis ſit arcui diurno tropici ♑, & </s>
            <s xml:id="echoid-s12880" xml:space="preserve">d M e, nocturno eiuſdem, (quod facile fiet, ſi arcubus M a, Mb,
              <lb/>
            æquales arcus ſumamus N d, N e, rectamq́; </s>
            <s xml:id="echoid-s12881" xml:space="preserve">d e, ducamus, ita vt rectæ a b, d e, ex diametro M </s>
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