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-div893" type="section" level="1" n="216">
          <p>
            <s xml:id="echoid-s17565" xml:space="preserve">
              <pb o="259" file="0275" n="275" rhead="LIBER SECVNDVS."/>
            horologii, vel horæ 12. </s>
            <s xml:id="echoid-s17566" xml:space="preserve">non autem horæ 6. </s>
            <s xml:id="echoid-s17567" xml:space="preserve">vt ibi. </s>
            <s xml:id="echoid-s17568" xml:space="preserve">Pari ratione in figura tertia eiuſdem propoſ. </s>
            <s xml:id="echoid-s17569" xml:space="preserve">26.
              <lb/>
            </s>
            <s xml:id="echoid-s17570" xml:space="preserve">lineam α β, quæ in horologio Meridiano pertinebat ad horam 6. </s>
            <s xml:id="echoid-s17571" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s17572" xml:space="preserve">eſſe lineam meridianam,
              <lb/>
            ſeu horæ 12 in horologio polari; </s>
            <s xml:id="echoid-s17573" xml:space="preserve">proximam verò illi parallelam pertinere ad horam 1. </s>
            <s xml:id="echoid-s17574" xml:space="preserve">& </s>
            <s xml:id="echoid-s17575" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17576" xml:space="preserve">à me
              <lb/>
            ridie, & </s>
            <s xml:id="echoid-s17577" xml:space="preserve">media nocte, &</s>
            <s xml:id="echoid-s17578" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17579" xml:space="preserve">In vtroque porrò horologio polari ſigna Borealia infra lineam æquino-
              <lb/>
              <note position="right" xlink:label="note-0275-01" xlink:href="note-0275-01a" xml:space="preserve">In horologio
                <lb/>
              polati tam Su-
                <lb/>
              periori, quàm
                <lb/>
              Inferioti ſigna
                <lb/>
              borealia ſunt
                <lb/>
              inſra lineã ęqui
                <lb/>
              noctialem, & au
                <lb/>
              ſiralia ſupra.</note>
            ctialem verſus auſtrum, & </s>
            <s xml:id="echoid-s17580" xml:space="preserve">ſupra eandem verſus boream auſtralia continentur, vt ex Analemmate,
              <lb/>
            ſeu figura prima propoſ. </s>
            <s xml:id="echoid-s17581" xml:space="preserve">26. </s>
            <s xml:id="echoid-s17582" xml:space="preserve">huius libri colligi poteſt. </s>
            <s xml:id="echoid-s17583" xml:space="preserve">Nam Sole exiſtente in ♋, vmbra ſtyli proii-
              <lb/>
            citur in partes inferiores lineæ meridianæ in vtroque horologio, nempe in punctum N, verſus au-
              <lb/>
            ſtrum tempore meridiei; </s>
            <s xml:id="echoid-s17584" xml:space="preserve">exiſtente verò eodem in ♑, in ſuperiores partes, vt in punctum Q, ver-
              <lb/>
            ſus boream.</s>
            <s xml:id="echoid-s17585" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Linea hor@zon-
            <lb/>
          talis in horolo-
            <lb/>
          g@o Polari quo
            <lb/>
          modo deſcriba-
            <lb/>
          @ur.</note>
          <p>
            <s xml:id="echoid-s17586" xml:space="preserve">QVONIAM verò planum horologii polaris ab Horizonte ſecatur, cum ei non ſit parallelũ,
              <lb/>
              <note position="left" xlink:label="note-0275-03" xlink:href="note-0275-03a" xml:space="preserve">10</note>
            quemadmodum & </s>
            <s xml:id="echoid-s17587" xml:space="preserve">circulus horæ 6. </s>
            <s xml:id="echoid-s17588" xml:space="preserve">à meridie, vel media nocte, cui horologium æquidiſtat, ab eo-
              <lb/>
            dem Horizonte ſecatur, deſcribemus communem ſectionem Horizontis, ac plani horologii, nem
              <lb/>
            pe lineam horizontalem, in quam vmbra ſtyli proiicitur, cum Soloritur, vel occidit, vt ex propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s17589" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17590" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17591" xml:space="preserve">conſtat, hac ratione. </s>
            <s xml:id="echoid-s17592" xml:space="preserve">Ad punctum B, vbi hora 3. </s>
            <s xml:id="echoid-s17593" xml:space="preserve">vel 9. </s>
            <s xml:id="echoid-s17594" xml:space="preserve">lineam æquinoctialem ſe-
              <lb/>
            cat, fiat angulus A B D, complemento altitudinis poli æqualis, ſecetq́ue recta B D, lineam meri-
              <lb/>
            dianam in D, ſupra quidem locum ſtyli in horologio ſuperiori, infra verò eundẽ in inferiori; </s>
            <s xml:id="echoid-s17595" xml:space="preserve">quod
              <lb/>
            facile fiet, ſi ex B, deſcribatur arcus circuli vltra lineam meridianam, in quo à recta C S, comple-
              <lb/>
            mentum altitudinis poli ſupputetur, & </s>
            <s xml:id="echoid-s17596" xml:space="preserve">ex ſine ſupputationis ad B, recta ducatur, &</s>
            <s xml:id="echoid-s17597" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17598" xml:space="preserve">Si enim per
              <lb/>
            D, lineæ æquinoctiali C S, parallela ducatur, erit hæc, linea horizontalis. </s>
            <s xml:id="echoid-s17599" xml:space="preserve">Nam quia recta A B,
              <lb/>
            longitudini ſtyli A E, eſt æqualis, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s17600" xml:space="preserve">25. </s>
            <s xml:id="echoid-s17601" xml:space="preserve">huius libri oſtendimus, ſi triangulum
              <lb/>
              <note position="left" xlink:label="note-0275-04" xlink:href="note-0275-04a" xml:space="preserve">20</note>
            D B A, circa rectam A D, intelligatur conuerti, donec ad planum horologii rectum ſit, & </s>
            <s xml:id="echoid-s17602" xml:space="preserve">in plano
              <lb/>
            Meridiani circuli exiſtat, tranſibit Horizon per punctum B, nempe per verticem ſtyli, ſeu centrum
              <lb/>
            mundi; </s>
            <s xml:id="echoid-s17603" xml:space="preserve">Nam recta A B, in illo ſitu, quem in illa conuerſione trianguli acquiſiuit, perpendicularis
              <lb/>
            eſt ad planum horologii, & </s>
            <s xml:id="echoid-s17604" xml:space="preserve">in plano Æ quatoris exiſtit, atque adeo B, erit vertex ſtyli, ſeu centrum
              <lb/>
            mundi. </s>
            <s xml:id="echoid-s17605" xml:space="preserve">Cum ergo angulus D B A, conſtitutus ſit æqualis complemento altitudinis poli, qualem
              <lb/>
            nimirum Horizon facit cum plano Æ quatoris, atque adeo reliquus B D A, altitudini poli æqualis
              <lb/>
            ſit, nempe inclinationi plani horologii ad Horizontem, tranſibit Horizon per rectam B D, occur-
              <lb/>
            retq́ue plano horologii in D; </s>
            <s xml:id="echoid-s17606" xml:space="preserve">quandoquidem hac ratione in plano Meridiani circuli cum A B, cõ-
              <lb/>
            muni ſectione Aequatoris, & </s>
            <s xml:id="echoid-s17607" xml:space="preserve">Meridiani conſtituit angulum complemento altitudinis poli æqua-
              <lb/>
            lem, cum recta verò A E, communi ſectione plani horologii, ac Meridiani angulum æqualem alti-
              <lb/>
              <note position="left" xlink:label="note-0275-05" xlink:href="note-0275-05a" xml:space="preserve">30</note>
            tudini poli, vt res exigit. </s>
            <s xml:id="echoid-s17608" xml:space="preserve">Quare per D, ducenda erit linea horizontalis. </s>
            <s xml:id="echoid-s17609" xml:space="preserve">Quia verò Aequator, Ho-
              <lb/>
            rizon, & </s>
            <s xml:id="echoid-s17610" xml:space="preserve">circulus horæ ſextæ habent vnam communem ſectionem, æquidiſtatq́ue plannm horolo
              <lb/>
            gij vni illorum, nempe circulo horæ 6. </s>
            <s xml:id="echoid-s17611" xml:space="preserve">erunt communes ſectiones factæ à plano horologii in aliis
              <lb/>
            duobus circulis, nempe linea æquinoctialis, & </s>
            <s xml:id="echoid-s17612" xml:space="preserve">horizontalis, parallelæ inter ſe, vt in ſcholio propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s17613" xml:space="preserve">22. </s>
            <s xml:id="echoid-s17614" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17615" xml:space="preserve">demonſtratum eſt. </s>
            <s xml:id="echoid-s17616" xml:space="preserve">Recta igitur per D, lineæ æquinoctiali parallela ducta, ho-
              <lb/>
            rizon talis linea eſt, quod eſt propoſitum.</s>
            <s xml:id="echoid-s17617" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17618" xml:space="preserve">INVENIEMVS quoque punctum D, per quod horizontalis linea ducenda eſt, hoc mo-
              <lb/>
              <note position="right" xlink:label="note-0275-06" xlink:href="note-0275-06a" xml:space="preserve">Alia deſcriptio
                <unsure/>
                <lb/>
              lineæ horizon-
                <lb/>
              talis in eodem
                <lb/>
              horologio Po.
                <lb/>
              lari.</note>
            do. </s>
            <s xml:id="echoid-s17619" xml:space="preserve">In Analemmate, ex quo arcus ſignorũ deſcripti ſunt, notentur puncta l, m, vbi diameter Hori-
              <lb/>
            zontis B D, parallelas L M, L M, per quas ducũtur horologiorum plana, interſecat, & </s>
            <s xml:id="echoid-s17620" xml:space="preserve">recta K l, vel
              <lb/>
            K m, trãsferatur in lineã meridianã ex loco ſtyli A, ſurſum verſus vſq; </s>
            <s xml:id="echoid-s17621" xml:space="preserve">ad D, in horologio ſuperio-
              <lb/>
              <note position="left" xlink:label="note-0275-07" xlink:href="note-0275-07a" xml:space="preserve">40</note>
            ri, deorſum autẽ verſus in inferiori. </s>
            <s xml:id="echoid-s17622" xml:space="preserve">Nam per D, ducenda eſt linea horizontalis, vt prius. </s>
            <s xml:id="echoid-s17623" xml:space="preserve">quoniã in
              <lb/>
            punctis l, & </s>
            <s xml:id="echoid-s17624" xml:space="preserve">m, planum Horizontis per B D, ductum occurrit planis horologiorum per L M, L M,
              <lb/>
            rectas ductis, ſupra K, quidem locũ ſtyli in horologio ſuperiori, infra verò in inferiori, &</s>
            <s xml:id="echoid-s17625" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17626" xml:space="preserve">Et quo-
              <lb/>
            niam recta K l, rectæ K m, æqualis eſt; </s>
            <s xml:id="echoid-s17627" xml:space="preserve">(Nam in triangulis E K l, E K m, anguli ad K, recti ſunt,
              <lb/>
              <note position="right" xlink:label="note-0275-08" xlink:href="note-0275-08a" xml:space="preserve">15. primi.</note>
            & </s>
            <s xml:id="echoid-s17628" xml:space="preserve">anguli ad verticem E, æquales; </s>
            <s xml:id="echoid-s17629" xml:space="preserve">Item & </s>
            <s xml:id="echoid-s17630" xml:space="preserve">latera E K, E K, ęqualia. </s>
            <s xml:id="echoid-s17631" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s17632" xml:space="preserve">latera K l, K m, æqualia
              <lb/>
              <note position="right" xlink:label="note-0275-09" xlink:href="note-0275-09a" xml:space="preserve">26. primi.</note>
            erunt) propterea diximus eandẽ K l, vel K m, transferendã in lineam meridianam ſupra vel infra
              <lb/>
            locum ſtyli in vtroque horologio, vt punctum reperiatur, per quod horizontalis linea ducatur.</s>
            <s xml:id="echoid-s17633" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17634" xml:space="preserve">PORRO ſi horologium polare ſuperius inuertatur, ita vt ſuperiora fiant inferiora, & </s>
            <s xml:id="echoid-s17635" xml:space="preserve">quæ
              <lb/>
              <note position="right" xlink:label="note-0275-10" xlink:href="note-0275-10a" xml:space="preserve">Si omnes par-
                <lb/>
              tes Superioris
                <lb/>
              horologii Pola-
                <lb/>
              ris inuertantur,
                <lb/>
              vt ſuperior fiat
                <lb/>
              inferior, & dex-
                <lb/>
              t@a ſiniſtra, fa-
                <lb/>
              ctum erit horo-
                <lb/>
              logiũ Inferius;
                <lb/>
              ſed horæ, quæ
                <lb/>
              prius numera-
                <lb/>
              bantur à n@er@
                <lb/>
              numerande sũt
                <lb/>
              à med. noc. &
                <lb/>
              contra.</note>
            dextra ſunt poſt eam inuerſionem, fiant ſiniſtra, & </s>
            <s xml:id="echoid-s17636" xml:space="preserve">contra, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s17637" xml:space="preserve">14. </s>
            <s xml:id="echoid-s17638" xml:space="preserve">huius libri ſcri-
              <lb/>
            pſimus, indicabit idem horas in facie oppoſita plani, hoc eſt, in inferiori, quæ ad Nadir ſpectat, vt
              <lb/>
              <note position="left" xlink:label="note-0275-11" xlink:href="note-0275-11a" xml:space="preserve">50</note>
            in dicto ſcholio demonſtrauimus. </s>
            <s xml:id="echoid-s17639" xml:space="preserve">Sed linea meridiana monſtrabit tunc horam 12. </s>
            <s xml:id="echoid-s17640" xml:space="preserve">mediæ noctis,
              <lb/>
            cum in ſuperiori hologio horam 12. </s>
            <s xml:id="echoid-s17641" xml:space="preserve">meridiei indicet: </s>
            <s xml:id="echoid-s17642" xml:space="preserve">reliquæ verò horæ, quæ in eodem ſuperio-
              <lb/>
            ri horologio à meridie numerantur, à media nocte ſupputandæ erunt in inferiori, & </s>
            <s xml:id="echoid-s17643" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s17644" xml:space="preserve">Quo-
              <lb/>
            niam enim Sol in alio ſemicirculo eiuſdem circuli horarij exiſtat neceſſe eſt, cum vmbra ſtyli in
              <lb/>
            ſuperius horologium cadit, & </s>
            <s xml:id="echoid-s17645" xml:space="preserve">in alio, cum in inferius, vt patet; </s>
            <s xml:id="echoid-s17646" xml:space="preserve">efficitur, vt linea, quæ in ſuperiori
              <lb/>
            horologio indicat horam à meridie, monſtret in inferiori eandem horam à media nocte, & </s>
            <s xml:id="echoid-s17647" xml:space="preserve">con-
              <lb/>
            tra; </s>
            <s xml:id="echoid-s17648" xml:space="preserve">quandoquidem vnus ſemicirculus ad horas à meridie, & </s>
            <s xml:id="echoid-s17649" xml:space="preserve">alter ad horas à media nocte perti-
              <lb/>
            net, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s17650" xml:space="preserve">9. </s>
            <s xml:id="echoid-s17651" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17652" xml:space="preserve">docuimus. </s>
            <s xml:id="echoid-s17653" xml:space="preserve">Arcus quoque vel paralleli ſignorum au-
              <lb/>
            ſtralium ſuperioris horologii mutantur in arcus borealium ſignorum in inferiori, & </s>
            <s xml:id="echoid-s17654" xml:space="preserve">contra; </s>
            <s xml:id="echoid-s17655" xml:space="preserve">vt
              <lb/>
            parallelus ♑, in parallelum ♋, parallelus ♐, & </s>
            <s xml:id="echoid-s17656" xml:space="preserve">♒, in parallelum ♊, & </s>
            <s xml:id="echoid-s17657" xml:space="preserve">♌, &</s>
            <s xml:id="echoid-s17658" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17659" xml:space="preserve">Quod oſtendemus,
              <lb/>
            vt in propoſ, 26. </s>
            <s xml:id="echoid-s17660" xml:space="preserve">huius libri idem demonſtrauimus in Meridiano horologio, hoc ſolum </s>
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