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-div933" type="section" level="1" n="226">
          <p>
            <s xml:id="echoid-s18306" xml:space="preserve">
              <pb o="271" file="0287" n="287" rhead="LIBER SECVNDVS."/>
            eandem quoque cum circulo horæ 6. </s>
            <s xml:id="echoid-s18307" xml:space="preserve">à meridie, vel media nocte, per propoſ. </s>
            <s xml:id="echoid-s18308" xml:space="preserve">17. </s>
            <s xml:id="echoid-s18309" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s18310" xml:space="preserve">ſu-
              <lb/>
            perioris; </s>
            <s xml:id="echoid-s18311" xml:space="preserve">efficitur, vt duo illi circuli, & </s>
            <s xml:id="echoid-s18312" xml:space="preserve">Aequator, & </s>
            <s xml:id="echoid-s18313" xml:space="preserve">circulus horæ 6. </s>
            <s xml:id="echoid-s18314" xml:space="preserve">à meridie, vel media nocte,
              <lb/>
            habeant vnam & </s>
            <s xml:id="echoid-s18315" xml:space="preserve">eandem ſectionem communem, nempe eam, per quam circulus dictæ horæ 6.
              <lb/>
            </s>
            <s xml:id="echoid-s18316" xml:space="preserve">Aequatorem ſecat. </s>
            <s xml:id="echoid-s18317" xml:space="preserve">Cum ergo huic circulo, atque adeo dictæ communi ſectioni omnium illorũ,
              <lb/>
            æquidiſtet planum horologij polaris, erunt per propoſ. </s>
            <s xml:id="echoid-s18318" xml:space="preserve">18. </s>
            <s xml:id="echoid-s18319" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18320" xml:space="preserve">reliquorum circulorum
              <lb/>
            ſectiones cum plano horologij, quales ſunt lineæ horæ 12. </s>
            <s xml:id="echoid-s18321" xml:space="preserve">& </s>
            <s xml:id="echoid-s18322" xml:space="preserve">24. </s>
            <s xml:id="echoid-s18323" xml:space="preserve">ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s18324" xml:space="preserve">linea æqui-
              <lb/>
            noctialis, inter ſe ſe parallelæ. </s>
            <s xml:id="echoid-s18325" xml:space="preserve">Atque hæc de horologio ſuperiori intelligenda ſunt. </s>
            <s xml:id="echoid-s18326" xml:space="preserve">Pro inferiori
              <lb/>
            autem ſatis erit, illud ex ſuperiori elicere, vt in ſequenti propoſ. </s>
            <s xml:id="echoid-s18327" xml:space="preserve">docebimus.</s>
            <s xml:id="echoid-s18328" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18329" xml:space="preserve">SIGNATIS quoque in lineis horarum à meridie, vel media nocte punctis, ſecundum do-
              <lb/>
              <note position="right" xlink:label="note-0287-01" xlink:href="note-0287-01a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horologii Itali-
                <lb/>
              ci polaris per ar
                <lb/>
              cus diurnos ho
                <lb/>
              rarũ 10. & 14.</note>
            ctrinam propoſ. </s>
            <s xml:id="echoid-s18330" xml:space="preserve">38. </s>
            <s xml:id="echoid-s18331" xml:space="preserve">huius libri, per quæ paralleli, quorum vnus ſit horarum 14. </s>
            <s xml:id="echoid-s18332" xml:space="preserve">& </s>
            <s xml:id="echoid-s18333" xml:space="preserve">alter 10. </s>
            <s xml:id="echoid-s18334" xml:space="preserve">du-
              <lb/>
              <note position="left" xlink:label="note-0287-02" xlink:href="note-0287-02a" xml:space="preserve">10</note>
            cuntur, deſcribemus beneficio illorum, & </s>
            <s xml:id="echoid-s18335" xml:space="preserve">tabularum, quas in ſcholio propoſ. </s>
            <s xml:id="echoid-s18336" xml:space="preserve">33. </s>
            <s xml:id="echoid-s18337" xml:space="preserve">ſuperioris lib.
              <lb/>
            </s>
            <s xml:id="echoid-s18338" xml:space="preserve">compoſuimus, horologium Italicum, vt in ſuperioribus horologijs tradidimus.</s>
            <s xml:id="echoid-s18339" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18340" xml:space="preserve">RVRSVS commodiſſime idem conſtruemus per duos parallelos, quorum vnus eſt ſemper
              <lb/>
              <note position="right" xlink:label="note-0287-03" xlink:href="note-0287-03a" xml:space="preserve">Alia a dhuc de-
                <lb/>
              ſcriptio eiuſdẽ
                <lb/>
              horologii Itali-
                <lb/>
              ci polatis per
                <lb/>
              arcum diurnũ,
                <lb/>
              nocturnum que
                <lb/>
              horarum 24.</note>
            apparentium maximus, hoc eſt, arcus diurnus horarum 24. </s>
            <s xml:id="echoid-s18341" xml:space="preserve">alter verò maximus perpetuo delite-
              <lb/>
            ſcentium, ſeu arcus nocturnus horarum 24. </s>
            <s xml:id="echoid-s18342" xml:space="preserve">ſi in horis à meridie, & </s>
            <s xml:id="echoid-s18343" xml:space="preserve">media nocte notentur puncta,
              <lb/>
            per quę tranſeunt. </s>
            <s xml:id="echoid-s18344" xml:space="preserve">Nam horæ ab ortu, vel occaſu tangunt dictos parallelos in plano horologij de-
              <lb/>
            ſcriptos in punctis, per quæ ducuntur horæ à meridie, vel media nocte, exceptis horis 6. </s>
            <s xml:id="echoid-s18345" xml:space="preserve">& </s>
            <s xml:id="echoid-s18346" xml:space="preserve">18. </s>
            <s xml:id="echoid-s18347" xml:space="preserve">quę
              <lb/>
            cum dictis hyperbolis non conueniunt, vt ex coroll. </s>
            <s xml:id="echoid-s18348" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s18349" xml:space="preserve">15. </s>
            <s xml:id="echoid-s18350" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18351" xml:space="preserve">conſtat. </s>
            <s xml:id="echoid-s18352" xml:space="preserve">Quænam
              <lb/>
            autem horæ ab occaſu tangant arcum diurnum horarum 24. </s>
            <s xml:id="echoid-s18353" xml:space="preserve">& </s>
            <s xml:id="echoid-s18354" xml:space="preserve">quæ arcum nocturnum horarum
              <lb/>
            24. </s>
            <s xml:id="echoid-s18355" xml:space="preserve">item & </s>
            <s xml:id="echoid-s18356" xml:space="preserve">in quibus horis à meridie, vel media nocte, pulchrè indicant tabulæ arcus diurni, & </s>
            <s xml:id="echoid-s18357" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0287-04" xlink:href="note-0287-04a" xml:space="preserve">20</note>
            arcus nocturni horarum 24. </s>
            <s xml:id="echoid-s18358" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s18359" xml:space="preserve">33. </s>
            <s xml:id="echoid-s18360" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18361" xml:space="preserve">Quoniam enim in horologio ſupe
              <lb/>
            riori polari continentur ſolum horæ 7. </s>
            <s xml:id="echoid-s18362" xml:space="preserve">8. </s>
            <s xml:id="echoid-s18363" xml:space="preserve">9. </s>
            <s xml:id="echoid-s18364" xml:space="preserve">10. </s>
            <s xml:id="echoid-s18365" xml:space="preserve">11. </s>
            <s xml:id="echoid-s18366" xml:space="preserve">& </s>
            <s xml:id="echoid-s18367" xml:space="preserve">12. </s>
            <s xml:id="echoid-s18368" xml:space="preserve">à media nocte. </s>
            <s xml:id="echoid-s18369" xml:space="preserve">Item 1. </s>
            <s xml:id="echoid-s18370" xml:space="preserve">2. </s>
            <s xml:id="echoid-s18371" xml:space="preserve">3. </s>
            <s xml:id="echoid-s18372" xml:space="preserve">4. </s>
            <s xml:id="echoid-s18373" xml:space="preserve">& </s>
            <s xml:id="echoid-s18374" xml:space="preserve">5. </s>
            <s xml:id="echoid-s18375" xml:space="preserve">à
              <lb/>
            meridie, accipiendæ erunt ex vtraque tabula horæ ab occaſu dictis horis reſpondentes, & </s>
            <s xml:id="echoid-s18376" xml:space="preserve">non alię.
              <lb/>
            </s>
            <s xml:id="echoid-s18377" xml:space="preserve">Vt ex tabula arcus diurni horarum 24. </s>
            <s xml:id="echoid-s18378" xml:space="preserve">ſumendæ ſunt hæ horæ ab occaſu 7. </s>
            <s xml:id="echoid-s18379" xml:space="preserve">8. </s>
            <s xml:id="echoid-s18380" xml:space="preserve">9. </s>
            <s xml:id="echoid-s18381" xml:space="preserve">10. </s>
            <s xml:id="echoid-s18382" xml:space="preserve">11. </s>
            <s xml:id="echoid-s18383" xml:space="preserve">12. </s>
            <s xml:id="echoid-s18384" xml:space="preserve">13. </s>
            <s xml:id="echoid-s18385" xml:space="preserve">
              <lb/>
            14. </s>
            <s xml:id="echoid-s18386" xml:space="preserve">15. </s>
            <s xml:id="echoid-s18387" xml:space="preserve">16. </s>
            <s xml:id="echoid-s18388" xml:space="preserve">& </s>
            <s xml:id="echoid-s18389" xml:space="preserve">17. </s>
            <s xml:id="echoid-s18390" xml:space="preserve">hæ enim dictum arcum tangunt in horis 7. </s>
            <s xml:id="echoid-s18391" xml:space="preserve">8. </s>
            <s xml:id="echoid-s18392" xml:space="preserve">9. </s>
            <s xml:id="echoid-s18393" xml:space="preserve">10. </s>
            <s xml:id="echoid-s18394" xml:space="preserve">11. </s>
            <s xml:id="echoid-s18395" xml:space="preserve">& </s>
            <s xml:id="echoid-s18396" xml:space="preserve">12. </s>
            <s xml:id="echoid-s18397" xml:space="preserve">à media nocte,
              <lb/>
            & </s>
            <s xml:id="echoid-s18398" xml:space="preserve">1. </s>
            <s xml:id="echoid-s18399" xml:space="preserve">2. </s>
            <s xml:id="echoid-s18400" xml:space="preserve">3. </s>
            <s xml:id="echoid-s18401" xml:space="preserve">4. </s>
            <s xml:id="echoid-s18402" xml:space="preserve">& </s>
            <s xml:id="echoid-s18403" xml:space="preserve">5. </s>
            <s xml:id="echoid-s18404" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s18405" xml:space="preserve">Ex tabula autem arcus no cturni horarum 24. </s>
            <s xml:id="echoid-s18406" xml:space="preserve">ſumendæ ſunt hæ ho
              <lb/>
            ræ ab occaſu 1. </s>
            <s xml:id="echoid-s18407" xml:space="preserve">2. </s>
            <s xml:id="echoid-s18408" xml:space="preserve">3. </s>
            <s xml:id="echoid-s18409" xml:space="preserve">4. </s>
            <s xml:id="echoid-s18410" xml:space="preserve">5. </s>
            <s xml:id="echoid-s18411" xml:space="preserve">19. </s>
            <s xml:id="echoid-s18412" xml:space="preserve">20. </s>
            <s xml:id="echoid-s18413" xml:space="preserve">21. </s>
            <s xml:id="echoid-s18414" xml:space="preserve">22. </s>
            <s xml:id="echoid-s18415" xml:space="preserve">23. </s>
            <s xml:id="echoid-s18416" xml:space="preserve">& </s>
            <s xml:id="echoid-s18417" xml:space="preserve">24. </s>
            <s xml:id="echoid-s18418" xml:space="preserve">Nam hæ contingunt arcum dictum in horis
              <lb/>
            1. </s>
            <s xml:id="echoid-s18419" xml:space="preserve">2. </s>
            <s xml:id="echoid-s18420" xml:space="preserve">3. </s>
            <s xml:id="echoid-s18421" xml:space="preserve">4. </s>
            <s xml:id="echoid-s18422" xml:space="preserve">& </s>
            <s xml:id="echoid-s18423" xml:space="preserve">5. </s>
            <s xml:id="echoid-s18424" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s18425" xml:space="preserve">in 7. </s>
            <s xml:id="echoid-s18426" xml:space="preserve">8. </s>
            <s xml:id="echoid-s18427" xml:space="preserve">9. </s>
            <s xml:id="echoid-s18428" xml:space="preserve">10. </s>
            <s xml:id="echoid-s18429" xml:space="preserve">11. </s>
            <s xml:id="echoid-s18430" xml:space="preserve">& </s>
            <s xml:id="echoid-s18431" xml:space="preserve">12. </s>
            <s xml:id="echoid-s18432" xml:space="preserve">à media nocte, vt ex prædictis tabu-
              <lb/>
            lis conſtat.</s>
            <s xml:id="echoid-s18433" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18434" xml:space="preserve">POSTREMO idem horologium Italicum conficiemus per lineam horæ 12. </s>
            <s xml:id="echoid-s18435" xml:space="preserve">ab ortu, vel oc
              <lb/>
              <note position="left" xlink:label="note-0287-05" xlink:href="note-0287-05a" xml:space="preserve">30</note>
              <note position="right" xlink:label="note-0287-06" xlink:href="note-0287-06a" xml:space="preserve">Alia adhuc de-
                <lb/>
              ſcriptio horolo
                <lb/>
              gii Italici pola-
                <lb/>
              ris per lineam
                <lb/>
              horæ 12. & li-
                <lb/>
              neam horæ 24.
                <lb/>
              ab or. vel occ.</note>
            caſu, vt ex tabula ſecunda propoſ. </s>
            <s xml:id="echoid-s18436" xml:space="preserve">20. </s>
            <s xml:id="echoid-s18437" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18438" xml:space="preserve">conſtat, cui titulus eſt, LINEA HORÆ
              <lb/>
            XII. </s>
            <s xml:id="echoid-s18439" xml:space="preserve">AB ORTV, VEL OCCASV. </s>
            <s xml:id="echoid-s18440" xml:space="preserve">Item per lineam horæ 24. </s>
            <s xml:id="echoid-s18441" xml:space="preserve">ab ortu, vel occaſu, vt ex
              <lb/>
            prima tabula propoſ. </s>
            <s xml:id="echoid-s18442" xml:space="preserve">20. </s>
            <s xml:id="echoid-s18443" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s18444" xml:space="preserve">ſuperioris colligitur, cui titulus eſt. </s>
            <s xml:id="echoid-s18445" xml:space="preserve">LINEA HORAE
              <lb/>
            XXIIII. </s>
            <s xml:id="echoid-s18446" xml:space="preserve">&</s>
            <s xml:id="echoid-s18447" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18448" xml:space="preserve">quæ quidem eadem omnino eſt, quæ horizontalis linea, vt perſpicuum eſt. </s>
            <s xml:id="echoid-s18449" xml:space="preserve">Vel
              <lb/>
            etiam beneficio vtriuſque lineæ, ſi diligenter in prędictis tabulis notentur puncta horarum à me-
              <lb/>
            ridie, vel media nocte, per quæ ducendæ ſint horæ Italicæ, &</s>
            <s xml:id="echoid-s18450" xml:space="preserve">c.</s>
            <s xml:id="echoid-s18451" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18452" xml:space="preserve">CAETERVM lineam horæ 12. </s>
            <s xml:id="echoid-s18453" xml:space="preserve">ab ortu, vel occaſu hac ratione deſcribemus. </s>
            <s xml:id="echoid-s18454" xml:space="preserve">In linea æqui-
              <lb/>
              <note position="right" xlink:label="note-0287-07" xlink:href="note-0287-07a" xml:space="preserve">Quo pacto li-
                <lb/>
              nea horæ 12. ab
                <lb/>
              or. vel occ. du-
                <lb/>
              cenda ſit in po-
                <lb/>
              lari horologio.</note>
            noctiali ex puncto A, vbi lineam meridianam interſecat, accipiemus rectam A B, æqualem ſtylo,
              <lb/>
            nempe rectam inter lineam meridianam, & </s>
            <s xml:id="echoid-s18455" xml:space="preserve">lineam horę 3. </s>
            <s xml:id="echoid-s18456" xml:space="preserve">vel 9. </s>
            <s xml:id="echoid-s18457" xml:space="preserve">à meridie, vel media nocte. </s>
            <s xml:id="echoid-s18458" xml:space="preserve">hæc
              <lb/>
            enim ſtylo æqualis eſt, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s18459" xml:space="preserve">25. </s>
            <s xml:id="echoid-s18460" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s18461" xml:space="preserve">oſtendimus. </s>
            <s xml:id="echoid-s18462" xml:space="preserve">Deinde ex B, termino il-
              <lb/>
              <note position="left" xlink:label="note-0287-08" xlink:href="note-0287-08a" xml:space="preserve">40</note>
            lius ad æquinoctialem lineam ducentes perpendicularem B f, qualis eſt ipſamet linea horæ 9. </s>
            <s xml:id="echoid-s18463" xml:space="preserve">vel
              <lb/>
            3. </s>
            <s xml:id="echoid-s18464" xml:space="preserve">producta, deſcribemus ex eodem puncto B, vt centro, circulum, in quo ſumemus arcum f g, al-
              <lb/>
            titudini poli æqualem, & </s>
            <s xml:id="echoid-s18465" xml:space="preserve">ex g, per centrum B, rectam ducemus, quæ ſecabit lineam meridianam
              <lb/>
            in puncto k, per quod ipſi ęquinoctiali lineę parallela acta, erit linea horæ 12. </s>
            <s xml:id="echoid-s18466" xml:space="preserve">ab ortu, vel occaſu.
              <lb/>
            </s>
            <s xml:id="echoid-s18467" xml:space="preserve">Intelligatur enim circulus f g, circa meridianam lineam F H, conuerti, donec cum Meridiano cir-
              <lb/>
            culo, & </s>
            <s xml:id="echoid-s18468" xml:space="preserve">eius centrum B, cum centro mundi, ſeu vertice ſtyli coniungatur. </s>
            <s xml:id="echoid-s18469" xml:space="preserve">Quo poſito, erit f, polus
              <lb/>
            mundi, & </s>
            <s xml:id="echoid-s18470" xml:space="preserve">g, punctum, in quo circulus horę 12. </s>
            <s xml:id="echoid-s18471" xml:space="preserve">ab ortu, vel occaſu parallelum omniũ ſemper ap-
              <lb/>
            parentium maximum tangit, ipſumq́ue Meridianum ſecat, cum hic parallelus à polo diſtet tot
              <lb/>
            gradibus, quot continentur in altitudine poli. </s>
            <s xml:id="echoid-s18472" xml:space="preserve">Quare recta ex g, per centrum circuli f g, emiſſa,
              <lb/>
            communis erit ſectio dicti circuli horæ 12. </s>
            <s xml:id="echoid-s18473" xml:space="preserve">& </s>
            <s xml:id="echoid-s18474" xml:space="preserve">Meridiani, ideoq́ue circulus horę 12. </s>
            <s xml:id="echoid-s18475" xml:space="preserve">ſecabit planũ
              <lb/>
              <note position="left" xlink:label="note-0287-09" xlink:href="note-0287-09a" xml:space="preserve">50</note>
            horologij in puncto K, in quo dicta recta meridianã lineam abrumpit. </s>
            <s xml:id="echoid-s18476" xml:space="preserve">Cum ergo ex ſcholio pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s18477" xml:space="preserve">22. </s>
            <s xml:id="echoid-s18478" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18479" xml:space="preserve">linea horę dictę 12. </s>
            <s xml:id="echoid-s18480" xml:space="preserve">& </s>
            <s xml:id="echoid-s18481" xml:space="preserve">ęquinoctialis parallelę ſint, liquido conſtat, paralle-
              <lb/>
            lam ipſi lineę ęquinoctiali per punctum K, meridianę lineę actam, eſſe lineam horę 12. </s>
            <s xml:id="echoid-s18482" xml:space="preserve">ab ortu,
              <lb/>
            vel occaſu, quod eſt propoſitum.</s>
            <s xml:id="echoid-s18483" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18484" xml:space="preserve">QVONIAM verò angulus altitudinis poli f B g, æqualis eſt angulo ad verticem K B L, ſit,
              <lb/>
              <note position="right" xlink:label="note-0287-10" xlink:href="note-0287-10a" xml:space="preserve">Alia daſeriptio
                <lb/>
              lineæ horæ 12.
                <lb/>
              ab or. vel occ.</note>
            vr ſi in linea ęquinoctiali accipiamus rectam gnomoni ęqualem, & </s>
            <s xml:id="echoid-s18485" xml:space="preserve">in extremo ad lineam ęquino-
              <lb/>
              <note position="right" xlink:label="note-0287-11" xlink:href="note-0287-11a" xml:space="preserve">15. primi.</note>
            ctialem conſtituamus angulum complementi altitudinis poli, qualis eſt reliquus ex recto A B K,
              <lb/>
            inueniamus in linea meridiana idem punctum K, per quod linea horę 12. </s>
            <s xml:id="echoid-s18486" xml:space="preserve">ab ortu, vel occaſu eſt
              <lb/>
              <note position="right" xlink:label="note-0287-12" xlink:href="note-0287-12a" xml:space="preserve">Alia adhuc de-
                <lb/>
              icriptio lineæ
                <lb/>
              horæ 12 ab o@.
                <lb/>
              vel occ.</note>
            ducenda. </s>
            <s xml:id="echoid-s18487" xml:space="preserve">Immò ſi rectę A D, abſcindamus ęqualem A K, habebimus idem punctum K. </s>
            <s xml:id="echoid-s18488" xml:space="preserve">Quoniã
              <lb/>
            enim angulus A B D, æqualis eſt conſtitutus complemento altitudinis poli, vt ex propoſ. </s>
            <s xml:id="echoid-s18489" xml:space="preserve">38. </s>
            <s xml:id="echoid-s18490" xml:space="preserve">huius
              <lb/>
            libri conſtat, & </s>
            <s xml:id="echoid-s18491" xml:space="preserve">angulus A B K, eidem cõplemento altitudinis poli æqualis, vt oſtendimus; </s>
            <s xml:id="echoid-s18492" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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