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

Table of Notes

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          <p>
            <s xml:id="echoid-s24210" xml:space="preserve">
              <pb o="368" file="0384" n="384" rhead="GNOMONICES"/>
            ſito exemplo eſt hora 3. </s>
            <s xml:id="echoid-s24211" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s24212" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s24213" xml:space="preserve">in arcu nocturno horarum 12. </s>
            <s xml:id="echoid-s24214" xml:space="preserve">horam 9. </s>
            <s xml:id="echoid-s24215" xml:space="preserve">ab occaſu. </s>
            <s xml:id="echoid-s24216" xml:space="preserve">Quo-
              <lb/>
            niam verò ſi velimus ducere lineam horæ 21. </s>
            <s xml:id="echoid-s24217" xml:space="preserve">ab occaſu, recta ex K, puncto horæ 21. </s>
            <s xml:id="echoid-s24218" xml:space="preserve">ab occaſu nõ
              <lb/>
            prius tranſit per centrum E, quàm per æquinoctialem lineam, accipiemus punctum oppoſitum
              <lb/>
            F, quod ſemper ab illo diſtat ſemicirculo integro, ſiue horis 12. </s>
            <s xml:id="echoid-s24219" xml:space="preserve">ita vt F, ſit punctum horæ 9. </s>
            <s xml:id="echoid-s24220" xml:space="preserve">ab
              <lb/>
            occaſu; </s>
            <s xml:id="echoid-s24221" xml:space="preserve">(quæ quidem habetur, ſi ad 21. </s>
            <s xml:id="echoid-s24222" xml:space="preserve">adijciamus 12. </s>
            <s xml:id="echoid-s24223" xml:space="preserve">& </s>
            <s xml:id="echoid-s24224" xml:space="preserve">ex ſumma, quoniam ſuperat 24. </s>
            <s xml:id="echoid-s24225" xml:space="preserve">abijcia-
              <lb/>
            mus 24.) </s>
            <s xml:id="echoid-s24226" xml:space="preserve">& </s>
            <s xml:id="echoid-s24227" xml:space="preserve">ex F, ducemus per E, & </s>
            <s xml:id="echoid-s24228" xml:space="preserve">K, rectam, quæ ſecet æquinoctialem lineam in L. </s>
            <s xml:id="echoid-s24229" xml:space="preserve">Nam recta
              <lb/>
            L H, ſecabit tropicum ♋, in M, puncto horæ 9. </s>
            <s xml:id="echoid-s24230" xml:space="preserve">ab occaſu, vt proximè dictum eſt, producta autem
              <lb/>
            vltra centrum H, ſecabit eundem tropicum in O, puncto horæ 21. </s>
            <s xml:id="echoid-s24231" xml:space="preserve">ab occaſu, vt demonſtrauimus
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s24232" xml:space="preserve">10. </s>
            <s xml:id="echoid-s24233" xml:space="preserve">ſuperioris libri. </s>
            <s xml:id="echoid-s24234" xml:space="preserve">Cum ergo hora 21. </s>
            <s xml:id="echoid-s24235" xml:space="preserve">ducatur quoque, vt habetur in tabula propoſ. </s>
            <s xml:id="echoid-s24236" xml:space="preserve">19.
              <lb/>
            </s>
            <s xml:id="echoid-s24237" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s24238" xml:space="preserve">1. </s>
            <s xml:id="echoid-s24239" xml:space="preserve">per horam 3. </s>
            <s xml:id="echoid-s24240" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s24241" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s24242" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s24243" xml:space="preserve">in linea æquinoctiali, indicabit recta per O, punctum, & </s>
            <s xml:id="echoid-s24244" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0384-01" xlink:href="note-0384-01a" xml:space="preserve">10</note>
            per horam 3. </s>
            <s xml:id="echoid-s24245" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s24246" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s24247" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s24248" xml:space="preserve">in linea æquinoctiali ducta horam 21. </s>
            <s xml:id="echoid-s24249" xml:space="preserve">ab occaſ
              <unsure/>
            u. </s>
            <s xml:id="echoid-s24250" xml:space="preserve">Sic etiam du-
              <lb/>
            cta recta ex P, puncto horæ 1. </s>
            <s xml:id="echoid-s24251" xml:space="preserve">ab occaſu per E, centrum, & </s>
            <s xml:id="echoid-s24252" xml:space="preserve">per R, punctum horæ 13. </s>
            <s xml:id="echoid-s24253" xml:space="preserve">ab occaſu ſe-
              <lb/>
            cat lineam æquinoctialem in A; </s>
            <s xml:id="echoid-s24254" xml:space="preserve">recta autem A H, ſecat tropicum ♋, in B, puncto horæ 1. </s>
            <s xml:id="echoid-s24255" xml:space="preserve">ab oc-
              <lb/>
            caſu, producta autem ſecat eundem in C, puncto horæ 13. </s>
            <s xml:id="echoid-s24256" xml:space="preserve">ab occaſu, &</s>
            <s xml:id="echoid-s24257" xml:space="preserve">c.</s>
            <s xml:id="echoid-s24258" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s24259" xml:space="preserve">IN alijs modis nulla eſt difficultas. </s>
            <s xml:id="echoid-s24260" xml:space="preserve">Per ſolum enim arcum diurnum horarum 14. </s>
            <s xml:id="echoid-s24261" xml:space="preserve">in ſuperio-
              <lb/>
              <note position="left" xlink:label="note-0384-02" xlink:href="note-0384-02a" xml:space="preserve">E
                <unsure/>
              iuſdem Itali-
                <lb/>
              ci horologii de
                <lb/>
              ſcriptio per ar-
                <lb/>
              cus diurnos, no
                <lb/>
              cturnosq́ue.</note>
            ri horologio, qui in portione nocturna eſt arcus nocturnus horarum 10. </s>
            <s xml:id="echoid-s24262" xml:space="preserve">commodiſſimè horæ ab
              <lb/>
            occaſu deſcribentur ſecundum tabulas propoſ. </s>
            <s xml:id="echoid-s24263" xml:space="preserve">33. </s>
            <s xml:id="echoid-s24264" xml:space="preserve">primi libri. </s>
            <s xml:id="echoid-s24265" xml:space="preserve">Sed quoniam pro ſingulis horis ab
              <lb/>
            occaſu ſingula tantum puncta habemus in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s24266" xml:space="preserve">ſumemus pro eiſdem nume
              <lb/>
            ro horis ab ortu alia puncta, ſiue in eodem arcu diurno horarum 14. </s>
            <s xml:id="echoid-s24267" xml:space="preserve">ſiue in nocturno horarũ 10.
              <lb/>
            </s>
            <s xml:id="echoid-s24268" xml:space="preserve">vt tabulæ propoſ. </s>
            <s xml:id="echoid-s24269" xml:space="preserve">33. </s>
            <s xml:id="echoid-s24270" xml:space="preserve">primi libri indicant. </s>
            <s xml:id="echoid-s24271" xml:space="preserve">Vt hora 23. </s>
            <s xml:id="echoid-s24272" xml:space="preserve">ab occaſu tranſit per horam 6. </s>
            <s xml:id="echoid-s24273" xml:space="preserve">à meridie
              <lb/>
              <note position="left" xlink:label="note-0384-03" xlink:href="note-0384-03a" xml:space="preserve">20</note>
            in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s24274" xml:space="preserve">at hora 23. </s>
            <s xml:id="echoid-s24275" xml:space="preserve">ab ortu per horam 4. </s>
            <s xml:id="echoid-s24276" xml:space="preserve">à media nocte in arcu nocturno ho
              <lb/>
            rarum 10. </s>
            <s xml:id="echoid-s24277" xml:space="preserve">Si igitur duo hæc puncta iungantur per lineam rectam, habebitur quidem in ſuperio-
              <lb/>
            ri horologio diurno hora 23. </s>
            <s xml:id="echoid-s24278" xml:space="preserve">ab occaſu, in nocturno verò hora 23. </s>
            <s xml:id="echoid-s24279" xml:space="preserve">ab ortu, vt ex demonſtratis ma-
              <lb/>
            nifeſtum eſt. </s>
            <s xml:id="echoid-s24280" xml:space="preserve">Hęc enim linea tangit maximum parallelorum ſemper apparentium. </s>
            <s xml:id="echoid-s24281" xml:space="preserve">Vnde vna pars
              <lb/>
            indicabit horam ab occaſu, & </s>
            <s xml:id="echoid-s24282" xml:space="preserve">altera horam ab ortu. </s>
            <s xml:id="echoid-s24283" xml:space="preserve">Hac etiam ratione pro hora 20. </s>
            <s xml:id="echoid-s24284" xml:space="preserve">ab occaſu du
              <lb/>
            ximus horam 20. </s>
            <s xml:id="echoid-s24285" xml:space="preserve">ab ortu per horam 1. </s>
            <s xml:id="echoid-s24286" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s24287" xml:space="preserve">nocte in arcu nocturno horarum 10. </s>
            <s xml:id="echoid-s24288" xml:space="preserve">& </s>
            <s xml:id="echoid-s24289" xml:space="preserve">per horam
              <lb/>
            2. </s>
            <s xml:id="echoid-s24290" xml:space="preserve">à media nocte in arcu nocturno horarum 12. </s>
            <s xml:id="echoid-s24291" xml:space="preserve">Hæc namque producta dat horam quoque 20. </s>
            <s xml:id="echoid-s24292" xml:space="preserve">ab
              <lb/>
            occaſu, &</s>
            <s xml:id="echoid-s24293" xml:space="preserve">c. </s>
            <s xml:id="echoid-s24294" xml:space="preserve">Propter anguſtiam autem ſpatij non eſt deſcripta tota Ellipſis ♋, quam ſecare deberẽt
              <lb/>
            horæ ſequentes ab occaſu 14. </s>
            <s xml:id="echoid-s24295" xml:space="preserve">15. </s>
            <s xml:id="echoid-s24296" xml:space="preserve">16. </s>
            <s xml:id="echoid-s24297" xml:space="preserve">17. </s>
            <s xml:id="echoid-s24298" xml:space="preserve">18. </s>
            <s xml:id="echoid-s24299" xml:space="preserve">19. </s>
            <s xml:id="echoid-s24300" xml:space="preserve">& </s>
            <s xml:id="echoid-s24301" xml:space="preserve">horæ ab ortu, de quibus in propoſ. </s>
            <s xml:id="echoid-s24302" xml:space="preserve">ſequenti
              <lb/>
            agemus, V. </s>
            <s xml:id="echoid-s24303" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s24304" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s24305" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s24306" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s24307" xml:space="preserve">X.</s>
            <s xml:id="echoid-s24308" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p>
            <s xml:id="echoid-s24309" xml:space="preserve">APTE etiam eaſdem horas deſcribemus ex tabula 7. </s>
            <s xml:id="echoid-s24310" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s24311" xml:space="preserve">33. </s>
            <s xml:id="echoid-s24312" xml:space="preserve">primi libri, ſi prius arcum
              <lb/>
            diurnum horarum 24. </s>
            <s xml:id="echoid-s24313" xml:space="preserve">deſignemus, qui lineas horarum 24. </s>
            <s xml:id="echoid-s24314" xml:space="preserve">& </s>
            <s xml:id="echoid-s24315" xml:space="preserve">12. </s>
            <s xml:id="echoid-s24316" xml:space="preserve">tanget, &</s>
            <s xml:id="echoid-s24317" xml:space="preserve">c.</s>
            <s xml:id="echoid-s24318" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s24319" xml:space="preserve">QVOD ſi per mutuas ſectiones horarum à meridie vel media nocte, & </s>
            <s xml:id="echoid-s24320" xml:space="preserve">ab ortu vel occaſu in-
              <lb/>
            ter ſe, quæ quidem in tabulis propoſ. </s>
            <s xml:id="echoid-s24321" xml:space="preserve">19. </s>
            <s xml:id="echoid-s24322" xml:space="preserve">& </s>
            <s xml:id="echoid-s24323" xml:space="preserve">20. </s>
            <s xml:id="echoid-s24324" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s24325" xml:space="preserve">1. </s>
            <s xml:id="echoid-s24326" xml:space="preserve">continentur, horologium deſcribere alicui
              <lb/>
            placeat, ducenda erit linea horæ 12. </s>
            <s xml:id="echoid-s24327" xml:space="preserve">ab ortu vel occaſu hoc modo. </s>
            <s xml:id="echoid-s24328" xml:space="preserve">In portione Analemmatis pro-
              <lb/>
              <note position="left" xlink:label="note-0384-05" xlink:href="note-0384-05a" xml:space="preserve">Linea horæ 12.
                <lb/>
              ab or. vel occ.
                <lb/>
              quomodo de-
                <lb/>
              ſctibatur.</note>
            poſ. </s>
            <s xml:id="echoid-s24329" xml:space="preserve">25. </s>
            <s xml:id="echoid-s24330" xml:space="preserve">huius libri à polo E, vtrinque numeretur altitudo poli ſupra Horizontem regionis, pro
              <lb/>
            qua horologium deſcribitur, vſque ad M, N, ducaturq́ue recta M N, quæ communis ſectio erit
              <lb/>
            Meridiani, & </s>
            <s xml:id="echoid-s24331" xml:space="preserve">paralleli omnium ſemper apparentium maximi, ſi polus E, fuerit ſeptentrionalis; </s>
            <s xml:id="echoid-s24332" xml:space="preserve">vel
              <lb/>
            maximi ſemper latentium, ſi E, ſit auſtralis polus. </s>
            <s xml:id="echoid-s24333" xml:space="preserve">Ductis deinde ex punctis M, N, per centrum
              <lb/>
            D, rectis M D, N D, erit vna illarum communis ſectio Meridiani, & </s>
            <s xml:id="echoid-s24334" xml:space="preserve">Horizontis, & </s>
            <s xml:id="echoid-s24335" xml:space="preserve">altera
              <lb/>
              <note position="left" xlink:label="note-0384-06" xlink:href="note-0384-06a" xml:space="preserve">40</note>
            ſectio communis Meridiani, & </s>
            <s xml:id="echoid-s24336" xml:space="preserve">circuli horæ 12. </s>
            <s xml:id="echoid-s24337" xml:space="preserve">ab ortu, vel occaſu; </s>
            <s xml:id="echoid-s24338" xml:space="preserve">cum Horizon, & </s>
            <s xml:id="echoid-s24339" xml:space="preserve">di-
              <lb/>
            ctus circulus parallelum illum maximum tangant in punctis M, N, Meridiani circuli. </s>
            <s xml:id="echoid-s24340" xml:space="preserve">Vtra
              <lb/>
            autem illarum ſit communis ſectio Horizontis, vel circuli horæ 12. </s>
            <s xml:id="echoid-s24341" xml:space="preserve">& </s>
            <s xml:id="echoid-s24342" xml:space="preserve">Meridiani, & </s>
            <s xml:id="echoid-s24343" xml:space="preserve">an E, ſit
              <lb/>
            polus arcticus, an artarcticus ſupra planum horologii eleuatus, apertè docebunt quatuor Ana-
              <lb/>
            lemmata propoſ. </s>
            <s xml:id="echoid-s24344" xml:space="preserve">25. </s>
            <s xml:id="echoid-s24345" xml:space="preserve">huius libri deſcripta. </s>
            <s xml:id="echoid-s24346" xml:space="preserve">Conſiderandum enim eſt, an Horizontis ſemi-
              <lb/>
            diameter auſtralis B E, an Borealis D E, per centrum extenſa occurrat plano ſuperioris horo-
              <lb/>
            logii M N; </s>
            <s xml:id="echoid-s24347" xml:space="preserve">& </s>
            <s xml:id="echoid-s24348" xml:space="preserve">in qua parte, an ſcilicet inter centrum M, & </s>
            <s xml:id="echoid-s24349" xml:space="preserve">punctum Aequatoris N, an verò vl-
              <lb/>
            tra centrum M, vel punctum N. </s>
            <s xml:id="echoid-s24350" xml:space="preserve">Nam in primo Analemmate Horizontis ſemidiameter auſtra-
              <lb/>
            lis B E, vltra centrum E, producta occurrit plano horologij M N, vltra N, punctum Aequato-
              <lb/>
            ris. </s>
            <s xml:id="echoid-s24351" xml:space="preserve">In ſecundo verò eadem ſemidiameter eidem plano occurrit inter centrum horologij M, & </s>
            <s xml:id="echoid-s24352" xml:space="preserve">N,
              <lb/>
              <note position="left" xlink:label="note-0384-07" xlink:href="note-0384-07a" xml:space="preserve">50</note>
            punctum Aequatoris. </s>
            <s xml:id="echoid-s24353" xml:space="preserve">In tertio autem ſemidiameter borealis Horizontis D E, vltra centrum E,
              <lb/>
            extenſa ſecat planum horologij M N, vltra M, centrum horologii. </s>
            <s xml:id="echoid-s24354" xml:space="preserve">In quarto denique eadem ſemi
              <lb/>
            diameter borealis idem planum ſecat inter M, & </s>
            <s xml:id="echoid-s24355" xml:space="preserve">centrum horologij, & </s>
            <s xml:id="echoid-s24356" xml:space="preserve">N, punctum Aequatoris.
              <lb/>
            </s>
            <s xml:id="echoid-s24357" xml:space="preserve">Ex his non difficile erit cognoſcere, quænam linea in dicta portione Analemmatis ſit communis
              <lb/>
            ſectio Meridiani, & </s>
            <s xml:id="echoid-s24358" xml:space="preserve">Horizontis, ac proinde, quæ communis ſectio ſit circuli horæ 12. </s>
            <s xml:id="echoid-s24359" xml:space="preserve">ab ortu,
              <lb/>
            vel occaſu; </s>
            <s xml:id="echoid-s24360" xml:space="preserve">& </s>
            <s xml:id="echoid-s24361" xml:space="preserve">an polus E, ſupra planum horologii eleuatus ſit arcticus, vel antarcticus. </s>
            <s xml:id="echoid-s24362" xml:space="preserve">Nam in
              <lb/>
            noſtro exemplo, quoniam planum inclinatum ex parte auſtrali ſupra Horizontem attollitur, ha-
              <lb/>
            betq́ue inclinationem maiorem complemento altitudinis poli, reſpondebit ei quartum Analem-
              <lb/>
            ma propoſitionis 25. </s>
            <s xml:id="echoid-s24363" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s24364" xml:space="preserve">Quare borealis ſemidiameter Horizontis planum horologii ſu
              <lb/>
            perioris ſecabit inter centrum horologij, & </s>
            <s xml:id="echoid-s24365" xml:space="preserve">linea æquinoctialem; </s>
            <s xml:id="echoid-s24366" xml:space="preserve">atque adeo recta M D, in dicta
              <lb/>
            portione Analemmatis eiuſdem propoſ. </s>
            <s xml:id="echoid-s24367" xml:space="preserve">25. </s>
            <s xml:id="echoid-s24368" xml:space="preserve">ſecans rectam per G, ductam inter H, centrum </s>
          </p>
        </div>
      </text>
    </echo>
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