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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          <pb o="196" file="0216" n="216" rhead="GNOMONICES"/>
          <p>
            <s xml:id="echoid-s13023" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s13024" xml:space="preserve">Deſcribantur in horologio Aſtronomico, per propoſ. </s>
            <s xml:id="echoid-s13025" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13026" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s13027" xml:space="preserve">duo paralleli
              <lb/>
              <note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">Alia deſctiptio
                <lb/>
              horologii Itali-
                <lb/>
              ci horizonalis,
                <lb/>
              per arcus diur-
                <lb/>
              nos.</note>
            arcuum diurnorum, vnus horarum 14. </s>
            <s xml:id="echoid-s13028" xml:space="preserve">& </s>
            <s xml:id="echoid-s13029" xml:space="preserve">horarum 10. </s>
            <s xml:id="echoid-s13030" xml:space="preserve">alter; </s>
            <s xml:id="echoid-s13031" xml:space="preserve">Vel potius (quod quidem ſatis erit
              <lb/>
            ad propoſitum negotium) in horis à meridie, & </s>
            <s xml:id="echoid-s13032" xml:space="preserve">à media nocte imprimantur puncta, per quæ di-
              <lb/>
            ctiarcus tranſire debent, etiamſi arcus ipſi non ducantur. </s>
            <s xml:id="echoid-s13033" xml:space="preserve">Deinde diligenter conſiderentur tabu-
              <lb/>
            læ arcuum diurnorum horarum 10. </s>
            <s xml:id="echoid-s13034" xml:space="preserve">12. </s>
            <s xml:id="echoid-s13035" xml:space="preserve">& </s>
            <s xml:id="echoid-s13036" xml:space="preserve">14. </s>
            <s xml:id="echoid-s13037" xml:space="preserve">quas in ſcholio propoſ. </s>
            <s xml:id="echoid-s13038" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13039" xml:space="preserve">præcedentis libri poſui-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s13040" xml:space="preserve">In his enim ſtatim apparebit, per quasnam horas à meridie, vel media nocte dictorum ar-
              <lb/>
            cuum ducendæ ſint horæ ab occaſu Solis. </s>
            <s xml:id="echoid-s13041" xml:space="preserve">Ita namque vides, horam 23. </s>
            <s xml:id="echoid-s13042" xml:space="preserve">ab occaſu ducendam eſſe
              <lb/>
            per horam quartam à meridie in arcu horarum 10. </s>
            <s xml:id="echoid-s13043" xml:space="preserve">& </s>
            <s xml:id="echoid-s13044" xml:space="preserve">per horam quintam à meridie in arcu ho-
              <lb/>
            rarum 12. </s>
            <s xml:id="echoid-s13045" xml:space="preserve">(qui idem eſt hic, quod æquinoctialis linea) & </s>
            <s xml:id="echoid-s13046" xml:space="preserve">per horam ſextam à meridie in arcu ho-
              <lb/>
            rarum 14. </s>
            <s xml:id="echoid-s13047" xml:space="preserve">& </s>
            <s xml:id="echoid-s13048" xml:space="preserve">ita de cæteris. </s>
            <s xml:id="echoid-s13049" xml:space="preserve">Horæ autem, quæ in arcu horarum 10. </s>
            <s xml:id="echoid-s13050" xml:space="preserve">non habent puncta reſponden-
              <lb/>
              <note position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">10</note>
            tia, quales ſunt omnes horæ ante horam 15. </s>
            <s xml:id="echoid-s13051" xml:space="preserve">in noſtro exemplo, ducendæ ſunt per puncta in arcu-
              <lb/>
            bus horarum 14. </s>
            <s xml:id="echoid-s13052" xml:space="preserve">& </s>
            <s xml:id="echoid-s13053" xml:space="preserve">12. </s>
            <s xml:id="echoid-s13054" xml:space="preserve">Hora verò duodecima ab occaſu ducenda eſt parallela lineæ æquinoctiali
              <lb/>
            (nam linea horæ duodecimæ ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s13055" xml:space="preserve">linea æquinoctialis, parallelæ ſunt in horolo-
              <lb/>
            gio horizontali, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s13056" xml:space="preserve">22. </s>
            <s xml:id="echoid-s13057" xml:space="preserve">præcedentis libri docuimus) per horam ſeptimam à me-
              <lb/>
            dia nocte in arcu horarum 14. </s>
            <s xml:id="echoid-s13058" xml:space="preserve">vt ex tabula dicti arcus conſtat. </s>
            <s xml:id="echoid-s13059" xml:space="preserve">Quoniam verò hora vndecima ab
              <lb/>
            occaſu ſolum in arcu horarum 14. </s>
            <s xml:id="echoid-s13060" xml:space="preserve">punctum habet, nempe horam ſextam à media nocte, ducemus
              <lb/>
            horam vndecimam ab ortu per horam quartam à meridie in arcu horarũ 14. </s>
            <s xml:id="echoid-s13061" xml:space="preserve">& </s>
            <s xml:id="echoid-s13062" xml:space="preserve">per horam quin-
              <lb/>
            tam à meridie in arcu horarum 12. </s>
            <s xml:id="echoid-s13063" xml:space="preserve">vt ex dictorum arcuum tabalis conſtat: </s>
            <s xml:id="echoid-s13064" xml:space="preserve">hæc enim producta
              <lb/>
            dabit horam vndecimam ab occaſu, cum cadat in alteram partem paralleli ſemper apparentium
              <lb/>
            maximi, vt conſtat, ſi hic parallelus deſcriberetur. </s>
            <s xml:id="echoid-s13065" xml:space="preserve">Nam hora quæcunque ab ortu vltra arcum, ſeu
              <lb/>
              <note position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">20</note>
            parallelum ſemper apparentium, vel latentium maximum producta, dat eandem numero horam
              <lb/>
            ab occaſu, & </s>
            <s xml:id="echoid-s13066" xml:space="preserve">è contrario, vt in ſequenti ſcholio oſtendemus. </s>
            <s xml:id="echoid-s13067" xml:space="preserve">Tranſibit autem neceſſario hæc ho-
              <lb/>
            ra vndecima ab ortu producta, ſi erratum non fuerit, per horam ſextam à media nocte in arcus ho
              <lb/>
            rarum 14. </s>
            <s xml:id="echoid-s13068" xml:space="preserve">per quam nimirum hora vndecima ab occaſu ducenda eſt, ex tabula arcu diurni hora-
              <lb/>
            rum 14. </s>
            <s xml:id="echoid-s13069" xml:space="preserve">Simili ratione, quia hora decima ab occaſu nullum habet punctum in prædictis arcubus
              <lb/>
            diurnis, ducemus horam decimam ab ortu per horam tertiam à meridie in arcu horarum 14. </s>
            <s xml:id="echoid-s13070" xml:space="preserve">& </s>
            <s xml:id="echoid-s13071" xml:space="preserve">
              <lb/>
            per horam quartam à meridie in arcu horarum 12. </s>
            <s xml:id="echoid-s13072" xml:space="preserve">vt ex horum arcuum tabulis cõſtat. </s>
            <s xml:id="echoid-s13073" xml:space="preserve">Nam hęc
              <lb/>
            producta exhibebit horam decimam ab occaſu, ob cauſam prius dictam. </s>
            <s xml:id="echoid-s13074" xml:space="preserve">Atque ita procedemus in
              <lb/>
            aliis horis ante decimam, ſi in horologio ducendæ fuerint.</s>
            <s xml:id="echoid-s13075" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13076" xml:space="preserve">COMMODISSIME quoque deſcribi poterunt horæ ab occaſu, ſi deſcribatur parallelus
              <lb/>
              <note position="left" xlink:label="note-0216-04" xlink:href="note-0216-04a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horologii Itali-
                <lb/>
              ci hotizontalis,
                <lb/>
              per parallelum
                <lb/>
              @emper apparẽ-
                <lb/>
              tium maximũ,
                <lb/>
              ſiue pet arcum
                <lb/>
              diurnum hora-
                <lb/>
              @um 24.</note>
              <note position="left" xlink:label="note-0216-05" xlink:href="note-0216-05a" xml:space="preserve">30</note>
            omnium ſemper apparentium maximus, ſiue arcus diurnus horarum 24. </s>
            <s xml:id="echoid-s13077" xml:space="preserve">Nam rectæ ductæ per
              <lb/>
            horas à meridie, vel media nocte in arcu dicto, ſecundum tabulam arcus diurni horarum 24. </s>
            <s xml:id="echoid-s13078" xml:space="preserve">in
              <lb/>
            ſcholio propoſ. </s>
            <s xml:id="echoid-s13079" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13080" xml:space="preserve">præcedentis libri poſitam, & </s>
            <s xml:id="echoid-s13081" xml:space="preserve">per horas à meridie, vel media nocte arcus diur-
              <lb/>
            ni horarum 12. </s>
            <s xml:id="echoid-s13082" xml:space="preserve">veluti tabula huius arcus in eodem ſcholio propoſ. </s>
            <s xml:id="echoid-s13083" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13084" xml:space="preserve">præcedentis libri poſita do
              <lb/>
            cet, dabunt horarias lineas ab occaſu. </s>
            <s xml:id="echoid-s13085" xml:space="preserve">Tranſit enim hora 23. </s>
            <s xml:id="echoid-s13086" xml:space="preserve">ab occaſu per horam vndecimam à
              <lb/>
            meridie illius paralleli, ſeu arcus diurni horarum 24. </s>
            <s xml:id="echoid-s13087" xml:space="preserve">& </s>
            <s xml:id="echoid-s13088" xml:space="preserve">per horam quintam à meridie lineæ ęqui
              <lb/>
            noctialis, vel arcus horarum 12. </s>
            <s xml:id="echoid-s13089" xml:space="preserve">Hora verò 22. </s>
            <s xml:id="echoid-s13090" xml:space="preserve">per horam decimam prioris arcus, & </s>
            <s xml:id="echoid-s13091" xml:space="preserve">horam quar-
              <lb/>
            tam æquinoctialis lineæ, vel arcus poſterioris, &</s>
            <s xml:id="echoid-s13092" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13093" xml:space="preserve">Vt manifeſtum eſt ex tabulis dictorum arcuum
              <lb/>
            in ſcholio propoſ. </s>
            <s xml:id="echoid-s13094" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13095" xml:space="preserve">præcedentis libri deſcriptis. </s>
            <s xml:id="echoid-s13096" xml:space="preserve">Hora autem duodecima ab occaſu ducitur pa-
              <lb/>
            rallela horæ ſextæ à meridie, vel media nocte, ſiue lineæ æquinoctiali, per punctum, quo linea me-
              <lb/>
              <note position="left" xlink:label="note-0216-06" xlink:href="note-0216-06a" xml:space="preserve">40</note>
            ridiana, ſeu horæ 12. </s>
            <s xml:id="echoid-s13097" xml:space="preserve">à media nocte, quæ eſt hora meridiei, arcum diurnum horarum 24. </s>
            <s xml:id="echoid-s13098" xml:space="preserve">id eſt,
              <lb/>
            parallelum ſemper apparentium maximum, interſecat: </s>
            <s xml:id="echoid-s13099" xml:space="preserve">quoniam linea horæ 12. </s>
            <s xml:id="echoid-s13100" xml:space="preserve">ab ortu, vel oc-
              <lb/>
            caſu, & </s>
            <s xml:id="echoid-s13101" xml:space="preserve">linea horæ ſextæ à meridie, vel media nocte, & </s>
            <s xml:id="echoid-s13102" xml:space="preserve">æquinoctialis linea, parallelæ ſunt, vt ex ijs,
              <lb/>
            quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s13103" xml:space="preserve">22. </s>
            <s xml:id="echoid-s13104" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s13105" xml:space="preserve">ſcripſimus, manifeſtum eſt; </s>
            <s xml:id="echoid-s13106" xml:space="preserve">& </s>
            <s xml:id="echoid-s13107" xml:space="preserve">linea horæ 12. </s>
            <s xml:id="echoid-s13108" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13109" xml:space="preserve">vel
              <lb/>
            occ. </s>
            <s xml:id="echoid-s13110" xml:space="preserve">tranſit per horam duodecimam à media nocte in arcu diurno horarum 24. </s>
            <s xml:id="echoid-s13111" xml:space="preserve">vt patet ex tabula
              <lb/>
            arcus diurni horarum 24. </s>
            <s xml:id="echoid-s13112" xml:space="preserve">in ſcholio propoſ. </s>
            <s xml:id="echoid-s13113" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13114" xml:space="preserve">eiuſdem libri poſita. </s>
            <s xml:id="echoid-s13115" xml:space="preserve">Immo linea horæ duodeci-
              <lb/>
            mæ ab or. </s>
            <s xml:id="echoid-s13116" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13117" xml:space="preserve">& </s>
            <s xml:id="echoid-s13118" xml:space="preserve">reliquæ omnes ab or. </s>
            <s xml:id="echoid-s13119" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13120" xml:space="preserve">tangunt prædictum parallelum, ſeu arcum diur
              <lb/>
            num horarum 24. </s>
            <s xml:id="echoid-s13121" xml:space="preserve">in punctis, in quibus eundem lineæ horarum à mer. </s>
            <s xml:id="echoid-s13122" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s13123" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s13124" xml:space="preserve">ſecant, vt
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s13125" xml:space="preserve">14. </s>
            <s xml:id="echoid-s13126" xml:space="preserve">antecedentis lib. </s>
            <s xml:id="echoid-s13127" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s13128" xml:space="preserve">Vel etiam in quibuſdam horologiis ex iis, quæ ſe-
              <lb/>
            quuntur, arcum diurnum hor. </s>
            <s xml:id="echoid-s13129" xml:space="preserve">o. </s>
            <s xml:id="echoid-s13130" xml:space="preserve">vel nocturnum horarum 24. </s>
            <s xml:id="echoid-s13131" xml:space="preserve">hoc eſt, parallelum ſemper occul-
              <lb/>
              <note position="left" xlink:label="note-0216-07" xlink:href="note-0216-07a" xml:space="preserve">50</note>
            torum maximum. </s>
            <s xml:id="echoid-s13132" xml:space="preserve">Vnde@, vt accuratius horæ ab ortu, vel occaſu ducantur, deſcribi poterunt
              <lb/>
            huiuſmodi arcus, vt propoſ. </s>
            <s xml:id="echoid-s13133" xml:space="preserve">34. </s>
            <s xml:id="echoid-s13134" xml:space="preserve">& </s>
            <s xml:id="echoid-s13135" xml:space="preserve">36. </s>
            <s xml:id="echoid-s13136" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s13137" xml:space="preserve">à nobis factum eſt in horologio Meridiano,
              <lb/>
            ac polari.</s>
            <s xml:id="echoid-s13138" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13139" xml:space="preserve">PORRO ducta vna aliqua hora ab occaſu, vel etiam ab ortu, vt in ſequenti propoſ. </s>
            <s xml:id="echoid-s13140" xml:space="preserve">dicemus,
              <lb/>
              <note position="left" xlink:label="note-0216-08" xlink:href="note-0216-08a" xml:space="preserve">Qua ratione, ſi
                <lb/>
              benefic
                <unsure/>
              io arcuũ
                <lb/>
              diurnorum, vcl
                <lb/>
              nocturnorum,
                <lb/>
              una aliqua ho
                <lb/>
              @a ab occaſu,
                <lb/>
              aut ab ortu du-
                <lb/>
              cta ſit
                <unsure/>
              , aliæ faci
                <lb/>
              li negotio de-
                <lb/>
              ſc
                <unsure/>
              ribi poſſint.</note>
            beneficio arcuum diurnorum, vel etiam nocturnorum, vt in ſequentibus horologiis patebit, duce-
              <lb/>
            mus alias facili negotio per ſequentia puncta, quę inter ſe reſpondent, nulla alia habita conſidera-
              <lb/>
            tione tabularum, quas in ſcholio propoſ. </s>
            <s xml:id="echoid-s13141" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13142" xml:space="preserve">pręcedentis libri compoſuimus. </s>
            <s xml:id="echoid-s13143" xml:space="preserve">Vt ducta v g. </s>
            <s xml:id="echoid-s13144" xml:space="preserve">hora
              <lb/>
            23. </s>
            <s xml:id="echoid-s13145" xml:space="preserve">ducemus 22. </s>
            <s xml:id="echoid-s13146" xml:space="preserve">per proximum punctum in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s13147" xml:space="preserve">& </s>
            <s xml:id="echoid-s13148" xml:space="preserve">per proximum in arcu
              <lb/>
            diurno horarum 12. </s>
            <s xml:id="echoid-s13149" xml:space="preserve">& </s>
            <s xml:id="echoid-s13150" xml:space="preserve">per proximum in arcu diurno horarum 10. </s>
            <s xml:id="echoid-s13151" xml:space="preserve">Item 21. </s>
            <s xml:id="echoid-s13152" xml:space="preserve">per alia ſequentia tria
              <lb/>
            puncta, & </s>
            <s xml:id="echoid-s13153" xml:space="preserve">ſic de cæteris, vt in exemplo apparet.</s>
            <s xml:id="echoid-s13154" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13155" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s13156" xml:space="preserve">Deſcribatur linea horæ duodecimę ab ortu, vel occaſu hac ratione. </s>
            <s xml:id="echoid-s13157" xml:space="preserve">In </s>
          </p>
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