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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GNOMONICES
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neis rectis in centro mundi ſe ſecantibus, per præcedentem propoſ. </
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<
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xml:space
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plani horologij ſectiones, id eſt, lineæ eorum horariæ, ſecent communes ſectiones illarum ſuper-
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ficierum conicarum, & </
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<
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xml:space
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">plani horologii, in illis punctis, in quibus lineæ illæ rectæ, quibus circuli
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horarij ſuperficies conicas ſecant, plano horologij, & </
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<
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xml:space
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">conicis ſectionibus occurrunt; </
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<
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xml:space
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">quandoqui-
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dem lineæ huiuſmodi horariæ, communes ſcilicet ſectiones circulorum horariorum, & </
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<
s
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xml:space
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">plani ho-
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rologij, exiſtunt in planis horariorum circulorum, qui ſuperficies conicas, atque adeo & </
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<
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conicas in plano horologij exiſtentes ibidem ſecant. </
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<
s
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xml:space
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">Hinc enim fit, vt cum planum horologij, & </
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<
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<
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plana circulorum horariorum in illis punctis ſe interſecent, & </
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<
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xml:space
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">tam illud quàm hæc plana intra
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conum, atque adeo & </
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<
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xml:space
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">intra conicas ſectiones tendant, earum communes ſectiones, nempe lineæ
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horariæ, cadant quoque ab illis punctis intra conum, ac proinde & </
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<
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xml:space
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">intra ſectiones conicas, cum
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poſt illa puncta neque à plano horologij, neque à planis dictorum circulorum recedant, ſed in
<
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vtriſque perpetuo exiſtant. </
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<
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xml:space
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">Conſtat ergo id, quod primo loco propoſitum eſt.</
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<
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</
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<
s
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xml:space
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">Q V I A vero circuli horarum ab ortu, vel occaſu tangunt eaſdem ſuperficies conicas, per
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candem propoſ. </
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<
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">antecedentem, in lineis illis, quibus eas ſecant circuli horarum à meridie, vel me-
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dia nocte; </
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<
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">efficitur, vt communes illorum, & </
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<
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">plani horologij ſectiones, hoc eſt, lineæ eorum ho-
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rariæ, tangant ſectiones conicas, quas facit horologij planum, in illis punctis, in quibus lineæ il-
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lę rectæ, quibus circuli horarii ſuperficies conicas tangunt, plano horologij, & </
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<
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occurrunt, in ijs nimirum, in quibus lineæ horarum à meridie, vel media nocte, ſectiones coni-
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cas ſecant; </
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<
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">quandoquidem lineæ horariæ ab ortu, vel occaſu, communes videlicet ſectiones cir-
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culorum horariorum, & </
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<
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">plani horologij, exiſtunt in planis circulorum horariorum, qui ibidem
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ſuperficies conicas, atque adeò & </
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<
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">conicas ſectiones in plano horologij exiſtentes tangunt. </
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<
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enim efficitur, vt cum planum horologij, & </
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<
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">plana circulorum horariorum in illis punctis ſe in-
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terſecent, & </
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<
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">illud quidem intra conum, atque adeo intra conicas ſectiones extendatur, hæc ve-
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ro plana extra conum, & </
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<
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">ideo extra ſectiones conicas protendantur, earum communes ſectiones,
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hoc eſt, horariæ lineæ, cadant ab illis punctis totæ extra conum, ac proinde & </
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<
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cas; </
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<
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">cum poſt illa puncta neque à plan o horologij, nec à planis dictorum circulorum recedant,
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ſed in vtriſque perpetuo exiſtant, quorum hæc tota extra conum, & </
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<
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</
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<
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<
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nocte ſecant, &</
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<
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">QVOD ſi planum horologij æquidiſtet alicui circulo horæ à meridie, vel media nocte, non ſecabit
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hic cir culus conicam ſectionem à plano horologij factam, cum nec ipſum planum horologij ſecet, vt con-
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ſtat. </
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<
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">Vnde neque linea horaria illius eandem conicam ſectionem ſecabit, at que adeo lineæ horariæ ab or-
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tu, vel occaſu, quarum circuli tangunt conicas ſuperficie
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s in lineis, in quibus à circulo illo horario à meri-
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die, vel media nocte ſccatur, non tangent conicas ſectiones, vt propoſ. </
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<
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<
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<
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<
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ab or. vel occ.
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quarum circuli
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tangunt paralle
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lum ſemper ap-
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parentium ma-
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ximum in eiſ-
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dem punctis, in
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quibus a circu-
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lo alicuius horę
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à mer. uel med.
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noc qui horolo
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gio æquidiſter,
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ſecatur, non cõ-
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ueniunt cum ſe
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ctionibus coni-
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cis, quas in ſu-
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perficiebus coni
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cis, quarum ba-
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ſes ſunt maxi-
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mi parallelorũ
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ſemper apparé-
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tium & laten-
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tium, facit horo
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logit planum:
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ſemper tamen
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longius produ-
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ctæ propinquio
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res fiunt coni-
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cis ſectionibus.</
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gij æquidiſtet, tangant autem maximum parallelorum ſemper apparen-
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tium duo circuli horarum ab ortu, vel occaſu in eiſdem punctis, in qui-
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bus à circulo illo horæ à meridie, vel media nocte ſecatur; </
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<
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illæ lineæ horarum ab ortu, vel occaſu ἀσύμπτοτοι, hoc eſt, non conue-
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nientes cum conicis ſectionibus, quas planum horologij facitin ſu-
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perficiebus conicis, quarum baſes ſunt maximi parallelorum ſemper ap-
<
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<
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parentium, & </
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<
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<
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cis ſectionibus propinquiores.</
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<
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">SECET ſuperficies conicas A B C, A D E, ad centrum A, coniunctas, quarum baſes ſint pa-
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rallelus D E, ſemper apparentium maximus, & </
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<
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Horizonte, circulus aliquis horarius à meridie, vel media nocte F G, per axem F G, rectis H I,
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K L, faciensq́, diametros parallelorum H K, L I, (cum eos, per propoſ. </
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<
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bifariam, atque adeo per eorum diametros) & </
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<
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">æquidiſtans plano horologij M N, quod per pro-
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poſ. </
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<
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<
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<
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<
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F G, M N, parallela ponuntur, erunt eorum communes ſectiones factæ à parallelo D E, </
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