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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LIBER TERTIVS.
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A, vt habeatur punctum O, orientalius, in quo Meridianus Horizontis Aequatorem ſecat ſupra
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Horizontem. </
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<
s
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echoid-s20280
"
xml:space
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">Si enim planũ horologii ponatur verſus meridiem, ita vt æquinoctialis linea G H,
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ſit infra punctum C, & </
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<
s
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"
xml:space
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">circulus ex L, deſcriptus circa rectam G H, circumuerti intelligatur, do-
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nec cum plano Aequatoris coniungatur, erit punctum N, verſus ſuperius hemiſphærium, & </
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<
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echoid-s20282
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xml:space
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tes ad ſiniſtram ipſius C N, verſus A, tendent occidentem verſus, & </
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>
<
s
xml:id
="
echoid-s20283
"
xml:space
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">partes ad dextram eiuſdem
<
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rectæ C N, verſus B, in orientem vergent. </
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>
<
s
xml:id
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echoid-s20284
"
xml:space
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">Si verò planum à meridie in occaſum declinet, ſuppu-
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tanda erit inclinatio dicta Meridianorum à puncto N, ad dextram partem verſus B, nempe ad
<
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partes orientales circuli ex L, deſcripti, ſi poſitionem illam, de qua proximè diximus, adeptus ſit:
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</
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<
s
xml:id
="
echoid-s20285
"
xml:space
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">quia tunc Meridianus plani declinantis eſt minus orientalis, quàm Meridianus Horizontis, vt
<
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ex ſphæra materiali facile colligi poteſt, & </
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>
<
s
xml:id
="
echoid-s20286
"
xml:space
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">ex ijs, quæ proximè ſcripſimus, quòd tunc polus eius ex
<
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<
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note-0317-01
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">10</
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parte meridie conſtitutus ſit in quadrante Horizontis auſtrali, atque occidentali.</
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<
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</
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<
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<
s
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"
xml:space
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">NON docemus autem, quamnam in partem numeranda ſit dicta Meridianorum inclinatio
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in plano, quod à ſeptentrione in ortum, vel occaſum declinat, ne præceptorum multitudine in-
<
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genium Lectoris confundatur, cum præſertim ex auſtrali horologio deſcripto boreale facilimo
<
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negotio deduci poſſit, vt in ſcholio propoſ. </
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>
<
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="
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xml:space
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">13. </
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>
<
s
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"
xml:space
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">libri ſuperioris docuimus, & </
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>
<
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="
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xml:space
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">clarius ex ſequenti
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ſcholio patebit. </
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>
<
s
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="
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"
xml:space
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">Accedit etiam, quòd ex præceptis traditis pro plano, quod à meridie declinat,
<
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quilibet proprio Marte inuenire ſine magno labore poterit, in quam partem numerare debeat di-
<
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ctam inclinationem in circulo ex L, deſcripto, obferuando diligenter, an Meridianus loci, ſeu pro-
<
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poſiti Horizontis in Aequatore infra Horizontem orientalior ſit, occidentaliorve Meridiano pro-
<
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prio plani declinantis. </
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>
<
s
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xml:space
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">Dico infra Horizontem, quia in boreali horologio punctum N, ſpectat
<
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<
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ad hemiſphærium inferius, adeò vt Meridianus proprius plani declinantis ipſum ſecet infra Ho-
<
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rizontem in N, puncto, vt patet, ſi rectè poſitio borealis horologii conſideretur, vna cum circulo
<
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deſcripto ex L. </
s
>
<
s
xml:id
="
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xml:space
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">Nam ſi orientalior fuerit, numeranda erit illa inclinatio ab N, verſus partes orien-
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tales; </
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>
<
s
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="
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xml:space
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">verſus occidentales verò, ſi occidentalior. </
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>
<
s
xml:id
="
echoid-s20296
"
xml:space
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">Non erit autem difficile iudicare, quænam par-
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tes circuli ex L, deſcripti ab N, tendant verſus ortum, & </
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>
<
s
xml:id
="
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xml:space
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">quæ occaſum verſus; </
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>
<
s
xml:id
="
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xml:space
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">ſi circulus ipſe vnà
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cum horologio boreali in proprio ſitu cogitetur eſſe poſitus, ita vt punctum N, ad inferius hemi-
<
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ſphærium ſpectet, & </
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>
<
s
xml:id
="
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">eius centrum cum centro mundi ſit coniunctum. </
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<
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xml:space
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">Partes enim ad ſiniſtram,
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nobis ad horologium boreale conuerſis, erunt orientales, & </
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<
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<
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</
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<
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<
s
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xml:space
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">IAM verò ſi per puncta diuiſionũ, & </
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<
s
xml:id
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xml:space
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">per centrum L, ducantur rectæ occultæ ſecantes lineam
<
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æquinoctialem G H, habebuntur puncta in linea æquinoctiali, per quæ lineæ emiſſæ ex centro C,
<
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<
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xlink:label
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">30</
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dabunt horas à meridie, vel media nocte, vt in horizontali horologio demonſtrauimus, ita ta-
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men, vt linea porrecta ex C, per punctum M, vbi recta O L, lineæ æquinoctiali occurrit, ſit linea
<
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horæ 12. </
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>
<
s
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="
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xml:space
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">meridiei in auſtrali horologio, mediæ noctis verò in boreali, non autem recta C G L,
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vt in horizontali horologio; </
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>
<
s
xml:id
="
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"
xml:space
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">quoniam in plano declinante, ſi circulus ex L, deſcriptus intelliga-
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tur in propria poſitione, nimirum in plano Aequatoris circa eius centrum deſcriptus, Meridia-
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nus Horizontis, ſeu circulus horæ 12. </
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>
<
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="
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xml:space
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">tranſit per punctum O, ac proinde per rectam O L, occur-
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rens plano horologij in M; </
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<
s
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">adeo, vt in auſtrali horologio punctum O, ſit in ſemicirculo Meridia-
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ni ſupra Horizontem, ac propterea meridiem indicet, in boreali verò idem exiſtat in reliquo ſemi
<
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circulo, atque adeo ad mediam noctem pertineat, vt manifeſtum eſt, ſi circulus ex L, deſcriptus
<
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in inferiori quoque horologio intelligatur in propria poſitione. </
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<
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xml:space
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">Reliquæ horæ hunc ordinem ha
<
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<
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bent. </
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<
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xml:space
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">In vtroque horologio lineæ, quæ 12. </
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<
s
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xml:space
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">horam ſequuntur verſus B, pertinent ad horas poſt
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meridiem; </
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<
s
xml:id
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echoid-s20312
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xml:space
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">quæ verò verſus A, ad horas poſt mediam noctem. </
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<
s
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">Stylus, eiuſq́ue locus in recta
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C N, reperietur, vt in horologio horizontali. </
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<
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xml:space
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">Nam ſi recta C K, ſumatur æqualis rectæ H G, por-
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tionis Analemmatis, erit K, locus ſtyli. </
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<
s
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xml:space
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">Quòd ſi fiat in horologio triangulum C G I, æquale trian
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gulo H I D, portionis Analemmatis ducaturq́; </
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<
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xml:id
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xml:space
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">recta K I, erit I K, longitudo ſtyli, & </
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<
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xml:id
="
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xml:space
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">omnino æqua-
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lis rectæ aſſumptæ D G, vt manifeſtum eſt. </
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<
s
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="
echoid-s20318
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xml:space
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">Cum enim latera C I, C K, trianguli C I K, æqualia
<
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ſint lateribus D H, H G, trianguli D H G, & </
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<
s
xml:id
="
echoid-s20319
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xml:space
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">anguli C, H, æquales, ex conſtructione; </
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<
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="
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">erunt & </
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<
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">ba
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<
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xml:space
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">4. primi.</
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ſes I K, D G, æquales inter ſe.</
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<
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</
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<
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<
s
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xml:space
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">POSSVMVS quoque eiuſdem horologii deſcriptionem inſtituere hoc modo. </
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<
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xml:space
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">Per propoſ.
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</
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<
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="
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xml:space
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<
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xlink:label
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note-0317-06
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xlink:href
="
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xml:space
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">Alia deſcriptio
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eiuſdem horo-
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logii declinan-
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tis à Verticali.</
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30. </
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<
s
xml:id
="
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xml:space
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">primi libri reperiatur arcus plani declinantis interceptus inter Meridianum Horizontis, & </
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<
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<
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<
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xlink:label
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xlink:href
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">50</
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>
circulum maximum, qui per polos eiuſdem plani ducitur, altitudinemq́ue poli ſupra ipſum me-
<
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titur, tanquam proprius eius Meridianus. </
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>
<
s
xml:id
="
echoid-s20328
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xml:space
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">Hic arcus in noſtro exemplo comprehendit grad. </
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<
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xml:id
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">29.
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</
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<
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<
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xlink:label
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xml:space
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">Quantus ſit ar-
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cus plani decli-
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nãtis inter eius
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Meridianum,
<
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& Meridianum
<
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Horizontis in-
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teriectus.</
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Min. </
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<
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<
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">ferè. </
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<
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<
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">29. </
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<
s
xml:id
="
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xml:space
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">eiuſdem primi libri inueniatur altitudo poli ſupra planum de-
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clinans, quæ in eodem noſtro exemplo continet grad. </
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<
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">40. </
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<
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">Min. </
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<
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">3. </
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<
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xml:space
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">fere. </
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<
s
xml:id
="
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xml:space
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">Deinde in plano aliquo
<
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ducatur recta C D, vtcunque pro linea meridiana, ſeu horæ 12. </
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>
<
s
xml:id
="
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xml:space
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">in qua ſumpto puncto quocun-
<
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que C, deſcribatur ex eo arcus D P, in quo à recta C D, nempe à D, puncto numeretur arcus pla-
<
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ni declinantis interceptus inter Meridianum ipſius, & </
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<
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xml:id
="
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xml:space
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">Meridianum Horizontis, vſque ad P,
<
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quem arcum diximus continere grad. </
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<
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xml:id
="
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xml:space
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">29. </
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>
<
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xml:id
="
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">Min. </
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<
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xml:id
="
echoid-s20345
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xml:space
="
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">3. </
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>
<
s
xml:id
="
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xml:space
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">ferè, ducaturq́ue ex C, per P, recta C P, quæ
<
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communis erit ſectio plani horologii declinantis, & </
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>
<
s
xml:id
="
echoid-s20347
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xml:space
="
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">Meridiani eiuſdem plani, vt infra mox de-
<
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monſtrabimus. </
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>
<
s
xml:id
="
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xml:space
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">Vtautem ſciamus, quam in partem numerandus ſit arcus D P, conſideranda
<
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ſunt ea, quæ in præcedenti deſcriptione tradidimus. </
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>
<
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="
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xml:space
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">Nam ſi planum à meridie declinet in </
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