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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duo anguli A B D, A B K, ęquales in triangulis A B D, A B K; </
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<
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<
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">anguli ad A, ęquales ſunt,
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vtpote recti, eſtq́ue latus A B, dictis angulis adiacens commune. </
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<
s
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xml:space
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">Igitur latera A D, A k, æqualia
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erunt; </
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<
s
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"
xml:space
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">atque adeo cum per K, tranſeat linea horę 12. </
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<
s
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"
xml:space
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">ab ortu, vel occaſu, vt demonſtrauimus, per-
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ſpicuum eſt, ſi ipſi A D, ſumatur æqualis A K, per K, ducendam eſſe dictam lineam horæ 12. </
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<
s
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xml:space
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">quę
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quidem in K, tangit parallelum ſem per apparentium maximum. </
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<
s
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echoid-s18499
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xml:space
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">Quamobrem horologium Ita
<
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licum polare deſcripſimus. </
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>
<
s
xml:id
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"
xml:space
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">Quod faciendum erat.</
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<
s
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</
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</
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<
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<
head
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xml:space
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">PROBLEMA 47. PROPOSITIO 47.</
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<
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<
s
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xml:space
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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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">DESCRIBEMVS hoc horologium eiſdem rationibus fermè, quibus Italicum delineaui-
<
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">Horologii Ba-
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bylonici polaris
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deſcriptio.</
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mus: </
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<
s
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xml:space
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">ſi tamen in primo modo diuiſio circuli F G H I, in partes 24. </
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<
s
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xml:space
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">æquales initium habeat à ter
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mino orientali arcus diurni tam tropici ♋, quàm tropici ♑, tum in puncto b, tum in e. </
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>
<
s
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xml:space
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">Linea
<
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autem horę 12. </
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>
<
s
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xml:space
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">ducenda eſt parallela lineę ęquinoctiali per punctum in tropico ♋, inuentum,
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vt prius.</
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<
s
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</
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<
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<
s
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xml:space
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">IN ſecundo modo nullum prorſus diſcrimen eſt, ſi modo pro horis ab occ. </
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>
<
s
xml:id
="
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xml:space
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">quarum mentio
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facta eſt in antecedenti propoſ. </
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<
s
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="
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xml:space
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">ſumantur eędem ab ortu, &</
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>
<
s
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">c. </
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>
<
s
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xml:space
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">Exemplum horologij Babylonici
<
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habes in figura præcedentis propoſ. </
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>
<
s
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">vbi lineę parallelę inter ſe, & </
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>
<
s
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xml:space
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">ad lineam ęquinoctialem per-
<
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<
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xlink:label
="
note-0288-04
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xlink:href
="
note-0288-04a
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xml:space
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">20</
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>
pendiculares indicant horas à meridie, vel media nocte, quarum numeri aſcripti ſunt arcui diur-
<
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no horarum 24. </
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>
<
s
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="
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xml:space
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">& </
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>
<
s
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xml:space
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">nocturno arcui totidem horarum. </
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>
<
s
xml:id
="
echoid-s18519
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xml:space
="
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">Deinde lineę, quibus appoſiti ſunt numeri
<
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infra lineam ęquinoctialem, indicant horas Italicas. </
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>
<
s
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="
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xml:space
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">Lineę denique, quibus numeri ſupra lineã
<
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ęquinoctialem aſcripti ſunt, horis Babylonicis, ſeu ab ortu, tribuendę ſunt. </
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>
<
s
xml:id
="
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xml:space
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">Horologium igitur
<
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Babylonicum polare delineauimus. </
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>
<
s
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xml:space
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">Quod erat faciendum.</
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<
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</
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</
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<
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rologium Itali
<
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cum polare dif-
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ferat a Eabylo-
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nico polari.</
note
>
<
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<
s
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="
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xml:space
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">EX figura præcedentis horologii manifeſtum eſt, horologium Babylonicum non differre ab Italico,
<
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niſi ſitu, & </
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<
s
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">ordine horarum, quemadmodum in horizontali horologio expoſuimus.</
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<
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</
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<
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<
s
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">HABET autem inferius horologium polare à ſuperiori ortum, ſi omnium horarum lineæ vltra ho-
<
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<
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">Qua ratione
<
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Infcrius horo-
<
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logium polare
<
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iam Italicum,
<
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quàm Babylo-
<
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nicum à Supe-
<
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riore ortum ha
<
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beat.</
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>
rizontalem lineam producantur, & </
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>
<
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xml:space
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">ſuperior pars mutetur in inferiorem, & </
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>
<
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xml:space
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">quæ dextra eſt poſt hanc mu
<
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tationem, vertatur in ſiniſtram, vt oſtendimus in ſcholio propoſ. </
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<
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<
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<
s
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xml:space
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">Quæ autem horæ in infe-
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riori horologio numerandę ſint ab occaſu, & </
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>
<
s
xml:id
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xml:space
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">quæ ab ortu, cognoſcemus ex iis, quæ in ſcholio propoſ. </
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<
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<
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</
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<
s
xml:id
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">huius lib. </
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<
s
xml:id
="
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xml:space
="
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">ſcripſimus.</
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>
<
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</
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<
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<
s
xml:id
="
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xml:space
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">NON eſt etiam prætereundum hoc loco, in ea regione, vbi altitudo poli æqualis eſt complemento
<
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<
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="
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">In latitudine
<
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loci gr. 66. Min.
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30. horæ ab or.
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& occ. tangunt
<
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duos tropicos.
<
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In maiori vero
<
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latitudine horę
<
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ab or. & occ. nõ
<
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perueniunt ad
<
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tropicos, ſed tan
<
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gunt alios pa-
<
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rallelos propin-
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quiores lineæ
<
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æquinoctiali, tã
<
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in horologio
<
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Meridiano, q̃
<
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in polari.</
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>
maximæ declinationis Solis, hoc eſt, grad. </
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<
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<
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">Min. </
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<
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">30. </
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<
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">duos tropicos fungi munere duorum parallelorum,
<
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quorum vnus ſemper apparentium, alter verò ſemper latentium maximus eſt. </
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>
<
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xml:space
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">Vnde lineę horarum ab
<
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ortu, vel occaſu tangent duos tropicos in horis à meridie, vel media nocte tam in utroque horologio Me-
<
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ridiano, quàm in Polari. </
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>
<
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="
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xml:space
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">In ea autem regione, ubi altitudo poli maior eſt, quàm grad. </
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<
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<
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<
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">30. </
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<
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">duos
<
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<
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>
prędictos parallelos cadere intra duos tropicos, ita vt lineæ horarum ab ortu, vel occaſu illos parallelos
<
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tangentes ad ipſos tropicos nullo modo perueniant. </
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>
<
s
xml:id
="
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xml:space
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">Vmbra enim ſtyli monſtrare tunc non poteſt horas
<
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ab ortu, uel occaſu Solis elapſas, cum Sol exiſtens in tropicis neque oriatur, neque occidat, ſed perpetuo
<
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ſupra Horizontem exiſtat, uel infra.</
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<
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</
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<
head
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xml:space
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">PROBLEMA 48. PROPOSITIO 48.</
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>
<
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<
s
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xml:space
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">HOROLOGIVM Antiquum polare conſtituere.</
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>
<
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</
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<
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<
s
xml:id
="
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">SECETVR arcus diurnus tam tropici ♋, a F b, quàm tropici ♑, d F e, in circulo F G H I,
<
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<
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>
<
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xlink:label
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xml:space
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">Deſcriptio ho-
<
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rologii Antiqui
<
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polaris.</
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>
in 12. </
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>
<
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="
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">partes ęquales. </
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>
<
s
xml:id
="
echoid-s18555
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xml:space
="
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">Ex his enim inueniemus in vtroque tropico puncta, per quæ ducendę erunt
<
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/>
horę inęquales, non aliter, ac in præcedentibus duabus propoſitionibus puncta horarum ab ortu,
<
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/>
& </
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>
<
s
xml:id
="
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xml:space
="
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">occaſu Solis in eiſdem tropicis inueſtigauimus. </
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>
<
s
xml:id
="
echoid-s18557
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xml:space
="
preserve
">Tranſibunt autem neceſſario horæ inæqua-
<
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/>
les per puncta horarum à meridie, vel media nocte in linea ęquinoctiali, vt ſupra docuimus in ho-
<
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rizontali horologio propoſ. </
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>
<
s
xml:id
="
echoid-s18558
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xml:space
="
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">12. </
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>
<
s
xml:id
="
echoid-s18559
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="
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">huius libri. </
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>
<
s
xml:id
="
echoid-s18560
"
xml:space
="
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">Certum autem eſt, vt ex figura appoſita apparet, ho-
<
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/>
ram 1. </
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>
<
s
xml:id
="
echoid-s18561
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xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s18562
"
xml:space
="
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">11. </
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>
<
s
xml:id
="
echoid-s18563
"
xml:space
="
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">non cadere in horologium ſuperius, cum Sol in principio ♋, exiſtit.</
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>
<
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"/>
</
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>
<
p
>
<
s
xml:id
="
echoid-s18565
"
xml:space
="
preserve
">PER arcus quoque duos diurnos in horologio deſcriptos, quorum vnus horas 18. </
s
>
<
s
xml:id
="
echoid-s18566
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s18567
"
xml:space
="
preserve
">al-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0288-12
"
xlink:href
="
note-0288-12a
"
xml:space
="
preserve
">Deſcriptio An-
<
lb
/>
tiqui horologii
<
lb
/>
polaris per ar-
<
lb
/>
cus diurnos ho
<
lb
/>
rarum 6. & 18.</
note
>
ter ſex comprehendat, conſtruemus idem horologium Antiquum, vt in ſuperioribus factum
<
lb
/>
eſt, propoſ. </
s
>
<
s
xml:id
="
echoid-s18568
"
xml:space
="
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">12. </
s
>
<
s
xml:id
="
echoid-s18569
"
xml:space
="
preserve
">24. </
s
>
<
s
xml:id
="
echoid-s18570
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s18571
"
xml:space
="
preserve
">36. </
s
>
<
s
xml:id
="
echoid-s18572
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s18573
"
xml:space
="
preserve
">Id quod figura appoſita perſpicuè docet. </
s
>
<
s
xml:id
="
echoid-s18574
"
xml:space
="
preserve
">Horologiũ igitur
<
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Antiquum polare conſtituimus. </
s
>
<
s
xml:id
="
echoid-s18575
"
xml:space
="
preserve
">Quod faciendum erat.</
s
>
<
s
xml:id
="
echoid-s18576
"
xml:space
="
preserve
"/>
</
p
>
</
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</
text
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</
echo
>