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 SECVNDVS.
"/>
ex Analemmate conſtat) quàm planum horologii horizontalis, ad Meridianum rectum eſt, erit & </
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communis eorum ſectio ad eundem Meridianum recta; </
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<
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">atque adeò, per defin. </
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<
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<
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<
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<
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xml:space
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">Euclidis,
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<
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xml:space
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">19. vndec.</
note
>
ad lineam meridianam in puncto G, perpendicularis. </
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>
<
s
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"
xml:space
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">Recta igitur A B, quæ per G, ducta eſt ad
<
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/>
meridianam lineam perpendicularis, communis ſectio eſt plani horologii, & </
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>
<
s
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echoid-s11044
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xml:space
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">Verticalis propriè
<
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dicti. </
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>
<
s
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="
echoid-s11045
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xml:space
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">Et quia circuli omnes Verticales ſecant Horizontem in partes 360. </
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>
<
s
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echoid-s11046
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xml:space
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">ęquales, atque adeo & </
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>
<
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="
echoid-s11047
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">
<
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circulum, quem planum horologii Horizonti ęquidiſtans in ſphęra, per propoſ. </
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>
<
s
xml:id
="
echoid-s11048
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xml:space
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">1. </
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>
<
s
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echoid-s11049
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xml:space
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">lib. </
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<
s
xml:id
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echoid-s11050
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xml:space
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">1. </
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>
<
s
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xml:space
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">Theodo-
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ſii, facit; </
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>
<
s
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"
xml:space
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">propterea quòd per Zenith, ſeu polum Horizontis tranſeuntes diuidant, per propoſ. </
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>
<
s
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="
echoid-s11053
"
xml:space
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">10.
<
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</
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<
s
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xml:space
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">lib.</
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>
<
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">
<
unsure
/>
2. </
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>
<
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">Theod. </
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>
<
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xml:space
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">Horizontem, & </
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>
<
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="
echoid-s11058
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xml:space
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">circulos Horizonti parallelos, in ſegmenta ſimilia; </
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>
<
s
xml:id
="
echoid-s11059
"
xml:space
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">fit vt omnes Ver-
<
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ticales circuli, atque adeò & </
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>
<
s
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="
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"
xml:space
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">communes ipſorum, ac plani horologij ſectiones, tranſeant per pun-
<
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cta, quibus dictus circulus à plano horologij in ſphęra factus in 360. </
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>
<
s
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="
echoid-s11061
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xml:space
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">partes ęquales diuiditur. </
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<
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">Sed
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<
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">10</
note
>
eędem ſectiones ducuntur quoque per punctum G, ex propoſ. </
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>
<
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">18. </
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<
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">ſuperioris lib. </
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>
<
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xml:space
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">in quo nimirum
<
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communis ſectio circulorum Verticalium plano horologij occurrit. </
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>
<
s
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="
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xml:space
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">Igitur eędem ſectiones tran-
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ſibunt quoque per puncta diuiſionum circuli ex G, deſcripti. </
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>
<
s
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xml:space
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">Cum enim G, punctum, in quod
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cadit axis Horizontis, & </
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>
<
s
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">circuli à plano horologii in ſphęra facti, centrum ſit, per propoſ. </
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>
<
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xml:space
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">10. </
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<
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">lib.
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</
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<
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">1. </
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>
<
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xml:space
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">Theod. </
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>
<
s
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xml:space
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">dicti circuli ab horologij plano in ſphęra procreati, efficitur, vt circulus hic, & </
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>
<
s
xml:id
="
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"
xml:space
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">ille, quẽ
<
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ex G, deſcripſimus, in arcus ſimiles diuidantur à rectis lineis è centro G, egredientibus, per ea, quę
<
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in commentarijs in ſphæram ad finem cap. </
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>
<
s
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">1. </
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>
<
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">demonſtrauimus: </
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>
<
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">Ac proinde cum prior ſecetur
<
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in partes æquales, ſecabitur & </
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>
<
s
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xml:space
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">poſterior, quem ex G, deſcripſimus, in æquales partes. </
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>
<
s
xml:id
="
echoid-s11079
"
xml:space
="
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">Sunt ergo re-
<
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ctę illę ex G, emiſſæ per puncta, quibus circulus ex G, deſcriptus in partes ęquales eſt diuiſus, com
<
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/>
munes ſectiones plani horologii, & </
s
>
<
s
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="
echoid-s11080
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xml:space
="
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">circulorum Verticalium. </
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>
<
s
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echoid-s11081
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xml:space
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">Circulos igitur Verticales, &</
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>
<
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">c. </
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<
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">in eo-
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>
dem horizontali horologio deſcripſimus. </
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<
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">Quod erat faciendum.</
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</
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</
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<
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style
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">SCHOLIVM.</
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>
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lium circulor@
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in hotologio
<
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deſcriptorum,
<
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quibus cogno-
<
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ſcimus, quonã
<
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in quadrãte he-
<
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miſphærii ſupe
<
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ri Sol exiſtat.</
note
>
<
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<
s
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xml:space
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">EX circulis Verticalibus addiſcimus quolibet momento temporis, quanam in parte ex quatuor illis,
<
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in quas hemiſphærium ſuperum à Verticali proprio, ac Meridiano dirimitur, Sol verſetur. </
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>
<
s
xml:id
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xml:space
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">Nam in eaſ-
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dem quatuor partes diuiditur planum horologij à recta A B, quæ communis ſectio eſt ipſius plani horolo
<
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gij, & </
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>
<
s
xml:id
="
echoid-s11088
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xml:space
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">Verticalis propriè dicti, & </
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>
<
s
xml:id
="
echoid-s11089
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xml:space
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">à linea meridiana, ſiue ſectione communi eiuſdem plani horologij, & </
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>
<
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<
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Meridiani; </
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>
<
s
xml:id
="
echoid-s11091
"
xml:space
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">ita vt pars contenta intra rectas G B, G C, dicatur Quarta occidentalis, & </
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>
<
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">borea; </
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>
<
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xml:space
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">pars au-
<
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<
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="
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xml:space
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">Quatuor qua-
<
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drantes hemi-
<
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ſphęrii ſuperi in
<
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horologio hori-
<
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zontali qui ſint.</
note
>
tem intra rectas G B, G H, comprehenſa, Quarta occidentalis, & </
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>
<
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">auſtrina; </
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<
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xml:space
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">pars deinde, quam continẽt
<
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<
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xlink:label
="
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">30</
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>
rectę G A, G C, Quarta orientalis, ac borea; </
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>
<
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xml:space
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">pars denique, quam rectæ G A, G H, complectuntur, Quar-
<
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ta orientalis, & </
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>
<
s
xml:id
="
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">auſtrina. </
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>
<
s
xml:id
="
echoid-s11098
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xml:space
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">Vnde cum Sol proijciat ſemper vmbram ſtyli in contrariam partem ei,
<
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in qua exiſtit, facile iudicabimus ex vmbra, quanam in Quarta hemiſphærij commoretur. </
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>
<
s
xml:id
="
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xml:space
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">Nam ſi vm-
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bra ſtyli cadat in Quartam occidentalem, boream{q́ue}, quam intra lineas G B, G C, contineri dixi-
<
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mus, dicemus Solem tunc exiſtere in Quarta oppoſita, nempe in Quarta orientali, atque auſtrina, & </
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>
<
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="
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<
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ſic de cæteris.</
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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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">PRAETEREA ex eiſdem Verticalibus cognoſcimus, quanta ſit Solis diſtantia Verticalis,
<
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<
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xml:space
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">Quo pacto e@
<
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circulis Vertica
<
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libus cognoſca-
<
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tur, quantus ſit
<
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arcus Horizon-
<
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tis inter Ver-
<
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ticalem propriè
<
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dictum, & Ver-
<
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ticalem, qui per
<
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Solem ducitur:
<
unsure
/>
<
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qui quidem ar-
<
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cus dici ſolet di
<
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/>
ſtantia Vertica
<
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/>
lis.</
note
>
hoc eſi, quantum Verticalis ille circulus, in quo Sol quouis momento temporis exiſtit, recedat in Ho-
<
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/>
rizonte à Verticali proprie dicto, ſiue à puncto veri ortus, occaſusve. </
s
>
<
s
xml:id
="
echoid-s11103
"
xml:space
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">Nam ſi, exempli gratia, Sol
<
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deprehenſus fuerit, per ea, quæ proximè tradidimus, exiſtere in Quarta orientali, & </
s
>
<
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xml:space
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">auſtrina, cadat
<
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<
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="
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="
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">40</
note
>
autem vmbra tunc temporis in Verticalem lineam, cui aſcriptus eſt numerus hic, 30. </
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>
<
s
xml:id
="
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xml:space
="
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">diſtabit Vertica-
<
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lis, in quo Sol tunc eſt, à puncto veri ortus verſus auſtrum grad. </
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>
<
s
xml:id
="
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xml:space
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">30. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">hoc eſt, ar cus Horizontis inter Ver-
<
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ticalem propriè dictum, & </
s
>
<
s
xml:id
="
echoid-s11108
"
xml:space
="
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">Verticalem, qui tunc per centrum Solis incedit, interpoſitus orientalis eſt, & </
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>
<
s
xml:id
="
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xml:space
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">
<
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austrinus, complectitur{q́ue} grad. </
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>
<
s
xml:id
="
echoid-s11110
"
xml:space
="
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">30. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">atque ita de cæteris erit iudicandum.</
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>
<
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</
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>
</
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>
<
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xml:id
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type
="
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="
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="
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">
<
head
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xml:space
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">PROBLEMA 5. PROPOSITIO 5.</
head
>
<
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>
<
s
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xml:space
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">PARALLELOS Horizontis, hoc eſt, circulos minores al-
<
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titudinum aſtrorum, quos Almucantarath vocant, in eodem horolo-
<
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/>
<
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="
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xlink:label
="
note-0191-09
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="
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xml:space
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">50</
note
>
gio horizontali deſcribere.</
s
>
<
s
xml:id
="
echoid-s11114
"
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="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
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">DESCRIBATVR quadrans circuli A B C, qui in 90. </
s
>
<
s
xml:id
="
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xml:space
="
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">partes ęquales diſtribuatur, initio
<
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/>
<
note
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="
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"
xlink:label
="
note-0191-10
"
xlink:href
="
note-0191-10a
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xml:space
="
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">Deſcriptio pa-
<
lb
/>
rallelorum Ho
<
lb
/>
rizontis, qui Al
<
lb
/>
mucantarath di
<
unsure
/>
<
lb
/>
cuntur, in eodẽ
<
lb
/>
horologio hori-
<
lb
/>
zon tali.</
note
>
facto à ſemidiametro A B. </
s
>
<
s
xml:id
="
echoid-s11117
"
xml:space
="
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">(Nos eundem in 9. </
s
>
<
s
xml:id
="
echoid-s11118
"
xml:space
="
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">partes tantum diuiſimus, ob ſpatii anguſtias, ita
<
lb
/>
vt ſingulæ denos complectantur gradus.) </
s
>
<
s
xml:id
="
echoid-s11119
"
xml:space
="
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">Sumpta deinde A D, longitudine ſtyli in ſemidiametro
<
lb
/>
A C, ducatur per D, alteri ſemidiametro A B, parallela D E. </
s
>
<
s
xml:id
="
echoid-s11120
"
xml:space
="
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">Poſtremo eductis è centro A, per
<
lb
/>
diuiſionum puncta rectis, ſi in horologio ex G, loco gnomonis, tanquam centro, ad interualla re-
<
lb
/>
ctarum inter D, & </
s
>
<
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xml:id
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xml:space
="
preserve
">rectas ex A, emiſſas, comprehenſarum, circuli deſcribantur, vt in figura pręce-
<
lb
/>
dentis propoſ. </
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>
<
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echoid-s11122
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xml:space
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preserve
">qui tamen tropicos horologii non tranſcendant, deſcripti erunt paralleli Hori-
<
lb
/>
zontis, ſeu circuli altitudinum; </
s
>
<
s
xml:id
="
echoid-s11123
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xml:space
="
preserve
">qui quidem omnes conicę ſectiones ſunt, in quas, ex coroll. </
s
>
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xml:id
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xml:space
="
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