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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111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
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281 - 290
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301 - 310
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GNOMONICES
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ſito exemplo eſt hora 3. </
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<
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<
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xml:id
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xml:space
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<
s
xml:id
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xml:space
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<
s
xml:id
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xml:space
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<
s
xml:id
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xml:space
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">ab occaſu. </
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<
s
xml:id
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xml:space
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<
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niam verò ſi velimus ducere lineam horæ 21. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ab occaſu, recta ex K, puncto horæ 21. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ab occaſu nõ
<
lb
/>
prius tranſit per centrum E, quàm per æquinoctialem lineam, accipiemus punctum oppoſitum
<
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/>
F, quod ſemper ab illo diſtat ſemicirculo integro, ſiue horis 12. </
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>
<
s
xml:id
="
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xml:space
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">ita vt F, ſit punctum horæ 9. </
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>
<
s
xml:id
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xml:space
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">ab
<
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occaſu; </
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<
s
xml:id
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xml:space
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">(quæ quidem habetur, ſi ad 21. </
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<
s
xml:id
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xml:space
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<
s
xml:id
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">ex ſumma, quoniam ſuperat 24. </
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<
s
xml:id
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mus 24.) </
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<
s
xml:id
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xml:space
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">& </
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<
s
xml:id
="
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"
xml:space
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">ex F, ducemus per E, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">K, rectam, quæ ſecet æquinoctialem lineam in L. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Nam recta
<
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/>
L H, ſecabit tropicum ♋, in M, puncto horæ 9. </
s
>
<
s
xml:id
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echoid-s24230
"
xml:space
="
preserve
">ab occaſu, vt proximè dictum eſt, producta autem
<
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/>
vltra centrum H, ſecabit eundem tropicum in O, puncto horæ 21. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ab occaſu, vt demonſtrauimus
<
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propoſ. </
s
>
<
s
xml:id
="
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"
xml:space
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">10. </
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>
<
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"
xml:space
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">ſuperioris libri. </
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>
<
s
xml:id
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xml:space
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">Cum ergo hora 21. </
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>
<
s
xml:id
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"
xml:space
="
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">ducatur quoque, vt habetur in tabula propoſ. </
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<
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xml:space
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<
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</
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<
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xml:space
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">lib. </
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<
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xml:space
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">1. </
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<
s
xml:id
="
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"
xml:space
="
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">per horam 3. </
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>
<
s
xml:id
="
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xml:space
="
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">à mer. </
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>
<
s
xml:id
="
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"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">noc. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">in linea æquinoctiali, indicabit recta per O, punctum, & </
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>
<
s
xml:id
="
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xml:space
="
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">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0384-01
"
xlink:href
="
note-0384-01a
"
xml:space
="
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">10</
note
>
per horam 3. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">à mer. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">noc. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">in linea æquinoctiali ducta horam 21. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ab occaſ
<
unsure
/>
u. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Sic etiam du-
<
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cta recta ex P, puncto horæ 1. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ab occaſu per E, centrum, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">per R, punctum horæ 13. </
s
>
<
s
xml:id
="
echoid-s24253
"
xml:space
="
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">ab occaſu ſe-
<
lb
/>
cat lineam æquinoctialem in A; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">recta autem A H, ſecat tropicum ♋, in B, puncto horæ 1. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">ab oc-
<
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/>
caſu, producta autem ſecat eundem in C, puncto horæ 13. </
s
>
<
s
xml:id
="
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xml:space
="
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">ab occaſu, &</
s
>
<
s
xml:id
="
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xml:space
="
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">c.</
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>
<
s
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="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
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">IN alijs modis nulla eſt difficultas. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Per ſolum enim arcum diurnum horarum 14. </
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>
<
s
xml:id
="
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"
xml:space
="
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">in ſuperio-
<
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<
note
position
="
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xlink:label
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xlink:href
="
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xml:space
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">E
<
unsure
/>
iuſdem Itali-
<
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/>
ci horologii de
<
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/>
ſcriptio per ar-
<
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/>
cus diurnos, no
<
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/>
cturnosq́ue.</
note
>
ri horologio, qui in portione nocturna eſt arcus nocturnus horarum 10. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">commodiſſimè horæ ab
<
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/>
occaſu deſcribentur ſecundum tabulas propoſ. </
s
>
<
s
xml:id
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xml:space
="
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">33. </
s
>
<
s
xml:id
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xml:space
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">primi libri. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Sed quoniam pro ſingulis horis ab
<
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occaſu ſingula tantum puncta habemus in arcu diurno horarum 14. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſumemus pro eiſdem nume
<
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/>
ro horis ab ortu alia puncta, ſiue in eodem arcu diurno horarum 14. </
s
>
<
s
xml:id
="
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xml:space
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">ſiue in nocturno horarũ 10.
<
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</
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>
<
s
xml:id
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xml:space
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">vt tabulæ propoſ. </
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<
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xml:id
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xml:space
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<
s
xml:id
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xml:space
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">primi libri indicant. </
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>
<
s
xml:id
="
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xml:space
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">Vt hora 23. </
s
>
<
s
xml:id
="
echoid-s24272
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xml:space
="
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">ab occaſu tranſit per horam 6. </
s
>
<
s
xml:id
="
echoid-s24273
"
xml:space
="
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">à meridie
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0384-03
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xlink:href
="
note-0384-03a
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xml:space
="
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">20</
note
>
in arcu diurno horarum 14. </
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>
<
s
xml:id
="
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xml:space
="
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">at hora 23. </
s
>
<
s
xml:id
="
echoid-s24275
"
xml:space
="
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">ab ortu per horam 4. </
s
>
<
s
xml:id
="
echoid-s24276
"
xml:space
="
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">à media nocte in arcu nocturno ho
<
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/>
rarum 10. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Si igitur duo hæc puncta iungantur per lineam rectam, habebitur quidem in ſuperio-
<
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/>
ri horologio diurno hora 23. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ab occaſu, in nocturno verò hora 23. </
s
>
<
s
xml:id
="
echoid-s24279
"
xml:space
="
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">ab ortu, vt ex demonſtratis ma-
<
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/>
nifeſtum eſt. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Hęc enim linea tangit maximum parallelorum ſemper apparentium. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Vnde vna pars
<
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/>
indicabit horam ab occaſu, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">altera horam ab ortu. </
s
>
<
s
xml:id
="
echoid-s24283
"
xml:space
="
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">Hac etiam ratione pro hora 20. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ab occaſu du
<
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/>
ximus horam 20. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ab ortu per horam 1. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">à med. </
s
>
<
s
xml:id
="
echoid-s24287
"
xml:space
="
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">nocte in arcu nocturno horarum 10. </
s
>
<
s
xml:id
="
echoid-s24288
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s24289
"
xml:space
="
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">per horam
<
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/>
2. </
s
>
<
s
xml:id
="
echoid-s24290
"
xml:space
="
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">à media nocte in arcu nocturno horarum 12. </
s
>
<
s
xml:id
="
echoid-s24291
"
xml:space
="
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">Hæc namque producta dat horam quoque 20. </
s
>
<
s
xml:id
="
echoid-s24292
"
xml:space
="
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">ab
<
lb
/>
occaſu, &</
s
>
<
s
xml:id
="
echoid-s24293
"
xml:space
="
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">c. </
s
>
<
s
xml:id
="
echoid-s24294
"
xml:space
="
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">Propter anguſtiam autem ſpatij non eſt deſcripta tota Ellipſis ♋, quam ſecare deberẽt
<
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/>
horæ ſequentes ab occaſu 14. </
s
>
<
s
xml:id
="
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xml:space
="
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">15. </
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<
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xml:id
="
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<
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xml:id
="
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">17. </
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>
<
s
xml:id
="
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="
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">18. </
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>
<
s
xml:id
="
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xml:space
="
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">19. </
s
>
<
s
xml:id
="
echoid-s24300
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s24301
"
xml:space
="
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">horæ ab ortu, de quibus in propoſ. </
s
>
<
s
xml:id
="
echoid-s24302
"
xml:space
="
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">ſequenti
<
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/>
agemus, V. </
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>
<
s
xml:id
="
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"
xml:space
="
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">VI. </
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>
<
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xml:id
="
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xml:space
="
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">VII. </
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>
<
s
xml:id
="
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xml:space
="
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">VIII. </
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>
<
s
xml:id
="
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"
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="
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">IX. </
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>
<
s
xml:id
="
echoid-s24307
"
xml:space
="
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">X.</
s
>
<
s
xml:id
="
echoid-s24308
"
xml:space
="
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"/>
</
p
>
<
note
position
="
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"
xml:space
="
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">30</
note
>
<
p
>
<
s
xml:id
="
echoid-s24309
"
xml:space
="
preserve
">APTE etiam eaſdem horas deſcribemus ex tabula 7. </
s
>
<
s
xml:id
="
echoid-s24310
"
xml:space
="
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">propoſ. </
s
>
<
s
xml:id
="
echoid-s24311
"
xml:space
="
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">33. </
s
>
<
s
xml:id
="
echoid-s24312
"
xml:space
="
preserve
">primi libri, ſi prius arcum
<
lb
/>
diurnum horarum 24. </
s
>
<
s
xml:id
="
echoid-s24313
"
xml:space
="
preserve
">deſignemus, qui lineas horarum 24. </
s
>
<
s
xml:id
="
echoid-s24314
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s24315
"
xml:space
="
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">12. </
s
>
<
s
xml:id
="
echoid-s24316
"
xml:space
="
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">tanget, &</
s
>
<
s
xml:id
="
echoid-s24317
"
xml:space
="
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">c.</
s
>
<
s
xml:id
="
echoid-s24318
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s24319
"
xml:space
="
preserve
">QVOD ſi per mutuas ſectiones horarum à meridie vel media nocte, & </
s
>
<
s
xml:id
="
echoid-s24320
"
xml:space
="
preserve
">ab ortu vel occaſu in-
<
lb
/>
ter ſe, quæ quidem in tabulis propoſ. </
s
>
<
s
xml:id
="
echoid-s24321
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s24322
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24323
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s24324
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s24325
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s24326
"
xml:space
="
preserve
">continentur, horologium deſcribere alicui
<
lb
/>
placeat, ducenda erit linea horæ 12. </
s
>
<
s
xml:id
="
echoid-s24327
"
xml:space
="
preserve
">ab ortu vel occaſu hoc modo. </
s
>
<
s
xml:id
="
echoid-s24328
"
xml:space
="
preserve
">In portione Analemmatis pro-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0384-05
"
xlink:href
="
note-0384-05a
"
xml:space
="
preserve
">Linea horæ 12.
<
lb
/>
ab or. vel occ.
<
lb
/>
quomodo de-
<
lb
/>
ſctibatur.</
note
>
poſ. </
s
>
<
s
xml:id
="
echoid-s24329
"
xml:space
="
preserve
">25. </
s
>
<
s
xml:id
="
echoid-s24330
"
xml:space
="
preserve
">huius libri à polo E, vtrinque numeretur altitudo poli ſupra Horizontem regionis, pro
<
lb
/>
qua horologium deſcribitur, vſque ad M, N, ducaturq́ue recta M N, quæ communis ſectio erit
<
lb
/>
Meridiani, & </
s
>
<
s
xml:id
="
echoid-s24331
"
xml:space
="
preserve
">paralleli omnium ſemper apparentium maximi, ſi polus E, fuerit ſeptentrionalis; </
s
>
<
s
xml:id
="
echoid-s24332
"
xml:space
="
preserve
">vel
<
lb
/>
maximi ſemper latentium, ſi E, ſit auſtralis polus. </
s
>
<
s
xml:id
="
echoid-s24333
"
xml:space
="
preserve
">Ductis deinde ex punctis M, N, per centrum
<
lb
/>
D, rectis M D, N D, erit vna illarum communis ſectio Meridiani, & </
s
>
<
s
xml:id
="
echoid-s24334
"
xml:space
="
preserve
">Horizontis, & </
s
>
<
s
xml:id
="
echoid-s24335
"
xml:space
="
preserve
">altera
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0384-06
"
xlink:href
="
note-0384-06a
"
xml:space
="
preserve
">40</
note
>
ſectio communis Meridiani, & </
s
>
<
s
xml:id
="
echoid-s24336
"
xml:space
="
preserve
">circuli horæ 12. </
s
>
<
s
xml:id
="
echoid-s24337
"
xml:space
="
preserve
">ab ortu, vel occaſu; </
s
>
<
s
xml:id
="
echoid-s24338
"
xml:space
="
preserve
">cum Horizon, & </
s
>
<
s
xml:id
="
echoid-s24339
"
xml:space
="
preserve
">di-
<
lb
/>
ctus circulus parallelum illum maximum tangant in punctis M, N, Meridiani circuli. </
s
>
<
s
xml:id
="
echoid-s24340
"
xml:space
="
preserve
">Vtra
<
lb
/>
autem illarum ſit communis ſectio Horizontis, vel circuli horæ 12. </
s
>
<
s
xml:id
="
echoid-s24341
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24342
"
xml:space
="
preserve
">Meridiani, & </
s
>
<
s
xml:id
="
echoid-s24343
"
xml:space
="
preserve
">an E, ſit
<
lb
/>
polus arcticus, an artarcticus ſupra planum horologii eleuatus, apertè docebunt quatuor Ana-
<
lb
/>
lemmata propoſ. </
s
>
<
s
xml:id
="
echoid-s24344
"
xml:space
="
preserve
">25. </
s
>
<
s
xml:id
="
echoid-s24345
"
xml:space
="
preserve
">huius libri deſcripta. </
s
>
<
s
xml:id
="
echoid-s24346
"
xml:space
="
preserve
">Conſiderandum enim eſt, an Horizontis ſemi-
<
lb
/>
diameter auſtralis B E, an Borealis D E, per centrum extenſa occurrat plano ſuperioris horo-
<
lb
/>
logii M N; </
s
>
<
s
xml:id
="
echoid-s24347
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24348
"
xml:space
="
preserve
">in qua parte, an ſcilicet inter centrum M, & </
s
>
<
s
xml:id
="
echoid-s24349
"
xml:space
="
preserve
">punctum Aequatoris N, an verò vl-
<
lb
/>
tra centrum M, vel punctum N. </
s
>
<
s
xml:id
="
echoid-s24350
"
xml:space
="
preserve
">Nam in primo Analemmate Horizontis ſemidiameter auſtra-
<
lb
/>
lis B E, vltra centrum E, producta occurrit plano horologij M N, vltra N, punctum Aequato-
<
lb
/>
ris. </
s
>
<
s
xml:id
="
echoid-s24351
"
xml:space
="
preserve
">In ſecundo verò eadem ſemidiameter eidem plano occurrit inter centrum horologij M, & </
s
>
<
s
xml:id
="
echoid-s24352
"
xml:space
="
preserve
">N,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0384-07
"
xlink:href
="
note-0384-07a
"
xml:space
="
preserve
">50</
note
>
punctum Aequatoris. </
s
>
<
s
xml:id
="
echoid-s24353
"
xml:space
="
preserve
">In tertio autem ſemidiameter borealis Horizontis D E, vltra centrum E,
<
lb
/>
extenſa ſecat planum horologij M N, vltra M, centrum horologii. </
s
>
<
s
xml:id
="
echoid-s24354
"
xml:space
="
preserve
">In quarto denique eadem ſemi
<
lb
/>
diameter borealis idem planum ſecat inter M, & </
s
>
<
s
xml:id
="
echoid-s24355
"
xml:space
="
preserve
">centrum horologij, & </
s
>
<
s
xml:id
="
echoid-s24356
"
xml:space
="
preserve
">N, punctum Aequatoris.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s24357
"
xml:space
="
preserve
">Ex his non difficile erit cognoſcere, quænam linea in dicta portione Analemmatis ſit communis
<
lb
/>
ſectio Meridiani, & </
s
>
<
s
xml:id
="
echoid-s24358
"
xml:space
="
preserve
">Horizontis, ac proinde, quæ communis ſectio ſit circuli horæ 12. </
s
>
<
s
xml:id
="
echoid-s24359
"
xml:space
="
preserve
">ab ortu,
<
lb
/>
vel occaſu; </
s
>
<
s
xml:id
="
echoid-s24360
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24361
"
xml:space
="
preserve
">an polus E, ſupra planum horologii eleuatus ſit arcticus, vel antarcticus. </
s
>
<
s
xml:id
="
echoid-s24362
"
xml:space
="
preserve
">Nam in
<
lb
/>
noſtro exemplo, quoniam planum inclinatum ex parte auſtrali ſupra Horizontem attollitur, ha-
<
lb
/>
betq́ue inclinationem maiorem complemento altitudinis poli, reſpondebit ei quartum Analem-
<
lb
/>
ma propoſitionis 25. </
s
>
<
s
xml:id
="
echoid-s24363
"
xml:space
="
preserve
">huius libri. </
s
>
<
s
xml:id
="
echoid-s24364
"
xml:space
="
preserve
">Quare borealis ſemidiameter Horizontis planum horologii ſu
<
lb
/>
perioris ſecabit inter centrum horologij, & </
s
>
<
s
xml:id
="
echoid-s24365
"
xml:space
="
preserve
">linea æquinoctialem; </
s
>
<
s
xml:id
="
echoid-s24366
"
xml:space
="
preserve
">atque adeo recta M D, in dicta
<
lb
/>
portione Analemmatis eiuſdem propoſ. </
s
>
<
s
xml:id
="
echoid-s24367
"
xml:space
="
preserve
">25. </
s
>
<
s
xml:id
="
echoid-s24368
"
xml:space
="
preserve
">ſecans rectam per G, ductam inter H, centrum </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>