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.
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eandem quoque cum circulo horæ 6. </
s
>
<
s
xml:id
="
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xml:space
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">à meridie, vel media nocte, per propoſ. </
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<
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xml:space
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">17. </
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<
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xml:id
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xml:space
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">eiuſdem lib. </
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<
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xml:space
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perioris; </
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<
s
xml:id
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xml:space
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">efficitur, vt duo illi circuli, & </
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>
<
s
xml:id
="
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xml:space
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">Aequator, & </
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>
<
s
xml:id
="
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xml:space
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">circulus horæ 6. </
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>
<
s
xml:id
="
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"
xml:space
="
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">à meridie, vel media nocte,
<
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habeant vnam & </
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>
<
s
xml:id
="
echoid-s18315
"
xml:space
="
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">eandem ſectionem communem, nempe eam, per quam circulus dictæ horæ 6.
<
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</
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>
<
s
xml:id
="
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"
xml:space
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">Aequatorem ſecat. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Cum ergo huic circulo, atque adeo dictæ communi ſectioni omnium illorũ,
<
lb
/>
æquidiſtet planum horologij polaris, erunt per propoſ. </
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>
<
s
xml:id
="
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"
xml:space
="
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">18. </
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>
<
s
xml:id
="
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xml:space
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">ſuperioris lib. </
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>
<
s
xml:id
="
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xml:space
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">reliquorum circulorum
<
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ſectiones cum plano horologij, quales ſunt lineæ horæ 12. </
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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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">24. </
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<
s
xml:id
="
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"
xml:space
="
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">ab ortu, vel occaſu, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">linea æqui-
<
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/>
noctialis, inter ſe ſe parallelæ. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Atque hæc de horologio ſuperiori intelligenda ſunt. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Pro inferiori
<
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autem ſatis erit, illud ex ſuperiori elicere, vt in ſequenti propoſ. </
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>
<
s
xml:id
="
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"
xml:space
="
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">docebimus.</
s
>
<
s
xml:id
="
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"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
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">SIGNATIS quoque in lineis horarum à meridie, vel media nocte punctis, ſecundum do-
<
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/>
<
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position
="
right
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xlink:label
="
note-0287-01
"
xlink:href
="
note-0287-01a
"
xml:space
="
preserve
">Alia deſcriptio
<
lb
/>
horologii Itali-
<
lb
/>
ci polaris per ar
<
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/>
cus diurnos ho
<
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/>
rarũ 10. & 14.</
note
>
ctrinam propoſ. </
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>
<
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="
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xml:space
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">38. </
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>
<
s
xml:id
="
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xml:space
="
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">huius libri, per quæ paralleli, quorum vnus ſit horarum 14. </
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>
<
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xml:id
="
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xml:space
="
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">& </
s
>
<
s
xml:id
="
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"
xml:space
="
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">alter 10. </
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>
<
s
xml:id
="
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"
xml:space
="
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">du-
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0287-02
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xlink:href
="
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xml:space
="
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">10</
note
>
cuntur, deſcribemus beneficio illorum, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">tabularum, quas in ſcholio propoſ. </
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>
<
s
xml:id
="
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"
xml:space
="
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">33. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſuperioris lib.
<
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/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
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">compoſuimus, horologium Italicum, vt in ſuperioribus horologijs tradidimus.</
s
>
<
s
xml:id
="
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xml:space
="
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"/>
</
p
>
<
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>
<
s
xml:id
="
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"
xml:space
="
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">RVRSVS commodiſſime idem conſtruemus per duos parallelos, quorum vnus eſt ſemper
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0287-03
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xlink:href
="
note-0287-03a
"
xml:space
="
preserve
">Alia a dhuc de-
<
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/>
ſcriptio eiuſdẽ
<
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/>
horologii Itali-
<
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/>
ci polatis per
<
lb
/>
arcum diurnũ,
<
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/>
nocturnum que
<
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/>
horarum 24.</
note
>
apparentium maximus, hoc eſt, arcus diurnus horarum 24. </
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>
<
s
xml:id
="
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xml:space
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">alter verò maximus perpetuo delite-
<
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ſcentium, ſeu arcus nocturnus horarum 24. </
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>
<
s
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xml:space
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">ſi in horis à meridie, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">media nocte notentur puncta,
<
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/>
per quę tranſeunt. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Nam horæ ab ortu, vel occaſu tangunt dictos parallelos in plano horologij de-
<
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/>
ſcriptos in punctis, per quæ ducuntur horæ à meridie, vel media nocte, exceptis horis 6. </
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>
<
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="
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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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">18. </
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<
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="
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xml:space
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">quę
<
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/>
cum dictis hyperbolis non conueniunt, vt ex coroll. </
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>
<
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xml:space
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">propoſ. </
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<
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">15. </
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<
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">ſuperioris lib. </
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>
<
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xml:space
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">conſtat. </
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<
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xml:space
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">Quænam
<
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autem horæ ab occaſu tangant arcum diurnum horarum 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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">quæ arcum nocturnum horarum
<
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/>
24. </
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>
<
s
xml:id
="
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xml:space
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">item & </
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<
s
xml:id
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xml:space
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">in quibus horis à meridie, vel media nocte, pulchrè indicant tabulæ arcus diurni, & </
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>
<
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xml:space
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<
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<
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position
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xlink:label
="
note-0287-04
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xlink:href
="
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xml:space
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">20</
note
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arcus nocturni horarum 24. </
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<
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<
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xml:space
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<
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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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riori polari continentur ſolum horæ 7. </
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<
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xml:space
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<
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<
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xml:id
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xml:space
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<
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xml:space
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">11. </
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<
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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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">12. </
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>
<
s
xml:id
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xml:space
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">à media nocte. </
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<
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xml:id
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xml:space
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">Item 1. </
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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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">& </
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<
s
xml:id
="
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xml:space
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">5. </
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>
<
s
xml:id
="
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xml:space
="
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">à
<
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meridie, accipiendæ erunt ex vtraque tabula horæ ab occaſu dictis horis reſpondentes, & </
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>
<
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xml:id
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xml:space
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<
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</
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<
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xml:id
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xml:space
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">Vt ex tabula arcus diurni horarum 24. </
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>
<
s
xml:id
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xml:space
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">ſumendæ ſunt hæ horæ ab occaſu 7. </
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<
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<
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<
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<
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<
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<
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<
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14. </
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<
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<
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<
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xml:id
="
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xml:space
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">& </
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<
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xml:id
="
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xml:space
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">17. </
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>
<
s
xml:id
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"
xml:space
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">hæ enim dictum arcum tangunt in horis 7. </
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<
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xml:space
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<
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<
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xml:id
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xml:space
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<
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xml:id
="
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xml:space
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>
<
s
xml:id
="
echoid-s18395
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s18396
"
xml:space
="
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">12. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">à media nocte,
<
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/>
& </
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>
<
s
xml:id
="
echoid-s18398
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xml:space
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">1. </
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<
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<
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xml:space
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<
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<
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xml:id
="
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xml:space
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">& </
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<
s
xml:id
="
echoid-s18403
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xml:space
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">5. </
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>
<
s
xml:id
="
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xml:space
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">à meridie. </
s
>
<
s
xml:id
="
echoid-s18405
"
xml:space
="
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">Ex tabula autem arcus no cturni horarum 24. </
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>
<
s
xml:id
="
echoid-s18406
"
xml:space
="
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">ſumendæ ſunt hæ ho
<
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ræ ab occaſu 1. </
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>
<
s
xml:id
="
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xml:space
="
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>
<
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xml:id
="
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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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>
<
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xml:id
="
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xml:space
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<
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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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xml:space
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">22. </
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>
<
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xml:id
="
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"
xml:space
="
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">23. </
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>
<
s
xml:id
="
echoid-s18416
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s18417
"
xml:space
="
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">24. </
s
>
<
s
xml:id
="
echoid-s18418
"
xml:space
="
preserve
">Nam hæ contingunt arcum dictum in horis
<
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/>
1. </
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>
<
s
xml:id
="
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xml:space
="
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">2. </
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>
<
s
xml:id
="
echoid-s18420
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s18421
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s18422
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s18423
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s18424
"
xml:space
="
preserve
">à meridie, & </
s
>
<
s
xml:id
="
echoid-s18425
"
xml:space
="
preserve
">in 7. </
s
>
<
s
xml:id
="
echoid-s18426
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s18427
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s18428
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s18429
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s18430
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s18431
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s18432
"
xml:space
="
preserve
">à media nocte, vt ex prædictis tabu-
<
lb
/>
lis conſtat.</
s
>
<
s
xml:id
="
echoid-s18433
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18434
"
xml:space
="
preserve
">POSTREMO idem horologium Italicum conficiemus per lineam horæ 12. </
s
>
<
s
xml:id
="
echoid-s18435
"
xml:space
="
preserve
">ab ortu, vel oc
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0287-05
"
xlink:href
="
note-0287-05a
"
xml:space
="
preserve
">30</
note
>
<
note
position
="
right
"
xlink:label
="
note-0287-06
"
xlink:href
="
note-0287-06a
"
xml:space
="
preserve
">Alia adhuc de-
<
lb
/>
ſcriptio horolo
<
lb
/>
gii Italici pola-
<
lb
/>
ris per lineam
<
lb
/>
horæ 12. & li-
<
lb
/>
neam horæ 24.
<
lb
/>
ab or. vel occ.</
note
>
caſu, vt ex tabula ſecunda propoſ. </
s
>
<
s
xml:id
="
echoid-s18436
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s18437
"
xml:space
="
preserve
">ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s18438
"
xml:space
="
preserve
">conſtat, cui titulus eſt, LINEA HORÆ
<
lb
/>
XII. </
s
>
<
s
xml:id
="
echoid-s18439
"
xml:space
="
preserve
">AB ORTV, VEL OCCASV. </
s
>
<
s
xml:id
="
echoid-s18440
"
xml:space
="
preserve
">Item per lineam horæ 24. </
s
>
<
s
xml:id
="
echoid-s18441
"
xml:space
="
preserve
">ab ortu, vel occaſu, vt ex
<
lb
/>
prima tabula propoſ. </
s
>
<
s
xml:id
="
echoid-s18442
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s18443
"
xml:space
="
preserve
">eiuſdem lib. </
s
>
<
s
xml:id
="
echoid-s18444
"
xml:space
="
preserve
">ſuperioris colligitur, cui titulus eſt. </
s
>
<
s
xml:id
="
echoid-s18445
"
xml:space
="
preserve
">LINEA HORAE
<
lb
/>
XXIIII. </
s
>
<
s
xml:id
="
echoid-s18446
"
xml:space
="
preserve
">&</
s
>
<
s
xml:id
="
echoid-s18447
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s18448
"
xml:space
="
preserve
">quæ quidem eadem omnino eſt, quæ horizontalis linea, vt perſpicuum eſt. </
s
>
<
s
xml:id
="
echoid-s18449
"
xml:space
="
preserve
">Vel
<
lb
/>
etiam beneficio vtriuſque lineæ, ſi diligenter in prędictis tabulis notentur puncta horarum à me-
<
lb
/>
ridie, vel media nocte, per quæ ducendæ ſint horæ Italicæ, &</
s
>
<
s
xml:id
="
echoid-s18450
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s18451
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18452
"
xml:space
="
preserve
">CAETERVM lineam horæ 12. </
s
>
<
s
xml:id
="
echoid-s18453
"
xml:space
="
preserve
">ab ortu, vel occaſu hac ratione deſcribemus. </
s
>
<
s
xml:id
="
echoid-s18454
"
xml:space
="
preserve
">In linea æqui-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0287-07
"
xlink:href
="
note-0287-07a
"
xml:space
="
preserve
">Quo pacto li-
<
lb
/>
nea horæ 12. ab
<
lb
/>
or. vel occ. du-
<
lb
/>
cenda ſit in po-
<
lb
/>
lari horologio.</
note
>
noctiali ex puncto A, vbi lineam meridianam interſecat, accipiemus rectam A B, æqualem ſtylo,
<
lb
/>
nempe rectam inter lineam meridianam, & </
s
>
<
s
xml:id
="
echoid-s18455
"
xml:space
="
preserve
">lineam horę 3. </
s
>
<
s
xml:id
="
echoid-s18456
"
xml:space
="
preserve
">vel 9. </
s
>
<
s
xml:id
="
echoid-s18457
"
xml:space
="
preserve
">à meridie, vel media nocte. </
s
>
<
s
xml:id
="
echoid-s18458
"
xml:space
="
preserve
">hæc
<
lb
/>
enim ſtylo æqualis eſt, vt in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s18459
"
xml:space
="
preserve
">25. </
s
>
<
s
xml:id
="
echoid-s18460
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s18461
"
xml:space
="
preserve
">oſtendimus. </
s
>
<
s
xml:id
="
echoid-s18462
"
xml:space
="
preserve
">Deinde ex B, termino il-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0287-08
"
xlink:href
="
note-0287-08a
"
xml:space
="
preserve
">40</
note
>
lius ad æquinoctialem lineam ducentes perpendicularem B f, qualis eſt ipſamet linea horæ 9. </
s
>
<
s
xml:id
="
echoid-s18463
"
xml:space
="
preserve
">vel
<
lb
/>
3. </
s
>
<
s
xml:id
="
echoid-s18464
"
xml:space
="
preserve
">producta, deſcribemus ex eodem puncto B, vt centro, circulum, in quo ſumemus arcum f g, al-
<
lb
/>
titudini poli æqualem, & </
s
>
<
s
xml:id
="
echoid-s18465
"
xml:space
="
preserve
">ex g, per centrum B, rectam ducemus, quæ ſecabit lineam meridianam
<
lb
/>
in puncto k, per quod ipſi ęquinoctiali lineę parallela acta, erit linea horæ 12. </
s
>
<
s
xml:id
="
echoid-s18466
"
xml:space
="
preserve
">ab ortu, vel occaſu.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s18467
"
xml:space
="
preserve
">Intelligatur enim circulus f g, circa meridianam lineam F H, conuerti, donec cum Meridiano cir-
<
lb
/>
culo, & </
s
>
<
s
xml:id
="
echoid-s18468
"
xml:space
="
preserve
">eius centrum B, cum centro mundi, ſeu vertice ſtyli coniungatur. </
s
>
<
s
xml:id
="
echoid-s18469
"
xml:space
="
preserve
">Quo poſito, erit f, polus
<
lb
/>
mundi, & </
s
>
<
s
xml:id
="
echoid-s18470
"
xml:space
="
preserve
">g, punctum, in quo circulus horę 12. </
s
>
<
s
xml:id
="
echoid-s18471
"
xml:space
="
preserve
">ab ortu, vel occaſu parallelum omniũ ſemper ap-
<
lb
/>
parentium maximum tangit, ipſumq́ue Meridianum ſecat, cum hic parallelus à polo diſtet tot
<
lb
/>
gradibus, quot continentur in altitudine poli. </
s
>
<
s
xml:id
="
echoid-s18472
"
xml:space
="
preserve
">Quare recta ex g, per centrum circuli f g, emiſſa,
<
lb
/>
communis erit ſectio dicti circuli horæ 12. </
s
>
<
s
xml:id
="
echoid-s18473
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s18474
"
xml:space
="
preserve
">Meridiani, ideoq́ue circulus horę 12. </
s
>
<
s
xml:id
="
echoid-s18475
"
xml:space
="
preserve
">ſecabit planũ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0287-09
"
xlink:href
="
note-0287-09a
"
xml:space
="
preserve
">50</
note
>
horologij in puncto K, in quo dicta recta meridianã lineam abrumpit. </
s
>
<
s
xml:id
="
echoid-s18476
"
xml:space
="
preserve
">Cum ergo ex ſcholio pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s18477
"
xml:space
="
preserve
">22. </
s
>
<
s
xml:id
="
echoid-s18478
"
xml:space
="
preserve
">ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s18479
"
xml:space
="
preserve
">linea horę dictę 12. </
s
>
<
s
xml:id
="
echoid-s18480
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s18481
"
xml:space
="
preserve
">ęquinoctialis parallelę ſint, liquido conſtat, paralle-
<
lb
/>
lam ipſi lineę ęquinoctiali per punctum K, meridianę lineę actam, eſſe lineam horę 12. </
s
>
<
s
xml:id
="
echoid-s18482
"
xml:space
="
preserve
">ab ortu,
<
lb
/>
vel occaſu, quod eſt propoſitum.</
s
>
<
s
xml:id
="
echoid-s18483
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18484
"
xml:space
="
preserve
">QVONIAM verò angulus altitudinis poli f B g, æqualis eſt angulo ad verticem K B L, ſit,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0287-10
"
xlink:href
="
note-0287-10a
"
xml:space
="
preserve
">Alia daſeriptio
<
lb
/>
lineæ horæ 12.
<
lb
/>
ab or. vel occ.</
note
>
vr ſi in linea ęquinoctiali accipiamus rectam gnomoni ęqualem, & </
s
>
<
s
xml:id
="
echoid-s18485
"
xml:space
="
preserve
">in extremo ad lineam ęquino-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0287-11
"
xlink:href
="
note-0287-11a
"
xml:space
="
preserve
">15. primi.</
note
>
ctialem conſtituamus angulum complementi altitudinis poli, qualis eſt reliquus ex recto A B K,
<
lb
/>
inueniamus in linea meridiana idem punctum K, per quod linea horę 12. </
s
>
<
s
xml:id
="
echoid-s18486
"
xml:space
="
preserve
">ab ortu, vel occaſu eſt
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0287-12
"
xlink:href
="
note-0287-12a
"
xml:space
="
preserve
">Alia adhuc de-
<
lb
/>
icriptio lineæ
<
lb
/>
horæ 12 ab o@.
<
lb
/>
vel occ.</
note
>
ducenda. </
s
>
<
s
xml:id
="
echoid-s18487
"
xml:space
="
preserve
">Immò ſi rectę A D, abſcindamus ęqualem A K, habebimus idem punctum K. </
s
>
<
s
xml:id
="
echoid-s18488
"
xml:space
="
preserve
">Quoniã
<
lb
/>
enim angulus A B D, æqualis eſt conſtitutus complemento altitudinis poli, vt ex propoſ. </
s
>
<
s
xml:id
="
echoid-s18489
"
xml:space
="
preserve
">38. </
s
>
<
s
xml:id
="
echoid-s18490
"
xml:space
="
preserve
">huius
<
lb
/>
libri conſtat, & </
s
>
<
s
xml:id
="
echoid-s18491
"
xml:space
="
preserve
">angulus A B K, eidem cõplemento altitudinis poli æqualis, vt oſtendimus; </
s
>
<
s
xml:id
="
echoid-s18492
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>