Clavius, Christoph
,
Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur
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LIBER TERTIVS.
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ſecat lineam æquinoctialem in puncto n, & </
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>
<
s
xml:id
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xml:space
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">recta ex C, pern, ducta ſecat tropicum ♑, in p, pun-
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cto horæ 9. </
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<
s
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xml:space
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">inæqualis, & </
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>
<
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xml:id
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">ſic de cæteris. </
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>
<
s
xml:id
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xml:space
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">Pro hora 11. </
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>
<
s
xml:id
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"
xml:space
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">inæquali tropici ♑, quoniam non contine-
<
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/>
tur in ſemicirculo A N B, cuius vnius puncta in tropicis inueniuntur, vt ſupra dictum eſt, acci-
<
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/>
piemus punctum ei oppoſitum D, quod cadit in horam 11. </
s
>
<
s
xml:id
="
echoid-s22199
"
xml:space
="
preserve
">inæqualem arcus nocturni tropici ♋,
<
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/>
vt mox demonſtrabimus, ex quo ſi per L, ducamus rectam, ſecabit hæc lineam æquinoctialem in
<
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/>
puncto quodam, nempe in R, (quod, quia remotiſſimum eſt, in noſtro horologio nõ continetur)
<
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/>
per quod recta ex C, emiſſa dabit in arcu nocturno tropici ♋, punctũ horæ 11. </
s
>
<
s
xml:id
="
echoid-s22200
"
xml:space
="
preserve
">inæqualis reſpon-
<
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/>
dens puncto D, eadem verò recta vltra cẽtrum C, eiecta offeret in arcu diurno ♑, punctum aliud
<
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/>
pro hora 11. </
s
>
<
s
xml:id
="
echoid-s22201
"
xml:space
="
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">diurna inæquali tropici ♑, vt ex demonſtratis conſtat. </
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>
<
s
xml:id
="
echoid-s22202
"
xml:space
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">Eadem ratione pro horis 11.
<
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/>
</
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>
<
s
xml:id
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echoid-s22203
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xml:space
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">10. </
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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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">9. </
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>
<
s
xml:id
="
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"
xml:space
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">inæqualibus tropici ♋, quoniam etiam extra dictum ſemicirculum A N D, cadunt, acci-
<
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<
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position
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xlink:label
="
note-0349-01
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xlink:href
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">10</
note
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piemus puncta ipſis oppoſita E, F, G, quæ cadunt in horas inæquales 11. </
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>
<
s
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="
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xml:space
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">10. </
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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-s22209
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xml:space
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">9. </
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>
<
s
xml:id
="
echoid-s22210
"
xml:space
="
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">arcus nocturni
<
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tropici ♑, vt mox oſtendemus, & </
s
>
<
s
xml:id
="
echoid-s22211
"
xml:space
="
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">ex ipſis rectas per L, ducemus, vt inueniamus in arcu nocturno
<
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/>
Capricorni puncta K, P, Q, reſpondẽtia punctis E, F, G, arcus nocturni tropici ♑. </
s
>
<
s
xml:id
="
echoid-s22212
"
xml:space
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">Quòd ſi quãdo
<
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hora aliqua cadat præcisè in punctum A, vel B, tum ducta recta per C, æquinoctiali lineæ æqui-
<
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/>
diſtãs, indicabit in tropico Capricorni duo puncta, quorũ illud, quod ad dextrã ipſius C L, exiſtet,
<
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/>
ad horam, quæ cadit in punctũ A, alterum verò, quod ad ſiniſtram ipſius CL, ſtatuetur, ad horam,
<
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/>
quæ in punctum B, cadit, pertinebit, vt conſtar ex ijs, quæ oſtendimus propoſ. </
s
>
<
s
xml:id
="
echoid-s22213
"
xml:space
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">1. </
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>
<
s
xml:id
="
echoid-s22214
"
xml:space
="
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">huius libri de
<
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/>
recta Cd, quæ per C, lineæ æquinoctiali ducta eſt parallela. </
s
>
<
s
xml:id
="
echoid-s22215
"
xml:space
="
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">Ea enim refert illam horam, à cuius
<
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/>
puncto in circulo ex L, deſcripto, recta ducta per L, lineæ æquinoctiali æquidiſtat, vt ad finem de-
<
lb
/>
monſtrationis modi prioris conſtruendi horologii declinantis oſtendimus propoſ. </
s
>
<
s
xml:id
="
echoid-s22216
"
xml:space
="
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">1. </
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>
<
s
xml:id
="
echoid-s22217
"
xml:space
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">huius libri.
<
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/>
</
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>
<
s
xml:id
="
echoid-s22218
"
xml:space
="
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">
<
note
position
="
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xlink:label
="
note-0349-02
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xlink:href
="
note-0349-02a
"
xml:space
="
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">20</
note
>
Si igitur reſpondentia puncta in tropicis iungantur lineis rectis, deſcriptum erit horologium An-
<
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tiquum; </
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>
<
s
xml:id
="
echoid-s22219
"
xml:space
="
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">tranſibuntq́ue omnes lineæ horarum inęqualium per horas à meridie, vel media nocte
<
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/>
in linea æquinoctiali, prout in tabulis 13. </
s
>
<
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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">14. </
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<
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<
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<
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">primi libri colligitur. </
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<
s
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xml:space
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">Quoniam verò
<
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puncta horarum 11. </
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<
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">10. </
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<
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">& </
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<
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">9. </
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<
s
xml:id
="
echoid-s22229
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xml:space
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">arcus ♑, non habent puncta reſpondentia in tropico ♋, iungemus
<
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/>
ea cum punctis arcus nocturni ♑, inuentis beneficio punctorum E, F, G, quæ eiſdem horis 11.
<
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/>
</
s
>
<
s
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xml:space
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">10. </
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<
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">9. </
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<
s
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xml:space
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">arcus diurni ♋, opponuntur, caduntq́ue in horas inæquales 11. </
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<
s
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<
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<
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xml:id
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xml:space
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">9. </
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<
s
xml:id
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xml:space
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">arcus no-
<
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<
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xlink:label
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xlink:href
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xml:space
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">Demonſtratio,
<
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quòd horę di-
<
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urnæ inæqua-
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les in tropico
<
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/>
Caneri, oppo-
<
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/>
nuntur per dia
<
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metrum eiſd@
<
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/>
horis inęquali-
<
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bu@ nocturnis
<
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/>
in tropico Ca-
<
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pricorni; & @
<
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in horologio
<
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horæ diurnę
<
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tropici Capri-
<
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corni, ducendæ
<
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ſint per eaſdem
<
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horas noctur-
<
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nas eiuſdẽ tro-
<
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pici.</
note
>
cturni Capricorni.</
s
>
<
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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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">QVOD autem hoc ita ſit, & </
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>
<
s
xml:id
="
echoid-s22239
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xml:space
="
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">lineæ horarum diurnarum tropici ♑, ducendæ ſint per eaſdem
<
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horas nocturnas eiuſdem tropici in horologio, ita demonſtrabimus. </
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>
<
s
xml:id
="
echoid-s22240
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xml:space
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">Quoniam v. </
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>
<
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="
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">g. </
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>
<
s
xml:id
="
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xml:space
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">recta ex E,
<
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puncto, quod opponitur horæ 11. </
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>
<
s
xml:id
="
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xml:space
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">♋, contineturq́ue in arcu nocturno ♑, per L, ducta ſecat æqui
<
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<
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>
noctialem lineam in H, & </
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>
<
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xml:id
="
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">recta C H, arcum nocturnum ♑, ſecat in K, ſecabit circulus maximus
<
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per polos mundi, & </
s
>
<
s
xml:id
="
echoid-s22245
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xml:space
="
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">horam 11. </
s
>
<
s
xml:id
="
echoid-s22246
"
xml:space
="
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">inæqualem tropici ♋, nec non per punctum E, ductus, planum ho
<
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rologii per rectam C H, atque adeo tropicum ♑, in K, vt conſtat ex demonſtratis propoſ. </
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>
<
s
xml:id
="
echoid-s22247
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xml:space
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">10. </
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>
<
s
xml:id
="
echoid-s22248
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xml:space
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">ſupe-
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rioris libri. </
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>
<
s
xml:id
="
echoid-s22249
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xml:space
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">Quoniam verò circulus ille maximus in circulo Ma Nb, neceſſario aufert arcum e E,
<
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horæ 11. </
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>
<
s
xml:id
="
echoid-s22250
"
xml:space
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">inæqualis arcus nocturni tropici ♑, d Me, (Nam quia arcus a M, e N, æquales ſunt, cum
<
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/>
dimidiatæ partes ſint arcuum æqualium a M b, e N d; </
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>
<
s
xml:id
="
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xml:space
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">ſi addatur communis arcus e M, fiet arcus
<
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a M e, ſemicirculo M e N, ęqualis. </
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>
<
s
xml:id
="
echoid-s22252
"
xml:space
="
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">Igitur recta ex a, ad e, @producta per centrum L, tranſibit, atq;
<
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</
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>
<
s
xml:id
="
echoid-s22253
"
xml:space
="
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">adeo in centro L, cum recta E L, ducta vſque ad horam 11. </
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>
<
s
xml:id
="
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"
xml:space
="
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">tropici ♋, conſtituet angulos ad verti-
<
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<
note
position
="
right
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xlink:label
="
note-0349-05
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xlink:href
="
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xml:space
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">15. primi.</
note
>
cem æquales; </
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>
<
s
xml:id
="
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xml:space
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">propteraq́ue arcus a 11, e E, æquales erunt. </
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>
<
s
xml:id
="
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xml:space
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">Sicut igitur a 11, eſt pars duodecima ar
<
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<
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xlink:label
="
note-0349-06
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xlink:href
="
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xml:space
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">26. tertij.</
note
>
cus diurni tropici ♋, a N b, ita e E, pars duodecima erit arcus nocturni tropici ♑, e M d; </
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>
<
s
xml:id
="
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xml:space
="
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">quando-
<
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<
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="
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xlink:label
="
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="
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xml:space
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">40</
note
>
quidem arcus a N b, e M d, æquales ſunt; </
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>
<
s
xml:id
="
echoid-s22258
"
xml:space
="
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">ac proindee E, arcus erit horæ 11. </
s
>
<
s
xml:id
="
echoid-s22259
"
xml:space
="
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">inæqualis in arcu no-
<
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cturno ♑) ſit, vt tranſeat per horam 11. </
s
>
<
s
xml:id
="
echoid-s22260
"
xml:space
="
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">nocturnam tropici ♑. </
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>
<
s
xml:id
="
echoid-s22261
"
xml:space
="
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">Cum enim dictus circulus maxi-
<
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mus, & </
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>
<
s
xml:id
="
echoid-s22262
"
xml:space
="
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">Meridianus auferant ex Aequatore, & </
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>
<
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xml:id
="
echoid-s22263
"
xml:space
="
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">tropico ♑, per propoſ. </
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>
<
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xml:id
="
echoid-s22264
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xml:space
="
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">10. </
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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:id
="
echoid-s22266
"
xml:space
="
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">2. </
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>
<
s
xml:id
="
echoid-s22267
"
xml:space
="
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">Theod arcus ſimi
<
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/>
les, contineat autem arcus M E, qui ſimilis eſt arcui Aequatoris inter dictum circulum maximũ,
<
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/>
& </
s
>
<
s
xml:id
="
echoid-s22268
"
xml:space
="
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">Meridianum interiecto, quinque ſextas partes arcus Me, qui ſimilis eſt arcui ſeminocturno tro
<
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/>
pici ♑, comprehendet quoque arcus tropici ♑, inter eundem circulum maximum, & </
s
>
<
s
xml:id
="
echoid-s22269
"
xml:space
="
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">Meridia-
<
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/>
num interpoſitus quinque ſextas partes ſui arcus ſeminocturni, atque adeo dictus maximus circu-
<
lb
/>
lus per horam 11. </
s
>
<
s
xml:id
="
echoid-s22270
"
xml:space
="
preserve
">inæqualem nocturnam tropici ♑, tranſibit. </
s
>
<
s
xml:id
="
echoid-s22271
"
xml:space
="
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">Et quoniam hora 11. </
s
>
<
s
xml:id
="
echoid-s22272
"
xml:space
="
preserve
">inæqualis in
<
lb
/>
arcu diurno tropici ♋, & </
s
>
<
s
xml:id
="
echoid-s22273
"
xml:space
="
preserve
">hora 11. </
s
>
<
s
xml:id
="
echoid-s22274
"
xml:space
="
preserve
">inæqualis in arcu nocturno tropici ♑, intercipiunt ex circulo
<
lb
/>
illo maximo per vtramque horam ducto ſemicirculum, (quoniam enim arcus ipſius inter paral-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0349-08
"
xlink:href
="
note-0349-08a
"
xml:space
="
preserve
">50</
note
>
lelum ♋, & </
s
>
<
s
xml:id
="
echoid-s22275
"
xml:space
="
preserve
">Aequatorem poſitus ſupra Horizontem) æqualis eſt arcui eiuſdem inter parallelum
<
lb
/>
♑, & </
s
>
<
s
xml:id
="
echoid-s22276
"
xml:space
="
preserve
">Aequatorem collocato infra Horizontem, quòd vterque per propoſ. </
s
>
<
s
xml:id
="
echoid-s22277
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s22278
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s22279
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s22280
"
xml:space
="
preserve
">Theod. </
s
>
<
s
xml:id
="
echoid-s22281
"
xml:space
="
preserve
">æqua-
<
lb
/>
lis ſit arcui maximæ declinationis; </
s
>
<
s
xml:id
="
echoid-s22282
"
xml:space
="
preserve
">ſi addatur communis arcus eiuſdem inter Aequatorem, & </
s
>
<
s
xml:id
="
echoid-s22283
"
xml:space
="
preserve
">tro-
<
lb
/>
picum ♑, poſitus, tranſiensq́ue per polum antarcticum, fient arcus eiuſdem æquales, quorũ vnus
<
lb
/>
quidem inter tropicum ♋, & </
s
>
<
s
xml:id
="
echoid-s22284
"
xml:space
="
preserve
">tropicum ♑, alter verò inter Aequatorem ponitur tranſiens per po
<
lb
/>
lum antarcticum. </
s
>
<
s
xml:id
="
echoid-s22285
"
xml:space
="
preserve
">Cum ergo Aequator ex illo auferat ſemicirculum ex propol. </
s
>
<
s
xml:id
="
echoid-s22286
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s22287
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s22288
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s22289
"
xml:space
="
preserve
">Theod.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s22290
"
xml:space
="
preserve
">erit quoque alter arcus ſemicirculus) ſit, vt neceſſario circulus alius maximus qui vnus eſt ex cir-
<
lb
/>
culis horarum inæqualium, & </
s
>
<
s
xml:id
="
echoid-s22291
"
xml:space
="
preserve
">per polos mundi non tranſit, & </
s
>
<
s
xml:id
="
echoid-s22292
"
xml:space
="
preserve
">qui dictum circulum maximũ per
<
lb
/>
polos mundi, & </
s
>
<
s
xml:id
="
echoid-s22293
"
xml:space
="
preserve
">horam 11. </
s
>
<
s
xml:id
="
echoid-s22294
"
xml:space
="
preserve
">tropici ♋, diurnam ductum ſecat in hora 11. </
s
>
<
s
xml:id
="
echoid-s22295
"
xml:space
="
preserve
">diurna tropici ♋, ſecet
<
lb
/>
eundem in puncto oppoſito, hoc eſt, in hora 11. </
s
>
<
s
xml:id
="
echoid-s22296
"
xml:space
="
preserve
">nocturna tropici ♑; </
s
>
<
s
xml:id
="
echoid-s22297
"
xml:space
="
preserve
">quandoquidem illum per
<
lb
/>
propoſ. </
s
>
<
s
xml:id
="
echoid-s22298
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s22299
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s22300
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s22301
"
xml:space
="
preserve
">Theod. </
s
>
<
s
xml:id
="
echoid-s22302
"
xml:space
="
preserve
">ſecat biſariam, oſtenſumq́ue eſt, circulum dictum maximum in hora 11.</
s
>
<
s
xml:id
="
echoid-s22303
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>