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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æquinoctiali in partes æquales, vt ex iis, quæ propoſ. </
s
>
<
s
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="
echoid-s19356
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xml:space
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">49. </
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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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echoid-s19358
"
xml:space
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">in ſcholio propoſ. </
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>
<
s
xml:id
="
echoid-s19359
"
xml:space
="
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">50. </
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>
<
s
xml:id
="
echoid-s19360
"
xml:space
="
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">huius libri ſcri-
<
lb
/>
pſimus, conſtat. </
s
>
<
s
xml:id
="
echoid-s19361
"
xml:space
="
preserve
">Quare cum circulus maximus per polos, & </
s
>
<
s
xml:id
="
echoid-s19362
"
xml:space
="
preserve
">per horam 24. </
s
>
<
s
xml:id
="
echoid-s19363
"
xml:space
="
preserve
">ductus ſecet paralle-
<
lb
/>
lum ♋, horologii in eo puncto, vbi eundem Horizon ſecat, quòd in illud punctum vmbra gno-
<
lb
/>
monis cadat, Sole exiſtente in communi ſectione Horizontis, ſeu paralleli ♋, & </
s
>
<
s
xml:id
="
echoid-s19364
"
xml:space
="
preserve
">dicti circuli, vt
<
lb
/>
ex demonſtratis in ſuperiori lib perſpicuum eſt; </
s
>
<
s
xml:id
="
echoid-s19365
"
xml:space
="
preserve
">incedent alij circuli maximi per alia puncta pa-
<
lb
/>
ralleli ♋, in horologio, quæ ipſum in partes æquales partiuntur, cum in ea cadat quoque vmbra
<
lb
/>
ſtyli, Sole exiſtente in communi ſectione paralleli ♋, & </
s
>
<
s
xml:id
="
echoid-s19366
"
xml:space
="
preserve
">illorum circulorum; </
s
>
<
s
xml:id
="
echoid-s19367
"
xml:space
="
preserve
">atque adeo per ea-
<
lb
/>
dem puncta circuli horarum ab occaſu tranſibunt, eadem de cauſa; </
s
>
<
s
xml:id
="
echoid-s19368
"
xml:space
="
preserve
">quia nimirum vmbra ſtyli in
<
lb
/>
ea puncta cadit, cum Sol in communibus ſectionibus paralleli ♋, & </
s
>
<
s
xml:id
="
echoid-s19369
"
xml:space
="
preserve
">circulorum horarum ab oc-
<
lb
/>
caſu, nec non circulorum maximorum per polos mundi, & </
s
>
<
s
xml:id
="
echoid-s19370
"
xml:space
="
preserve
">per horas ab occaſu in parallelo ♋,
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0303-01
"
xlink:href
="
note-0303-01a
"
xml:space
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">10</
note
>
tranſeuntium exiſtit. </
s
>
<
s
xml:id
="
echoid-s19371
"
xml:space
="
preserve
">Radius enim Solis à communibus ſectionibus illorum circulorum maxi-
<
lb
/>
morum tunc non differet, cum hæ ſectiones per centrum mundi, hoc eſt, per verticem ſtyli, ſicut
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s19372
"
xml:space
="
preserve
">radius Solis, ducantur. </
s
>
<
s
xml:id
="
echoid-s19373
"
xml:space
="
preserve
">Cum ergo tunc radius Solis cadat in prædicta puncta paralleli ♋, in
<
lb
/>
horologio, cadent quoque in eadem communes illę ſectiones; </
s
>
<
s
xml:id
="
echoid-s19374
"
xml:space
="
preserve
">ac proinde in illis punctis plana
<
lb
/>
circulorum horarum ab occaſu plano horologii occurrent. </
s
>
<
s
xml:id
="
echoid-s19375
"
xml:space
="
preserve
">Eodem modo oſtendemus, circulos
<
lb
/>
horarum ab occaſu trãſire per puncta aliorum parallelorum in horologio, quæ ipſos in partes di-
<
lb
/>
ſtribuunt æquales, ſi videlicet concipiantur duci alii circuli maximi per polos mundi, & </
s
>
<
s
xml:id
="
echoid-s19376
"
xml:space
="
preserve
">per ho-
<
lb
/>
ras ab occaí
<
unsure
/>
u in ipſis parallellis. </
s
>
<
s
xml:id
="
echoid-s19377
"
xml:space
="
preserve
">Quare rectæ lineæ puncta dicta arcuum ſignorum connectentes,
<
lb
/>
ſunt communes ſectiones plani horologii, & </
s
>
<
s
xml:id
="
echoid-s19378
"
xml:space
="
preserve
">circulorum horas ab occaſu Solis monſtrantium.</
s
>
<
s
xml:id
="
echoid-s19379
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s19380
"
xml:space
="
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">EADEM ratione inferius horologium Italicum conſtruemus, ſi diuiſionem parallelorum
<
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/>
<
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position
="
left
"
xlink:label
="
note-0303-02
"
xlink:href
="
note-0303-02a
"
xml:space
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">20</
note
>
in inferiori horologio, quod nobis repreſentat portio abſciſſa à linea horizontali, inchoemus ex
<
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/>
ea parte, in quam vmbra ſtyli proiicitur ſub ſolis occaſum, qualis eſt pars dextra ad ortum vergẽs.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s19381
"
xml:space
="
preserve
">Voco partem dextram, quę nobis ad horologium inferius, hoc eſt, ad portionem à linea horizon-
<
lb
/>
tali abciſſam conuerſis, & </
s
>
<
s
xml:id
="
echoid-s19382
"
xml:space
="
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">horizontali linea ſuperiorem occupante locum, ad dexteram poſita eſt: </
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>
<
s
xml:id
="
echoid-s19383
"
xml:space
="
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">
<
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/>
non enim ad hanc rem vtimur illa inuerſione partium, de qua in ſuperioribus locuti ſumus. </
s
>
<
s
xml:id
="
echoid-s19384
"
xml:space
="
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">Nam
<
lb
/>
proxima linea ſupra lineam horizontalem dabit horam 1. </
s
>
<
s
xml:id
="
echoid-s19385
"
xml:space
="
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">ab occaſu, quæ nimirum in ſ@periori
<
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/>
horologio indicabat horam 23. </
s
>
<
s
xml:id
="
echoid-s19386
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s19387
"
xml:space
="
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">ſequens, quæ erat linea horæ 22. </
s
>
<
s
xml:id
="
echoid-s19388
"
xml:space
="
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">dabit 2. </
s
>
<
s
xml:id
="
echoid-s19389
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s19390
"
xml:space
="
preserve
">ſic deinceps, aſſumẽ
<
lb
/>
do ſemper complementa horarum ſuperioris horologij vſque ad 24. </
s
>
<
s
xml:id
="
echoid-s19391
"
xml:space
="
preserve
">ita vt linea horæ 1. </
s
>
<
s
xml:id
="
echoid-s19392
"
xml:space
="
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">ab occa-
<
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/>
ſu in horologio ſuperiori; </
s
>
<
s
xml:id
="
echoid-s19393
"
xml:space
="
preserve
">quæ nimirum eſt prima ſub linea horizontali in inferiori horologio, in
<
lb
/>
dicet horam 23. </
s
>
<
s
xml:id
="
echoid-s19394
"
xml:space
="
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">ab occaſu, &</
s
>
<
s
xml:id
="
echoid-s19395
"
xml:space
="
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">c. </
s
>
<
s
xml:id
="
echoid-s19396
"
xml:space
="
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">Hæc autem complementa horarum non ſcripſimus in figura, ſed
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0303-03
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xlink:href
="
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xml:space
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">30</
note
>
cogitatione tantum intelligenda ſunt.</
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>
<
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xml:space
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"/>
</
p
>
<
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>
<
s
xml:id
="
echoid-s19398
"
xml:space
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">ALITER. </
s
>
<
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="
echoid-s19399
"
xml:space
="
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">Per doctrinam propoſ. </
s
>
<
s
xml:id
="
echoid-s19400
"
xml:space
="
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">51. </
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>
<
s
xml:id
="
echoid-s19401
"
xml:space
="
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">huius libri deſcribatur arcus diurnus horarum 14. </
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>
<
s
xml:id
="
echoid-s19402
"
xml:space
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">cu
<
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/>
<
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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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">Alia deſcriptio
<
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horologii Itali-
<
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/>
ci ęquinoctialis
<
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/>
per arcus diur-
<
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/>
nos nocturnos-
<
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/>
que horarum
<
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/>
14. & 10.</
note
>
ius portio à linea horizontali abſciſſa erit arcus diurnus horarum 10. </
s
>
<
s
xml:id
="
echoid-s19403
"
xml:space
="
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">in inferiori horologio, vel
<
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/>
arcus nocturnus horarum 10. </
s
>
<
s
xml:id
="
echoid-s19404
"
xml:space
="
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">in horologio nocturno, quod idem eſt, quod horologium Inſerius,
<
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/>
cum portio illa horologij, quam horizontalis linea abſcindit, vtrumque horologiũ exhibeat & </
s
>
<
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xml:id
="
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"
xml:space
="
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">
<
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/>
inferius, & </
s
>
<
s
xml:id
="
echoid-s19406
"
xml:space
="
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">nocturnum, vt ex ſuperioribus perſpicuum eſt. </
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>
<
s
xml:id
="
echoid-s19407
"
xml:space
="
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">Si enim per horas à meridie, vel media
<
lb
/>
nocte in arcu diurno horarum 14. </
s
>
<
s
xml:id
="
echoid-s19408
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s19409
"
xml:space
="
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">nocturno horarum 10. </
s
>
<
s
xml:id
="
echoid-s19410
"
xml:space
="
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">reſpondentes horis ab occaſu, vt in ta
<
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/>
bula 3. </
s
>
<
s
xml:id
="
echoid-s19411
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s19412
"
xml:space
="
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">4. </
s
>
<
s
xml:id
="
echoid-s19413
"
xml:space
="
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">ſcholii propoſ. </
s
>
<
s
xml:id
="
echoid-s19414
"
xml:space
="
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">33 ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s19415
"
xml:space
="
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">videre licet, lineas rectas duxerimus, deſcriptũ erit ho-
<
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/>
rologium Italicum ſuperius, vt prius. </
s
>
<
s
xml:id
="
echoid-s19416
"
xml:space
="
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">Aduertendum tamen eſt, horas ſingulas ab occaſu, ſingulas
<
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/>
tantum horas à meridie, vel media nocte reſpondentes habere in dictis tabulis. </
s
>
<
s
xml:id
="
echoid-s19417
"
xml:space
="
preserve
">Vnde vt recte duci
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0303-05
"
xlink:href
="
note-0303-05a
"
xml:space
="
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">40</
note
>
poſſint, ſumendæ erunt quoque horæ à meridie, vel media nocte reſpondentes eiſdem numero
<
lb
/>
horis ab ortu ex eiſdem tabulis. </
s
>
<
s
xml:id
="
echoid-s19418
"
xml:space
="
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">Exempli gratia Hora 23. </
s
>
<
s
xml:id
="
echoid-s19419
"
xml:space
="
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">ab occaſu ducitur per horam 6. </
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>
<
s
xml:id
="
echoid-s19420
"
xml:space
="
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">à meridie
<
lb
/>
in arcu diurno horarum 14. </
s
>
<
s
xml:id
="
echoid-s19421
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s19422
"
xml:space
="
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">quia eadem vltra. </
s
>
<
s
xml:id
="
echoid-s19423
"
xml:space
="
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">arcum diurnum horarum 24. </
s
>
<
s
xml:id
="
echoid-s19424
"
xml:space
="
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">qui horizontalem
<
lb
/>
lineam in puncto m, tangit, producta indicat horam 23. </
s
>
<
s
xml:id
="
echoid-s19425
"
xml:space
="
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">ab ortu, vt in ſcholio propoſ. </
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>
<
s
xml:id
="
echoid-s19426
"
xml:space
="
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">10. </
s
>
<
s
xml:id
="
echoid-s19427
"
xml:space
="
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">huius
<
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/>
libri docuimus; </
s
>
<
s
xml:id
="
echoid-s19428
"
xml:space
="
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">tranſit autem hora 23. </
s
>
<
s
xml:id
="
echoid-s19429
"
xml:space
="
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">ab ortu per horam 4. </
s
>
<
s
xml:id
="
echoid-s19430
"
xml:space
="
preserve
">à media nocte in arcu nocturno ho-
<
lb
/>
rarum 10. </
s
>
<
s
xml:id
="
echoid-s19431
"
xml:space
="
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">idcirco, vt recte hora 23. </
s
>
<
s
xml:id
="
echoid-s19432
"
xml:space
="
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">ab occaſu ducatur per horam 6. </
s
>
<
s
xml:id
="
echoid-s19433
"
xml:space
="
preserve
">à meridie in arcu diurno ho-
<
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/>
rarum 14. </
s
>
<
s
xml:id
="
echoid-s19434
"
xml:space
="
preserve
">accipienda etiam erit hora 4. </
s
>
<
s
xml:id
="
echoid-s19435
"
xml:space
="
preserve
">à media nocte reſpondens horæ 23. </
s
>
<
s
xml:id
="
echoid-s19436
"
xml:space
="
preserve
">ab ortu in arcu noctur
<
lb
/>
no horarum 10. </
s
>
<
s
xml:id
="
echoid-s19437
"
xml:space
="
preserve
">Eodem pacto hora 22. </
s
>
<
s
xml:id
="
echoid-s19438
"
xml:space
="
preserve
">ab occaſu ducitur per horam 5. </
s
>
<
s
xml:id
="
echoid-s19439
"
xml:space
="
preserve
">à meridie in arcu diurno
<
lb
/>
horarum 14. </
s
>
<
s
xml:id
="
echoid-s19440
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s19441
"
xml:space
="
preserve
">per horam 3. </
s
>
<
s
xml:id
="
echoid-s19442
"
xml:space
="
preserve
">à media nocte in arcu nocturno horarum 10. </
s
>
<
s
xml:id
="
echoid-s19443
"
xml:space
="
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">quæ horæ 22. </
s
>
<
s
xml:id
="
echoid-s19444
"
xml:space
="
preserve
">ab ortu
<
lb
/>
correſpondet. </
s
>
<
s
xml:id
="
echoid-s19445
"
xml:space
="
preserve
">Sic quoque (vt rem totam paucis complectar) hora 11. </
s
>
<
s
xml:id
="
echoid-s19446
"
xml:space
="
preserve
">ab occaſu incedit per horam
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0303-06
"
xlink:href
="
note-0303-06a
"
xml:space
="
preserve
">50</
note
>
6. </
s
>
<
s
xml:id
="
echoid-s19447
"
xml:space
="
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">à media nocte in arcu diurno horarum 14. </
s
>
<
s
xml:id
="
echoid-s19448
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s19449
"
xml:space
="
preserve
">per horam 4. </
s
>
<
s
xml:id
="
echoid-s19450
"
xml:space
="
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">à meridie in eodem arcu, quæ horæ
<
lb
/>
11. </
s
>
<
s
xml:id
="
echoid-s19451
"
xml:space
="
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">ab ortu reſpondet. </
s
>
<
s
xml:id
="
echoid-s19452
"
xml:space
="
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">Item hora 1. </
s
>
<
s
xml:id
="
echoid-s19453
"
xml:space
="
preserve
">ab occaſu ducta eſt per horam 8. </
s
>
<
s
xml:id
="
echoid-s19454
"
xml:space
="
preserve
">à meridie in arcu nocturno
<
lb
/>
horarum 10. </
s
>
<
s
xml:id
="
echoid-s19455
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s19456
"
xml:space
="
preserve
">per horam 6. </
s
>
<
s
xml:id
="
echoid-s19457
"
xml:space
="
preserve
">à media nocte in arcu diurno horarum 14. </
s
>
<
s
xml:id
="
echoid-s19458
"
xml:space
="
preserve
">horæ 1. </
s
>
<
s
xml:id
="
echoid-s19459
"
xml:space
="
preserve
">ab ortu re-
<
lb
/>
ſpondentem, &</
s
>
<
s
xml:id
="
echoid-s19460
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s19461
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
right
"
xml:space
="
preserve
">Quomodo In-
<
lb
/>
ferius horolo-
<
lb
/>
gium Italicum
<
lb
/>
ex ſuperiori col
<
lb
/>
ligatur.</
note
>
<
p
>
<
s
xml:id
="
echoid-s19462
"
xml:space
="
preserve
">NON aliter horologium Italicum inferius conficiemus. </
s
>
<
s
xml:id
="
echoid-s19463
"
xml:space
="
preserve
">Sed ſatius erit illud ex ſuperiori col-
<
lb
/>
ligere. </
s
>
<
s
xml:id
="
echoid-s19464
"
xml:space
="
preserve
">Nam horæ ab occaſu ſuperioris horologij productæ vltra lineam horizõtalem dabunt eaſ-
<
lb
/>
dem numero horas ab occaſu in inferiori horologio, ſi tamen omnes eius partes inuertantur, vt
<
lb
/>
in ſuperioribus dictum eſt, & </
s
>
<
s
xml:id
="
echoid-s19465
"
xml:space
="
preserve
">demonſtratum in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s19466
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s19467
"
xml:space
="
preserve
">huius libri.</
s
>
<
s
xml:id
="
echoid-s19468
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
right
"
xml:space
="
preserve
">Eiuſdem horo-
<
lb
/>
logii@ Italici æ-
<
lb
/>
quinoctialis de
<
lb
/>
ſcriptio, per ar-
<
lb
/>
cum diurnum
<
lb
/>
horarum 24.</
note
>
<
p
>
<
s
xml:id
="
echoid-s19469
"
xml:space
="
preserve
">FACILI quoque negotio idem Italicum horologium abſoluemus per arcum diurnum ho-
<
lb
/>
rarum 24. </
s
>
<
s
xml:id
="
echoid-s19470
"
xml:space
="
preserve
">ſeu parallelum omnium ſemper apparentium maximum, qui horizontalem lineam
<
lb
/>
tangit in m, eſtq; </
s
>
<
s
xml:id
="
echoid-s19471
"
xml:space
="
preserve
">in inferiori horologio arcus nocturnus horarum 24. </
s
>
<
s
xml:id
="
echoid-s19472
"
xml:space
="
preserve
">ſiue parallelus ſemper </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>