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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GNOMONICES
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certe ex tabulis, quas ad finem ſcholii propoſ. </
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<
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xml:space
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<
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">eiuſdem lib. </
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<
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">conſtruximus, facile cognoſcemus,
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<
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r
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um tabularũ
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propoſ. 20. præ-
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cedentis lib. in
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deſcribendis ho
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@is ab occaſu.</
note
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quęnam horę ab ortu, vel occaſu horam quamcunque à meridie, vel media nocte in vno, & </
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<
s
xml:id
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xml:space
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<
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puncto ſecent. </
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<
s
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xml:space
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">Quæ res & </
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<
s
xml:id
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xml:space
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">facilem admodum reddit deſcriptionem linearum horarum ab occa-
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ſu, & </
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<
s
xml:id
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xml:space
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">modum prębet, quo deſcriptio huiuſmodi poſſit examinari. </
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<
s
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xml:space
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">Horologium igitur Italicum
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Horizontale conſtituimus, &</
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<
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xml:space
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">c. </
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<
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xml:space
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">Quod erat faciendum.</
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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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<
head
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style
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xml:space
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">SCHOLIVM.</
head
>
<
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<
s
xml:id
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xml:space
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">HIC notatu dignum eſt, quamcunque horam ab occaſu productam vltra punctum illud, vbi paral-
<
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/>
<
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position
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left
"
xlink:label
="
note-0218-02
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xlink:href
="
note-0218-02a
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xml:space
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">Quælibet hora
<
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ab occaſu pro-
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ducta vlt
<
unsure
/>
ra pun
<
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/>
ctum, vbi arcũ
<
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/>
diurnum, no-
<
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/>
cturnumve ho
<
lb
/>
rarum 24. tan-
<
lb
/>
git, pertinet ad
<
lb
/>
eandem horam
<
lb
/>
@umero ab or-
<
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/>
@u; & contra.</
note
>
<
note
position
="
left
"
xlink:label
="
note-0218-03
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xlink:href
="
note-0218-03a
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xml:space
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">10</
note
>
lelum ſemper apparentium maximum, ſiue arcum diurnum horarum 24. </
s
>
<
s
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="
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xml:space
="
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">vel etiam nocturnum arcum,
<
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/>
qui eſt alter parallelus oppoſitus, & </
s
>
<
s
xml:id
="
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xml:space
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">latentium maximus, tangit, indicare eandem numero horam ab or-
<
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/>
tu; </
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>
<
s
xml:id
="
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xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s13339
"
xml:space
="
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">contra, quamuis horam ab ortu productam vltra illud punctum exhibere eandem numero horam
<
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/>
ab occaſu. </
s
>
<
s
xml:id
="
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xml:space
="
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">Id quod in propoſ. </
s
>
<
s
xml:id
="
echoid-s13341
"
xml:space
="
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">hac, vt verũ, aſſumpſimus, nunc autem ita demonſtrabimus. </
s
>
<
s
xml:id
="
echoid-s13342
"
xml:space
="
preserve
">Si Sol ponere-
<
lb
/>
tur in illo puncto cœli, in quo circulus aliquis horarius ab ortu, vel occaſu parallelum ſemper apparẽtium
<
lb
/>
maximũ, vel ſemper latentium maximũ tangit, vmbra ſtyli caderet præcisè in punctũ illud horologij, vbi
<
lb
/>
linea horæ illius circuli arcum diurnum, vel nocturnum horarum 24. </
s
>
<
s
xml:id
="
echoid-s13343
"
xml:space
="
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">tangit, vt facile ex demonſtratis in
<
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/>
præcedenti lib. </
s
>
<
s
xml:id
="
echoid-s13344
"
xml:space
="
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">ostendi poteſt. </
s
>
<
s
xml:id
="
echoid-s13345
"
xml:space
="
preserve
">Quia enim, Sole in illo parallelo exiſtente, vmbra ſtyli proijcitur in arcum
<
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/>
illius paralleli in horologio deſcriptum, vt conſtat ex propoſ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">12. </
s
>
<
s
xml:id
="
echoid-s13347
"
xml:space
="
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">præcedentis libri. </
s
>
<
s
xml:id
="
echoid-s13348
"
xml:space
="
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">Item Sole exiſtente in
<
lb
/>
illo circulo horario, eadem vmbra in communem ſectionem illius, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">plani horologij, hoc est, in lineam ho
<
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/>
<
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position
="
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"
xlink:label
="
note-0218-04
"
xlink:href
="
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xml:space
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">20</
note
>
rariam illius circuli proijcitur, vt propoſ. </
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>
<
s
xml:id
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xml:space
="
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">11. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">eiuſdem libri oſtendimus; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">fit vt vmbra cadat in dictum pun
<
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/>
ctum, quod commune eſt & </
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>
<
s
xml:id
="
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"
xml:space
="
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">arcui illius paralleli, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">lineæ horariæ prædicti circuli. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quod cum ita ſe ha-
<
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/>
beat, perſpicuum eſt, ſi nos in puncto illo contactus paralleli ſemper apparentium, vel latentium maxi-
<
lb
/>
mi poſiti eſſemus, ita vt vnus ſemicirculus circuli illius horarij foret nobis ad dexteram, & </
s
>
<
s
xml:id
="
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xml:space
="
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">alter ad ſini
<
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/>
stram, Sol autem exiſteret in ſemicir culo dextro, vmbram ſtyli proijci in partem ſiniſtram prædictæ li-
<
lb
/>
neę horariæ, nempe in oppoſitam partem; </
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>
<
s
xml:id
="
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"
xml:space
="
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">Si autem Sol exiſteret in ſemicirculo ſiniſtro, eandem vmbrã
<
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/>
ſtyli cadere in partem dextram eiuſdem lineę, ſumendo partem dextram, & </
s
>
<
s
xml:id
="
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xml:space
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">ſiniſtram reſpectu puncti con
<
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/>
tactus in arcu diurno, vel nocturno horarum 24. </
s
>
<
s
xml:id
="
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xml:space
="
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">in horologio. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Cum ergo Sole in diuerſis ſemicirculis il-
<
lb
/>
lius horarij circuli exiſtente, vmbra ſtyli cadat in diuerſas partes eius lineæ horariæ, nempè modo vltra
<
lb
/>
punctum contactus, modo citra idem; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">eorum autem ſemicirculorum vnus indicet horam ab ortu So-
<
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/>
<
note
position
="
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xlink:label
="
note-0218-05
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xlink:href
="
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xml:space
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">30</
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>
lis, & </
s
>
<
s
xml:id
="
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xml:space
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">alter ab occaſu, vt in ſcholio propoſ. </
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>
<
s
xml:id
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xml:space
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">10. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſuperioris libri diximus; </
s
>
<
s
xml:id
="
echoid-s13365
"
xml:space
="
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">pertinebit quoque vna
<
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/>
pars lineæ eius horariæ in puncto contactus terminata ad horas ab ortu, in quam nimirum proijcitur
<
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/>
vmbra, Sole in ſemicirculo illo, qui horam ab ortu ſignificat, constituto, & </
s
>
<
s
xml:id
="
echoid-s13366
"
xml:space
="
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">altera ad horas ab occaſu.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s13367
"
xml:space
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">Quod idem verum eſt in alijs horologijs, quæ non ſunt horizontalia, & </
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>
<
s
xml:id
="
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xml:space
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">in omnibus lineis horarijs ab or-
<
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tu, vel occaſu.</
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>
<
s
xml:id
="
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xml:space
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"/>
</
p
>
<
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style
="
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<
s
xml:id
="
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"
xml:space
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">IDEM quoque hac ratione perſpicuum fiet, etiamſi nec Solem, nec nos in illo puncto contactus con-
<
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/>
ſtituamus. </
s
>
<
s
xml:id
="
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"
xml:space
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">Quilibet ſemicirculus horarius à meridie, vel media nocte præciſe poſitus eſt in medio duo-
<
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/>
rum ſemicirculorum illius circuli horarij ab ortu, vel occaſu, qui in eodem puncto tangit parallelum ſem-
<
lb
/>
per apparentium, vel latentium maximum, in quo ſemicir culus ille horarius à meridie, vel media nocte
<
lb
/>
eundem parallelum ſecat, cum per polum illius tranſeat, ex propoſ. </
s
>
<
s
xml:id
="
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xml:space
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">5. </
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<
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xml:space
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">libri 2. </
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<
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xml:space
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">Theodoſii; </
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>
<
s
xml:id
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xml:space
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">ita vt vnum
<
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<
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xlink:label
="
note-0218-06
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">40</
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>
habeat ad dextram, & </
s
>
<
s
xml:id
="
echoid-s13376
"
xml:space
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">alterum ad ſinistram. </
s
>
<
s
xml:id
="
echoid-s13377
"
xml:space
="
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">Quoniam autem, Sole exiſtente in ſemicirculo illo hora-
<
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/>
rio à meridie, vel media nocte, vmbra ſtyli cadit in lineam eius horariam, quæ arcum diurnum, vel noctur
<
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/>
num horarum 24. </
s
>
<
s
xml:id
="
echoid-s13378
"
xml:space
="
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">ſecat; </
s
>
<
s
xml:id
="
echoid-s13379
"
xml:space
="
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">perſpicuum eſt, Sole exiſtente in eo ſemicir ulo horario ab ortu, vel occaſu, qui
<
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/>
orientalis eſt reſpectu illius ſemicirculi horarij à meridie, vel media nocte, vmbram proijci in partem op-
<
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/>
poſitam in plano horologij, nempe in partem occidentalem reſpectu lineæ illius horariæ à meridie, vel me-
<
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/>
dia nocte, in ipſam tamen lineam horariam ab ortu, vel occaſu, vt ex propoſ. </
s
>
<
s
xml:id
="
echoid-s13380
"
xml:space
="
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">11. </
s
>
<
s
xml:id
="
echoid-s13381
"
xml:space
="
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">præcedentis libri con-
<
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/>
ſtat: </
s
>
<
s
xml:id
="
echoid-s13382
"
xml:space
="
preserve
">Sole verò exiſtente in altero ſemicir culo occidentali, vmbram cadere in partem orientalem horolo-
<
lb
/>
gij reſpectu illius lineæ horariæ à meridie, vel media nocte, in ipſam tamen lineam horariam ab ortu, vel
<
lb
/>
occaſu, per eandem propoſ. </
s
>
<
s
xml:id
="
echoid-s13383
"
xml:space
="
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">11. </
s
>
<
s
xml:id
="
echoid-s13384
"
xml:space
="
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">antecedentis libri. </
s
>
<
s
xml:id
="
echoid-s13385
"
xml:space
="
preserve
">Cum ergo linea illa horaria à meridie, vel media no-
<
lb
/>
cte lineam horariam ab ortu, vel occaſu ſecet in puncto contactus arcus diurni, vel nocturni horarum
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0218-07
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xlink:href
="
note-0218-07a
"
xml:space
="
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">50</
note
>
24. </
s
>
<
s
xml:id
="
echoid-s13386
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s13387
"
xml:space
="
preserve
">vnus ſemicir culus horarius ab ortu, vel occaſu monſtret horam ab ortu
<
gap
/>
er horam ab
<
lb
/>
occaſu, liquido conſtat, vnam portionem lineæ horariæ illius ab ortu, vel
<
gap
/>
ſque ad pun-
<
lb
/>
ctum contactus, indicare horam ab ortu, reliquam verò portionem monſtrare h
<
gap
/>
ndem numero ab
<
lb
/>
occaſu Solis.</
s
>
<
s
xml:id
="
echoid-s13388
"
xml:space
="
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"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s13389
"
xml:space
="
preserve
">EX dictis facile intelligi poteſt, vſum horologij Italici eſſe, vt ex eo cognoſcamus, quot horæ à pro-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0218-08
"
xlink:href
="
note-0218-08a
"
xml:space
="
preserve
">Vſus horologii
<
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/>
Italici eſt, vt
<
lb
/>
intelligamus,
<
lb
/>
quot horæ ſint
<
lb
/>
elapſæ à proxi-
<
lb
/>
mo occaſu So-
<
lb
/>
lis, quotque ad
<
lb
/>
alterum ſuper-
<
lb
/>
ſint.</
note
>
ximo Solis occaſu elapſæ ſint, & </
s
>
<
s
xml:id
="
echoid-s13390
"
xml:space
="
preserve
">quot ſuperſint ad ſequentem occaſum; </
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>
<
s
xml:id
="
echoid-s13391
"
xml:space
="
preserve
">adeo vt vmbra gnomonis caden-
<
lb
/>
te in aliquam lineam horariam ab occaſu, nempe in lineam horæ 19. </
s
>
<
s
xml:id
="
echoid-s13392
"
xml:space
="
preserve
">certi ſimus, tranſactas eſſe horas 19.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s13393
"
xml:space
="
preserve
">à proximo occaſu Solis, ac proinde, quoniam ab vno occaſu ad alterum intercedunt horæ 24. </
s
>
<
s
xml:id
="
echoid-s13394
"
xml:space
="
preserve
">ſupereſſe
<
lb
/>
vſque ad ſequentem occaſum horas quinque, quæ nimirum deſunt horis 19. </
s
>
<
s
xml:id
="
echoid-s13395
"
xml:space
="
preserve
">ad complendum numerum ho
<
unsure
/>
<
lb
/>
rarum 24. </
s
>
<
s
xml:id
="
echoid-s13396
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s13397
"
xml:space
="
preserve
">ſic de cæteris.</
s
>
<
s
xml:id
="
echoid-s13398
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>