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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Table of Notes
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LIBER SECVNDVS.
"/>
gio, quę æquinoctialem lineam ſecat, eum ſemicirculũ cœleſtem referre, cuius communis ſectio facta in cir-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0167-01
"
xlink:href
="
note-0167-01a
"
xml:space
="
preserve
">Quem ſemicir-
<
lb
/>
culum cęleſtem
<
lb
/>
quælibet linea
<
lb
/>
in horologio
<
lb
/>
repræſentet.</
note
>
culo, quem ex E, centro Aequatoris, atque in eius plano deſcripſimus, (ſi nimirum eius centrum E, cum
<
lb
/>
centro mundi D, coniungatur) per centrum E, tranſit, antequam æquinoctiali lineę in horologio oc-
<
lb
/>
currat: </
s
>
<
s
xml:id
="
echoid-s9463
"
xml:space
="
preserve
">nimirum rectam H A, eſſe horam primam à meridie, hoc eſt, referre ſemicirculum illum cœle-
<
lb
/>
ſtem, in quo Sol hora prima à meridie exiſtit; </
s
>
<
s
xml:id
="
echoid-s9464
"
xml:space
="
preserve
">quia in A, cadit O E, per centrum E, ducta, quæ quidẽ O E,
<
lb
/>
communis ſectio eſt ſemicirculi horæ 1. </
s
>
<
s
xml:id
="
echoid-s9465
"
xml:space
="
preserve
">à meridie per punctum O, ducti, tranſit{q́ue} per centrũ E, priuſquam
<
lb
/>
ęquinoctialem lineam ſecat in A; </
s
>
<
s
xml:id
="
echoid-s9466
"
xml:space
="
preserve
">vt conſtat, ſi circulus ex E, deſcriptus concipiatur eſſe in plano Aequa
<
lb
/>
toris, centrum{q́ue} E, cum centro mundi D, coniunctum. </
s
>
<
s
xml:id
="
echoid-s9467
"
xml:space
="
preserve
">Cauſa huius rei eſt, quia Sol proijcit radium ſuum
<
lb
/>
prius ad centrum mundi, ſeu verticem ſtyli, antequam vmbra ſtyli in horologij planum cadat, vt perſpi-
<
lb
/>
cuum eſt. </
s
>
<
s
xml:id
="
echoid-s9468
"
xml:space
="
preserve
">Hac rationc erit quoque recta H K, hora 7. </
s
>
<
s
xml:id
="
echoid-s9469
"
xml:space
="
preserve
">à media nocte, hoc eſt, illum ſemicirculum cœle-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0167-02
"
xlink:href
="
note-0167-02a
"
xml:space
="
preserve
">10</
note
>
ſtem repræſentabit, in quo Sol exiſtit hora 7. </
s
>
<
s
xml:id
="
echoid-s9470
"
xml:space
="
preserve
">à med. </
s
>
<
s
xml:id
="
echoid-s9471
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s9472
"
xml:space
="
preserve
">quia in K, cadit V E, per centrum E, ducta, quæ
<
lb
/>
quidem V E, communis ſectio eſt ſemicir culi horæ 7. </
s
>
<
s
xml:id
="
echoid-s9473
"
xml:space
="
preserve
">à media nocte, per punctum V, ducti, tranſit{q́ue} per
<
lb
/>
centrum E, antequam lineam ęquinoctialem ſecat in k, vt perſpicuum eſt; </
s
>
<
s
xml:id
="
echoid-s9474
"
xml:space
="
preserve
">atque ita de cęteris.</
s
>
<
s
xml:id
="
echoid-s9475
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9476
"
xml:space
="
preserve
">NON eſt etiam omittendum, lineam cuiuſcunque horę à meridie vltra centrum horologij productam
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0167-03
"
xlink:href
="
note-0167-03a
"
xml:space
="
preserve
">Linea cuiuſuis
<
lb
/>
horę à meridie
<
lb
/>
vltra centrum
<
lb
/>
horologij pro-
<
lb
/>
ducta indicat
<
lb
/>
eiuſdem nume-
<
lb
/>
ri horã à med.
<
lb
/>
noc. & contra.</
note
>
monſtrare eiuſdem numeri horam à media nocte, & </
s
>
<
s
xml:id
="
echoid-s9477
"
xml:space
="
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">contra. </
s
>
<
s
xml:id
="
echoid-s9478
"
xml:space
="
preserve
">Quod ita demonſtrabimus. </
s
>
<
s
xml:id
="
echoid-s9479
"
xml:space
="
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">Sumatur exem-
<
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/>
pli gratia, circulus horæ quintæ à mer. </
s
>
<
s
xml:id
="
echoid-s9480
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s9481
"
xml:space
="
preserve
">med. </
s
>
<
s
xml:id
="
echoid-s9482
"
xml:space
="
preserve
">nocte faciens in horologio lineam eiuſdem horæ per centrũ
<
lb
/>
H, ductam. </
s
>
<
s
xml:id
="
echoid-s9483
"
xml:space
="
preserve
">Quoniam igitur, ſi Sol in polo arctico poneretur, vmbra ſtyli caderet in punctum H, cum ra-
<
lb
/>
dius Solis tunc idem eſſet, qui axis mundi, qui quidem per verticem ſtyli ductus in puncto H, occurrit pla
<
lb
/>
no horologij, efficitur, vt Sole existente in ſemicirculo dicti circuli, qui oceidentalior eſt, quàm Meridia-
<
lb
/>
nus, vmbra ſtyli cadat in partem oppoſitam, nempe in eam partem lineæ horę quintæ, quæ orientalior eſt
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0167-04
"
xlink:href
="
note-0167-04a
"
xml:space
="
preserve
">20</
note
>
in horologio, quàm linea meridiana; </
s
>
<
s
xml:id
="
echoid-s9484
"
xml:space
="
preserve
">exiſtente autem Sole in eiuſdem circuli altero ſemicirculo, quiorien
<
lb
/>
talior eſt Meridiano, vmbra ſtyli in partem eiuſdem lineę horę quintæ, quæ occidentalior eſt, quàm linea
<
lb
/>
meridiana, cadat. </
s
>
<
s
xml:id
="
echoid-s9485
"
xml:space
="
preserve
">Semper enim vmbra in dictam lineam cadit, dum Sol in dicto circulo exiſtit, vt pro-
<
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/>
poſ. </
s
>
<
s
xml:id
="
echoid-s9486
"
xml:space
="
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">11. </
s
>
<
s
xml:id
="
echoid-s9487
"
xml:space
="
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">ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s9488
"
xml:space
="
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">oſtendimus. </
s
>
<
s
xml:id
="
echoid-s9489
"
xml:space
="
preserve
">Cum ergo ſemicirculus occidentalis pertineat ad horam quintam pome
<
lb
/>
ridianam, & </
s
>
<
s
xml:id
="
echoid-s9490
"
xml:space
="
preserve
">orientalis ad quintam poſt mediam noctem, indicabit orientalis portio illius lineæ, quæni-
<
lb
/>
mirum ex centro H, tendit ad partem orienta lem horologij, (Diuidit porrò linea meridiana horologium
<
lb
/>
totum in partem orientalem, & </
s
>
<
s
xml:id
="
echoid-s9491
"
xml:space
="
preserve
">occidentalem, quemadmodum & </
s
>
<
s
xml:id
="
echoid-s9492
"
xml:space
="
preserve
">Meridianus totam ſphęram cœleſtem
<
lb
/>
in hemiſphærium orientale, & </
s
>
<
s
xml:id
="
echoid-s9493
"
xml:space
="
preserve
">occidentale partitur) horam quintam à meridie, reliqua autem portio eiuſ-
<
lb
/>
dem lineæ in partem occidentalem vergens, horam quintam à media nocte. </
s
>
<
s
xml:id
="
echoid-s9494
"
xml:space
="
preserve
">Eadem{q́ue} ratio eſt de cęteris
<
lb
/>
lineis, in alijs etiam horologijs, quæ non ſunt horizontalia.</
s
>
<
s
xml:id
="
echoid-s9495
"
xml:space
="
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"/>
</
p
>
<
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position
="
left
"
xml:space
="
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">30</
note
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9496
"
xml:space
="
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">IDEM hac etiam ratione oſtendemus, & </
s
>
<
s
xml:id
="
echoid-s9497
"
xml:space
="
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">breuius. </
s
>
<
s
xml:id
="
echoid-s9498
"
xml:space
="
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">Quoniam vmbra styli ante meridiem cadit in par
<
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/>
tem occidentalem horologij, poſt meridiem verò in orientalem, cum in contrariam ſemper partem Solis
<
lb
/>
proijciatur, pertinebunt omnes lineæ horariæ in parte occidentali (quam quidem linea meridiana ab
<
lb
/>
orientali dirimit in omni horologio) in centro H, terminatæ, ad horas antemeridianas, ſiue poſt mediam
<
lb
/>
noctem, reliquæ verò in orientali parte ad pomeridianas. </
s
>
<
s
xml:id
="
echoid-s9499
"
xml:space
="
preserve
">Cum ergo horariæ lineæ in parte orientali horo-
<
lb
/>
logij productæ vltra centrum exhibeant lineas earundem horarum in parte occidentali, & </
s
>
<
s
xml:id
="
echoid-s9500
"
xml:space
="
preserve
">econtrario,
<
lb
/>
perſpicuum eſt, quod proponitur.</
s
>
<
s
xml:id
="
echoid-s9501
"
xml:space
="
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"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9502
"
xml:space
="
preserve
">HINC colligitur quemcunque circulum maximum per polos mundi tranſeuntem facere in horologio
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0167-06
"
xlink:href
="
note-0167-06a
"
xml:space
="
preserve
">Quilibet circu-
<
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/>
lus maximus P
<
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/>
polos mũdi du-
<
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/>
ctus facit in ho
<
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/>
rologio rectam
<
lb
/>
lineã, cuius una
<
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/>
portio in cen-
<
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/>
tro terminata
<
lb
/>
pertinet ad vnũ
<
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/>
ſemicirculũ, &
<
lb
/>
altera ad alterũ.</
note
>
ſectionem, lineam rectam, cuius vna portio in centro terminata pertinet ad vnum ſemicirculum, & </
s
>
<
s
xml:id
="
echoid-s9503
"
xml:space
="
preserve
">al-
<
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/>
tera ad alterum. </
s
>
<
s
xml:id
="
echoid-s9504
"
xml:space
="
preserve
">Hoc enim demonſtratum eſt in circulis horarum à meridie & </
s
>
<
s
xml:id
="
echoid-s9505
"
xml:space
="
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">media nocte. </
s
>
<
s
xml:id
="
echoid-s9506
"
xml:space
="
preserve
">Idem{q́ue} ve-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0167-07
"
xlink:href
="
note-0167-07a
"
xml:space
="
preserve
">40</
note
>
rum eſt de circulis Meridianis, de quibus agemus propoſ. </
s
>
<
s
xml:id
="
echoid-s9507
"
xml:space
="
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">6. </
s
>
<
s
xml:id
="
echoid-s9508
"
xml:space
="
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">huius libri. </
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>
<
s
xml:id
="
echoid-s9509
"
xml:space
="
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">Item de Verticalibus circulis, de
<
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/>
quibus propoſ. </
s
>
<
s
xml:id
="
echoid-s9510
"
xml:space
="
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">4. </
s
>
<
s
xml:id
="
echoid-s9511
"
xml:space
="
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">huius lib. </
s
>
<
s
xml:id
="
echoid-s9512
"
xml:space
="
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">diſputabimus, dummodo loco poli mundi accipiamus verticem capitis, ſeu Ze-
<
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/>
nith, hoc eſt, polum Horizontis, & </
s
>
<
s
xml:id
="
echoid-s9513
"
xml:space
="
preserve
">in horologio loco centri horologij ſumamus punctũ verticale, in quod
<
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/>
cadit axis Horizontis, cuiuſmodi eſt in horizontali horologio, quod deſcripſimus, punctum G.</
s
>
<
s
xml:id
="
echoid-s9514
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9515
"
xml:space
="
preserve
">EX his perfacile iudicare poterimus, quęnam lineæ horarię ad horas à meridie pertineant, & </
s
>
<
s
xml:id
="
echoid-s9516
"
xml:space
="
preserve
">quæ
<
lb
/>
ad horas à media nocte. </
s
>
<
s
xml:id
="
echoid-s9517
"
xml:space
="
preserve
">Quoniam enim, ſi circulus ex E, deſcriptus in proprio ſitu collocetur, punctum
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0167-08
"
xlink:href
="
note-0167-08a
"
xml:space
="
preserve
">Qua ratione iu
<
lb
/>
dicandum ſit,
<
lb
/>
quæ lineæ hora
<
lb
/>
riæ pertineant
<
lb
/>
ad horas à mer.
<
lb
/>
& quæ ad horas
<
lb
/>
à med. noc. in
<
lb
/>
horologio de-
<
lb
/>
ſcripto.</
note
>
N, Meridianum ſecat ſupra Horizontem, pertinebit illud ad horam 12. </
s
>
<
s
xml:id
="
echoid-s9518
"
xml:space
="
preserve
">meridiei, ita vt recta NE, ſit
<
lb
/>
communis ſectio Meridiani, ſeu circuli horæ 12. </
s
>
<
s
xml:id
="
echoid-s9519
"
xml:space
="
preserve
">à meridie. </
s
>
<
s
xml:id
="
echoid-s9520
"
xml:space
="
preserve
">Cum ergo NE, per centrum E, tranſeat, at-
<
lb
/>
que æquinoctialem lineam ſecet in I, indicabit recta H I E, horam 12. </
s
>
<
s
xml:id
="
echoid-s9521
"
xml:space
="
preserve
">meridiei, & </
s
>
<
s
xml:id
="
echoid-s9522
"
xml:space
="
preserve
">reliqua eius portio
<
lb
/>
vltra centrum horologij H, horam 12. </
s
>
<
s
xml:id
="
echoid-s9523
"
xml:space
="
preserve
">mediæ noctis. </
s
>
<
s
xml:id
="
echoid-s9524
"
xml:space
="
preserve
">Eadem ratione pertinebunt rectę H A, H B, & </
s
>
<
s
xml:id
="
echoid-s9525
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0167-09
"
xlink:href
="
note-0167-09a
"
xml:space
="
preserve
">50</
note
>
cæteræ in parte orientali horologij poſitæ, ad horas poſt meridiem: </
s
>
<
s
xml:id
="
echoid-s9526
"
xml:space
="
preserve
">quia referunt ſemicirculos horarios
<
lb
/>
ſectionum O E, Q E, & </
s
>
<
s
xml:id
="
echoid-s9527
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s9528
"
xml:space
="
preserve
">qui quidem horas à meridie indicant in circulo ex E, deſcripto. </
s
>
<
s
xml:id
="
echoid-s9529
"
xml:space
="
preserve
">Denique li-
<
lb
/>
neę in parte occidentali horologij poſitæ, id eſt, ad dextram lineæ ipſius meridianæ, horas à media nocte ſi-
<
lb
/>
gnificabunt: </
s
>
<
s
xml:id
="
echoid-s9530
"
xml:space
="
preserve
">quoniam referunt ſemicirculos horarios, quorum ſectiones in circulo ex E, deſcripto rece-
<
lb
/>
dunt à recta N E, verſus orientalem plagam, monſtrant{q́ue} horas ante meridiem, vel à@media nocte.</
s
>
<
s
xml:id
="
echoid-s9531
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9532
"
xml:space
="
preserve
">HOC ſi attentè conſideretur, cognoſcemus facillimè etiam in omnibus alijs horologijs, de quibus in
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0167-10
"
xlink:href
="
note-0167-10a
"
xml:space
="
preserve
">Quomodo indi
<
lb
/>
candum ſit in
<
lb
/>
omni horolo-
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/>
gio, quæ lineæ
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lb
/>
horariæ ad ho-
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ras à mer. & quę
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ad horas à med.
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/>
noc. pertinean@.</
note
>
ſequentibus agemus, quęnam horæ ſint à meridie numerandæ, & </
s
>
<
s
xml:id
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xml:space
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preserve
">quæ à media nocte.</
s
>
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s
xml:id
="
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xml:space
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preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
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"
xml:space
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preserve
">MONENDVS quoque lector eſt, nos hactenus horologium horizontale conſtruxiſſe in plana qua-
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lb
/>
cunque ſuperficie, vt illud poſtea in proprio ſitu collocetur, vel in planum aliquod ſtabile, quod Horizonti
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lb
/>
ſit parallelum, transferatur, ita vt recta H E, ſit linea meridiana, & </
s
>
<
s
xml:id
="
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"
xml:space
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preserve
">punctum H, ad auſtrum, punctum
<
lb
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verò E, ad boream vergat, velut in hoc ſcholio tradidimus. </
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>
<
s
xml:id
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xml:space
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preserve
">Quòd ſiplanum aliquod ſtabile, quod </
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>
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>
</
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>
</
echo
>