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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391 - 420
421 - 432
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<
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0511
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LIBER QVINTVS.
"/>
lo ♊, vel ♌, per earum latitudines vmbrarum, longitudineſq́ue in dicto parallelo inuentas.</
s
>
<
s
xml:id
="
echoid-s31855
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xml:space
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</
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<
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>
<
s
xml:id
="
echoid-s31856
"
xml:space
="
preserve
">QVOD ſi tropici deſcripti ſint, facilius horologium Italicum deſcribemus vel per ſolas lon-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0511-01
"
xlink:href
="
note-0511-01a
"
xml:space
="
preserve
">Si deſcripti ſint
<
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/>
tropici, qua ra-
<
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/>
tione facilius
<
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/>
Italicum horo-
<
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logium deſcri-
<
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batur.</
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>
gitudines vmbrarum, vel per ſolas latitudines. </
s
>
<
s
xml:id
="
echoid-s31857
"
xml:space
="
preserve
">Si enim beneficio circini longitudines vmbrarum
<
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/>
ex recta I H, accipiantur, & </
s
>
<
s
xml:id
="
echoid-s31858
"
xml:space
="
preserve
">ex E, arcus occulti deſcribantur ſecantes tropicos; </
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>
<
s
xml:id
="
echoid-s31859
"
xml:space
="
preserve
">vel ſi lineæ occultę
<
lb
/>
latitudinum vmbrarum ducantur ſecantes tropicos, habebuntur in vtroque tropico puncta ho-
<
lb
/>
rarum ab occ. </
s
>
<
s
xml:id
="
echoid-s31860
"
xml:space
="
preserve
">Si igitur reſpondentia puncta connectantur lineis rectis per horas à mer. </
s
>
<
s
xml:id
="
echoid-s31861
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s31862
"
xml:space
="
preserve
">med.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s31863
"
xml:space
="
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">noc. </
s
>
<
s
xml:id
="
echoid-s31864
"
xml:space
="
preserve
">in linea æquinoctiali tranſeuntibus, deſcriptum erit horologium Italicum.</
s
>
<
s
xml:id
="
echoid-s31865
"
xml:space
="
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"/>
</
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>
<
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>
<
s
xml:id
="
echoid-s31866
"
xml:space
="
preserve
">POSSVNT quoque longitudines vmbrarum ex altitudinibus Solis inueſtigari Geometrice,
<
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<
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="
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"
xlink:label
="
note-0511-02
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xlink:href
="
note-0511-02a
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xml:space
="
preserve
">Longitudines
<
lb
/>
vmbrarũ quo
<
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/>
pacto Geometri
<
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/>
cæ inueniantur
<
lb
/>
ex datis altitu-
<
lb
/>
dinibus Solis
<
lb
/>
in horologio.</
note
>
vt ad finem ſcholij propoſ. </
s
>
<
s
xml:id
="
echoid-s31867
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s31868
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s31869
"
xml:space
="
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">tradidimus. </
s
>
<
s
xml:id
="
echoid-s31870
"
xml:space
="
preserve
">Sit enim circulus, vel potius (quod ſatis
<
lb
/>
<
note
position
="
left
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xlink:label
="
note-0511-03
"
xlink:href
="
note-0511-03a
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xml:space
="
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">10</
note
>
<
figure
xlink:label
="
fig-0511-01
"
xlink:href
="
fig-0511-01a
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number
="
318
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<
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file
="
0511-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0511-01
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<
note
position
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xlink:label
="
note-0511-04
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xlink:href
="
note-0511-04a
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xml:space
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">20</
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>
eſt) ſemicirculus A B C, cuius centrum D, & </
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>
<
s
xml:id
="
echoid-s31871
"
xml:space
="
preserve
">in quo diameter B C, quam ad rectos angulos ſecet
<
lb
/>
ſemidiameter A D. </
s
>
<
s
xml:id
="
echoid-s31872
"
xml:space
="
preserve
">Accipiatur in A D, producta gnomoni horologij æqualis recta D E, & </
s
>
<
s
xml:id
="
echoid-s31873
"
xml:space
="
preserve
">per E,
<
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/>
<
note
position
="
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"
xlink:label
="
note-0511-05
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xlink:href
="
note-0511-05a
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xml:space
="
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">30</
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>
diametro B C, parallela agatur I G. </
s
>
<
s
xml:id
="
echoid-s31874
"
xml:space
="
preserve
">Si igitur v. </
s
>
<
s
xml:id
="
echoid-s31875
"
xml:space
="
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">g. </
s
>
<
s
xml:id
="
echoid-s31876
"
xml:space
="
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">ſumatur arcus B F, æqualis altitudini Solis, quã
<
lb
/>
habet hora 16. </
s
>
<
s
xml:id
="
echoid-s31877
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s31878
"
xml:space
="
preserve
">in tropico ♑, hoc eſt, gr. </
s
>
<
s
xml:id
="
echoid-s31879
"
xml:space
="
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">8. </
s
>
<
s
xml:id
="
echoid-s31880
"
xml:space
="
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">M. </
s
>
<
s
xml:id
="
echoid-s31881
"
xml:space
="
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">14. </
s
>
<
s
xml:id
="
echoid-s31882
"
xml:space
="
preserve
">ducaturq́ue recta F D G, ſecans rectã
<
lb
/>
I G, in G, erit E G, longitudo vmbræ à ſtvlo D E, proiectæ, vt ex ijs conſtat, quæ ad initium pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s31883
"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s31884
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s31885
"
xml:space
="
preserve
">ad ſinem ſcholij eiuſdem propoſ. </
s
>
<
s
xml:id
="
echoid-s31886
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s31887
"
xml:space
="
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">oſtendimus. </
s
>
<
s
xml:id
="
echoid-s31888
"
xml:space
="
preserve
">Hac eadem arte inuenietur
<
lb
/>
E I, longitudo vmbræ pro hora 23. </
s
>
<
s
xml:id
="
echoid-s31889
"
xml:space
="
preserve
">in tropico ♑, ex C H, arcu altitudinis Solis eiuſdem horæ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s31890
"
xml:space
="
preserve
">Item ex C K, arcu altitudinis Solis horæ 21. </
s
>
<
s
xml:id
="
echoid-s31891
"
xml:space
="
preserve
">in tropico ♑, reperietur longitudo vmbræ E L, pro
<
lb
/>
eadẽ hora 21. </
s
>
<
s
xml:id
="
echoid-s31892
"
xml:space
="
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">ab occ. </
s
>
<
s
xml:id
="
echoid-s31893
"
xml:space
="
preserve
">Ita quoque B M, arcus altitudinis Solis horæ 18. </
s
>
<
s
xml:id
="
echoid-s31894
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s31895
"
xml:space
="
preserve
">in tropico ♑, dabit
<
lb
/>
E N, longitudinem vmbræ eiuſdem horæ; </
s
>
<
s
xml:id
="
echoid-s31896
"
xml:space
="
preserve
">Et C O, arcus altitudinis. </
s
>
<
s
xml:id
="
echoid-s31897
"
xml:space
="
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">Solis eiuſdem horæ in tro-
<
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/>
pico ♋, præbebit longitudinem vmbræ E P: </
s
>
<
s
xml:id
="
echoid-s31898
"
xml:space
="
preserve
">Denique ex B Q, arcu altitudinis Solis horæ 21. </
s
>
<
s
xml:id
="
echoid-s31899
"
xml:space
="
preserve
">ab
<
lb
/>
occ. </
s
>
<
s
xml:id
="
echoid-s31900
"
xml:space
="
preserve
">in tropico ♑, veniemus in cognitionem longitudinis vmbræ E R, & </
s
>
<
s
xml:id
="
echoid-s31901
"
xml:space
="
preserve
">ſic de cæteris. </
s
>
<
s
xml:id
="
echoid-s31902
"
xml:space
="
preserve
">Operæpre-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0511-06
"
xlink:href
="
note-0511-06a
"
xml:space
="
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">40</
note
>
tium autẽ erit longitudines vmbrarũ pro horis orientalibus inueſtigare ex vna parte ſtyli, ne@pe
<
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/>
dextra, ex altera vero, nimirum ſiniſtra, pro occidentalibus, vt in figura factum eſt. </
s
>
<
s
xml:id
="
echoid-s31903
"
xml:space
="
preserve
">Niſi enim ita
<
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/>
fiat, ſæpenumero inter ſe confundentur vmbræ, quæ ferè ſunt æquales, cuiuſmodi ſunt duæ vm-
<
lb
/>
bræ E P, E R, vel E L, E N, quæ ferme æquales inter ſe ſunt.</
s
>
<
s
xml:id
="
echoid-s31904
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s31905
"
xml:space
="
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">PRO vmbrarum latitudinibus vſurpare poſſumus commodiſſime arcubus horarijs, quos
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0511-07
"
xlink:href
="
note-0511-07a
"
xml:space
="
preserve
">Deſcriptio horo
<
lb
/>
logij horizonta
<
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/>
lis ex tabulis ar
<
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/>
cuũ horario rũ,
<
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/>
qui per propoſ.
<
lb
/>
4. huius lib. ſup
<
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/>
putantur.</
note
>
propoſ. </
s
>
<
s
xml:id
="
echoid-s31906
"
xml:space
="
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">4. </
s
>
<
s
xml:id
="
echoid-s31907
"
xml:space
="
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">huius lib. </
s
>
<
s
xml:id
="
echoid-s31908
"
xml:space
="
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">ſupputare docuimus, in ijs horologijs, in quibus commode centrum deſi-
<
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/>
gnari poteſt. </
s
>
<
s
xml:id
="
echoid-s31909
"
xml:space
="
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">Quod in hunc modum fieri poteſt. </
s
>
<
s
xml:id
="
echoid-s31910
"
xml:space
="
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">Ex centro horologij M, deſcribatur circulus
<
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/>
cuiuſcunque magnitudinis i p l m n, in quo diameter ducatur i m, ad meridianam lineam A C
<
emph
style
="
sub
">3</
emph
>
<
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style
="
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">1</
emph
>
,
<
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/>
perpendicularis, quæ cõmunis ſectio erit plani horologij, & </
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>
<
s
xml:id
="
echoid-s31911
"
xml:space
="
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">circuli horæ 6. </
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>
<
s
xml:id
="
echoid-s31912
"
xml:space
="
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">à mer. </
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>
<
s
xml:id
="
echoid-s31913
"
xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s31914
"
xml:space
="
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">med. </
s
>
<
s
xml:id
="
echoid-s31915
"
xml:space
="
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">noc.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s31916
"
xml:space
="
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">vt propoſ. </
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>
<
s
xml:id
="
echoid-s31917
"
xml:space
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">1. </
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>
<
s
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xml:space
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">lib. </
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<
s
xml:id
="
echoid-s31919
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">2. </
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>
<
s
xml:id
="
echoid-s31920
"
xml:space
="
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">demonſtrauimus. </
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>
<
s
xml:id
="
echoid-s31921
"
xml:space
="
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">Inueniaur iam, per propoſ. </
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<
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xml:id
="
echoid-s31922
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xml:space
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">4. </
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>
<
s
xml:id
="
echoid-s31923
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xml:space
="
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">huius lib. </
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>
<
s
xml:id
="
echoid-s31924
"
xml:space
="
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">arcus horarius
<
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/>
<
note
position
="
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xlink:label
="
note-0511-08
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xlink:href
="
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xml:space
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">50</
note
>
v.</
s
>
<
s
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="
echoid-s31925
"
xml:space
="
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">g. </
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>
<
s
xml:id
="
echoid-s31926
"
xml:space
="
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">pro hora 23. </
s
>
<
s
xml:id
="
echoid-s31927
"
xml:space
="
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">ab occ. </
s
>
<
s
xml:id
="
echoid-s31928
"
xml:space
="
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">in tropico ♋, inter circulum horæ 6. </
s
>
<
s
xml:id
="
echoid-s31929
"
xml:space
="
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">à mer. </
s
>
<
s
xml:id
="
echoid-s31930
"
xml:space
="
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">vel med. </
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>
<
s
xml:id
="
echoid-s31931
"
xml:space
="
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">noc. </
s
>
<
s
xml:id
="
echoid-s31932
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s31933
"
xml:space
="
preserve
">alium cir-
<
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/>
culum maximum per polos mundi, & </
s
>
<
s
xml:id
="
echoid-s31934
"
xml:space
="
preserve
">horam 23. </
s
>
<
s
xml:id
="
echoid-s31935
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s31936
"
xml:space
="
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">in tropico ♋, ductum incluſus, qui cõ-
<
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/>
tinet grad. </
s
>
<
s
xml:id
="
echoid-s31937
"
xml:space
="
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">11. </
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>
<
s
xml:id
="
echoid-s31938
"
xml:space
="
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">M. </
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>
<
s
xml:id
="
echoid-s31939
"
xml:space
="
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">52. </
s
>
<
s
xml:id
="
echoid-s31940
"
xml:space
="
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">eſtq́ue occidentalis, & </
s
>
<
s
xml:id
="
echoid-s31941
"
xml:space
="
preserve
">borealis, propterea quod diſtantia Solis à Meri-
<
lb
/>
diano ſuperat quadrantem. </
s
>
<
s
xml:id
="
echoid-s31942
"
xml:space
="
preserve
">Hic autem arcus numeretur à puncto m, verſus partes boreales vſque
<
lb
/>
ad l, ducaturq́ue recta occulta l M f. </
s
>
<
s
xml:id
="
echoid-s31943
"
xml:space
="
preserve
">Nam ſi beneficio circini accipiatur longitudo vmbræ pro
<
lb
/>
hora 23. </
s
>
<
s
xml:id
="
echoid-s31944
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s31945
"
xml:space
="
preserve
">in tropico ♋, & </
s
>
<
s
xml:id
="
echoid-s31946
"
xml:space
="
preserve
">ex E, loco ſtyli transferatur verſus f, ſecabitur recta M f, in f,
<
lb
/>
puncto horæ 23. </
s
>
<
s
xml:id
="
echoid-s31947
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s31948
"
xml:space
="
preserve
">in tropico ♋. </
s
>
<
s
xml:id
="
echoid-s31949
"
xml:space
="
preserve
">Quoniam enim circulus horæ 6. </
s
>
<
s
xml:id
="
echoid-s31950
"
xml:space
="
preserve
">à mer. </
s
>
<
s
xml:id
="
echoid-s31951
"
xml:space
="
preserve
">vel med. </
s
>
<
s
xml:id
="
echoid-s31952
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s31953
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s31954
"
xml:space
="
preserve
">
<
lb
/>
maximus ille circulus per polos mundi, & </
s
>
<
s
xml:id
="
echoid-s31955
"
xml:space
="
preserve
">horã 23. </
s
>
<
s
xml:id
="
echoid-s31956
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s31957
"
xml:space
="
preserve
">in tropico ♋, ductus, per axem mundi
<
lb
/>
ducuntur, occurruntq́ue Horizonti, cui horologium horizontale æquidiſtat, in centro mundi,
<
lb
/>
hoceſt, in F, vertice ſtyli ad p@anum horologij recti, fit vt cum Horizonte faciant communes
<
lb
/>
ſectiones, rectas lineas, quæ in mundi centro angulum conſtituant, cui ſubtenditur arcus Horizõ-
<
lb
/>
tis, qui inter circulum horæ 6 à mer. </
s
>
<
s
xml:id
="
echoid-s31958
"
xml:space
="
preserve
">vel med. </
s
>
<
s
xml:id
="
echoid-s31959
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s31960
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s31961
"
xml:space
="
preserve
">alium illũ circulum maximũ interijcitur.</
s
>
<
s
xml:id
="
echoid-s31962
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>
