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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31 - 60
61 - 71
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<
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95
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file
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0115
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115
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LIBER PRIMVS.
"/>
nationis ad Horizontem, ad aliud, inuenietur hic ferè ſinus 74306. </
s
>
<
s
xml:id
="
echoid-s5363
"
xml:space
="
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">cuius arcus grad. </
s
>
<
s
xml:id
="
echoid-s5364
"
xml:space
="
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">48. </
s
>
<
s
xml:id
="
echoid-s5365
"
xml:space
="
preserve
">ferè inter
<
lb
/>
Horizontem, & </
s
>
<
s
xml:id
="
echoid-s5366
"
xml:space
="
preserve
">planum inclinatum eſt poſitus. </
s
>
<
s
xml:id
="
echoid-s5367
"
xml:space
="
preserve
">Quod eſt propoſitum.</
s
>
<
s
xml:id
="
echoid-s5368
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5369
"
xml:space
="
preserve
">QVOD ſi planum tam ad Horizontem, quàm ad Meridianum inclinatum directo ad ortũ
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-01
"
xlink:href
="
note-0115-01a
"
xml:space
="
preserve
">Quando planũ
<
lb
/>
rectũ eſt ad Ver
<
lb
/>
ticalem.</
note
>
vel occaſum ſpectet, hoc eſt, ſi ad Verticalem ſit rectum, nullus intercipietur arcus Meridiani inter
<
lb
/>
ipſum planum, & </
s
>
<
s
xml:id
="
echoid-s5370
"
xml:space
="
preserve
">Horizontem, quia tunc planum per communes ſectiones Meridiani, & </
s
>
<
s
xml:id
="
echoid-s5371
"
xml:space
="
preserve
">Hori-
<
lb
/>
zontis incedit, vt conſtat.</
s
>
<
s
xml:id
="
echoid-s5372
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5373
"
xml:space
="
preserve
">SI verò planum ad Horizontem tantum inclinatum fuerit, hoc eſt, ſi per communes ſectio-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-02
"
xlink:href
="
note-0115-02a
"
xml:space
="
preserve
">Quando planũ
<
lb
/>
rectũ eſt ad Me
<
lb
/>
tidianum.</
note
>
nes Horizontis, ac Verticalis, ſeu polos Meridiani tranſierit, atque adeo ad Meridianum ſuerit re-
<
lb
/>
ctum, erit ipſa inclinatio ad Horizontem arcus Meridiani inter planum, & </
s
>
<
s
xml:id
="
echoid-s5374
"
xml:space
="
preserve
">Horizontem poſitus:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5375
"
xml:space
="
preserve
">quia tunc Meridianus inclinationem metitur, vt patet.</
s
>
<
s
xml:id
="
echoid-s5376
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
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">10</
note
>
<
p
>
<
s
xml:id
="
echoid-s5377
"
xml:space
="
preserve
">SI denique planum inclinatum tantum fuerit ad Meridianum, hoc eſt, ſi per verticem, ſeu
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-04
"
xlink:href
="
note-0115-04a
"
xml:space
="
preserve
">Quando planũ
<
lb
/>
rectũ eſt ad Ho
<
lb
/>
rizontem.</
note
>
polum Horizontis tranſierit, ideoq́uead Horizontem fuerit rectum, intercipietur inter ipſum pla
<
lb
/>
num, & </
s
>
<
s
xml:id
="
echoid-s5378
"
xml:space
="
preserve
">Horizontem quarta pars Meridiani circuli, vt manifeſtum eſt. </
s
>
<
s
xml:id
="
echoid-s5379
"
xml:space
="
preserve
">Dato ergo plano velad Ho
<
lb
/>
rizontem & </
s
>
<
s
xml:id
="
echoid-s5380
"
xml:space
="
preserve
">Meridianum, vel ad Meridianum tantum, &</
s
>
<
s
xml:id
="
echoid-s5381
"
xml:space
="
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">c. </
s
>
<
s
xml:id
="
echoid-s5382
"
xml:space
="
preserve
">Quod erat faciendum.</
s
>
<
s
xml:id
="
echoid-s5383
"
xml:space
="
preserve
"/>
</
p
>
</
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>
<
div
xml:id
="
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type
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level
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1
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n
="
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<
head
xml:id
="
echoid-head127
"
xml:space
="
preserve
">SCHOLIVM I.</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">Quando arcus
<
lb
/>
Meridiani in-
<
lb
/>
ter Horizontẽ
<
lb
/>
& planũ incli-
<
lb
/>
natũ reperiatur
<
lb
/>
ſupra Horizon
<
lb
/>
tem, & quando
<
lb
/>
infra.</
note
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s5384
"
xml:space
="
preserve
">SI inclinatio plani ad Horizontem cadat in partem hemiſphærij ſuperni Borealem, iuxta ea, quæ
<
lb
/>
propoſitione 23. </
s
>
<
s
xml:id
="
echoid-s5385
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s5386
"
xml:space
="
preserve
">docuimus, ſecabitur Meridianus ex parte poli arctici ſupra Horizontem, at-
<
lb
/>
que arcus inter Horizontem & </
s
>
<
s
xml:id
="
echoid-s5387
"
xml:space
="
preserve
">planum poſitus ſupra Horizontem extabit ex parte poli arctici. </
s
>
<
s
xml:id
="
echoid-s5388
"
xml:space
="
preserve
">Si ve-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0115-06
"
xlink:href
="
note-0115-06a
"
xml:space
="
preserve
">20</
note
>
ro inclinatio in partem eiuſdem hemiſphærij auſtralem cadat, ſecabit planum circulum Meridianum ex
<
lb
/>
parte poli arctici infra Horizontem, arcus{q́ue} propterea Meridiani inter planum, ac Horizontem interie-
<
lb
/>
ctus ſub Horizonte occultabitur. </
s
>
<
s
xml:id
="
echoid-s5389
"
xml:space
="
preserve
">Ratio hui{us} rei eſt, quia cum inter circulum maximum metientem in-
<
lb
/>
clinationem plani, & </
s
>
<
s
xml:id
="
echoid-s5390
"
xml:space
="
preserve
">planum ipſum intercipiatur quadrans Horizontis, quòd dictus circulus ſegmentum
<
lb
/>
Horizontis inter planum inclinatum, quod quidem ſemicirculus est, ſecet bifariam, per propoſ. </
s
>
<
s
xml:id
="
echoid-s5391
"
xml:space
="
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">9. </
s
>
<
s
xml:id
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echoid-s5392
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xml:space
="
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">lib. </
s
>
<
s
xml:id
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"
xml:space
="
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">2.
<
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/>
</
s
>
<
s
xml:id
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echoid-s5394
"
xml:space
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">Theod. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">fit vt cadente inclinatione in partem borealem, Meridianus ex eadem parte boreali ſecet planum
<
lb
/>
inclinatum ſupra Horizontem. </
s
>
<
s
xml:id
="
echoid-s5396
"
xml:space
="
preserve
">Eodem modo, cadente inclinatione ad partes auſtrales, ſecabit Meridia-
<
lb
/>
nus ex eadem parte australi planum inclinatum ſupra Horizontem, ac proinde ſub Horizonte ex parte
<
lb
/>
boreali. </
s
>
<
s
xml:id
="
echoid-s5397
"
xml:space
="
preserve
">Id quod facile intelligetur, ſi diligenter expendatur ſitus ac poſitio circulorum in ſphæra.</
s
>
<
s
xml:id
="
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xml:space
="
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"/>
</
p
>
<
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="
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xml:space
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">30</
note
>
</
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>
<
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type
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<
head
xml:id
="
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"
xml:space
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preserve
">COROLLARIVM.</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">Arcus Meridia
<
lb
/>
ni inter planũ
<
lb
/>
inclinatũ, & po
<
lb
/>
lum arcticũ po-
<
lb
/>
ſitus, quo pacto
<
lb
/>
cognoſcat@@.</
note
>
<
p
>
<
s
xml:id
="
echoid-s5399
"
xml:space
="
preserve
">EX his non difficile erit, quantus ſit arcus Meridiani inter planum inclinatum, & </
s
>
<
s
xml:id
="
echoid-s5400
"
xml:space
="
preserve
">polum mundi ar-
<
lb
/>
cticum interpoſitus, inuenire. </
s
>
<
s
xml:id
="
echoid-s5401
"
xml:space
="
preserve
">Nam ſi arcus Meridiani inter planum, & </
s
>
<
s
xml:id
="
echoid-s5402
"
xml:space
="
preserve
">Horizontem fuerit ſub Horizon-
<
lb
/>
te ex parte poli arctici, erit arcus, qui ex ipſo, & </
s
>
<
s
xml:id
="
echoid-s5403
"
xml:space
="
preserve
">arcu altitudinem poli ſupra Horizontem metiente com-
<
lb
/>
<
figure
xlink:label
="
fig-0115-01
"
xlink:href
="
fig-0115-01a
"
number
="
81
">
<
image
file
="
0115-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0115-01
"/>
</
figure
>
ponitur, interiectus inter planum inclinatum, & </
s
>
<
s
xml:id
="
echoid-s5404
"
xml:space
="
preserve
">polum mundi arcti-
<
lb
/>
cum, ſi quadratem non exceſſerit; </
s
>
<
s
xml:id
="
echoid-s5405
"
xml:space
="
preserve
">ſi enim exceſſerit quadrantem,
<
lb
/>
erit eius cõplementum ad ſemicirculũ dictus arcus, qui quidem ſupra
<
lb
/>
Horizontẽ cõtinetur verſus auſtrũ, quemadmodum ille partim ſupra
<
lb
/>
Horizontẽ & </
s
>
<
s
xml:id
="
echoid-s5406
"
xml:space
="
preserve
">partim infra. </
s
>
<
s
xml:id
="
echoid-s5407
"
xml:space
="
preserve
">Si verò ſupra Horizontẽ extiterit, erit ar-
<
lb
/>
cus, quo ipſe differt ab arcu altitudinẽ poli ſupra Horizõtem metien
<
lb
/>
te, inter planũ ipſum, & </
s
>
<
s
xml:id
="
echoid-s5408
"
xml:space
="
preserve
">polum mundi arcticũ interceptus, cõtinebi-
<
lb
/>
turq́; </
s
>
<
s
xml:id
="
echoid-s5409
"
xml:space
="
preserve
">ſupra Horizontem modo verſus boream, modo verſus auſtrum.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5410
"
xml:space
="
preserve
">Quę quidem omnia ex hac appoſita figura perſpicua fient, in qua
<
lb
/>
Meridianus A B C D; </
s
>
<
s
xml:id
="
echoid-s5411
"
xml:space
="
preserve
">axis mundi E F; </
s
>
<
s
xml:id
="
echoid-s5412
"
xml:space
="
preserve
">polus arcticus E, antarcti-
<
lb
/>
cus F; </
s
>
<
s
xml:id
="
echoid-s5413
"
xml:space
="
preserve
">communis ſectio Horizontis ac Meridiani
<
unsure
/>
B D; </
s
>
<
s
xml:id
="
echoid-s5414
"
xml:space
="
preserve
">communis ſe-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0115-09
"
xlink:href
="
note-0115-09a
"
xml:space
="
preserve
">40</
note
>
ctio Verticalis, & </
s
>
<
s
xml:id
="
echoid-s5415
"
xml:space
="
preserve
">Meridiani A C; </
s
>
<
s
xml:id
="
echoid-s5416
"
xml:space
="
preserve
">communis ſectio plani inclinati,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s5417
"
xml:space
="
preserve
">Meridiani G H, vel I k, vel L M, vel N O. </
s
>
<
s
xml:id
="
echoid-s5418
"
xml:space
="
preserve
">Vides igitur arcum
<
lb
/>
G E, compoſitum ex arcu G D, inter planum inclinatum, ac Horizon
<
lb
/>
tem ſub Horizonte, & </
s
>
<
s
xml:id
="
echoid-s5419
"
xml:space
="
preserve
">arcu D E, altitudinis poli ſupra Horizontem; </
s
>
<
s
xml:id
="
echoid-s5420
"
xml:space
="
preserve
">arcum item I E, vel L E, quo differt
<
lb
/>
arcus D I, vel D L, inter planum inclinatum & </
s
>
<
s
xml:id
="
echoid-s5421
"
xml:space
="
preserve
">Horizontem ſupra Horizontẽ ab arcu D E, altitudinis
<
lb
/>
poli ſupra Horizontem, interceptum eſſe inter planum inclinatum, & </
s
>
<
s
xml:id
="
echoid-s5422
"
xml:space
="
preserve
">polum arcticum E. </
s
>
<
s
xml:id
="
echoid-s5423
"
xml:space
="
preserve
">Item arcum
<
lb
/>
E N, inter planum N O, & </
s
>
<
s
xml:id
="
echoid-s5424
"
xml:space
="
preserve
">polum eſſe ſumendum, quamuis arcus D O, inter planum, & </
s
>
<
s
xml:id
="
echoid-s5425
"
xml:space
="
preserve
">Horizontem ſit
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0115-10
"
xlink:href
="
note-0115-10a
"
xml:space
="
preserve
">50</
note
>
ſub Horizonte, quia totus arcus E O, quadrantem ſuperat.</
s
>
<
s
xml:id
="
echoid-s5426
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5427
"
xml:space
="
preserve
">QVOD ſi planum inclinatum, fuerit rectum ad Verticalem circulum, hoc eſt, ſi directè ad ortum,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-11
"
xlink:href
="
note-0115-11a
"
xml:space
="
preserve
">Quando planũ
<
lb
/>
rectũ eſt ad Ver
<
lb
/>
ticalem.</
note
>
vel occaſum ſpectet, tranſeatq́; </
s
>
<
s
xml:id
="
echoid-s5428
"
xml:space
="
preserve
">per communes ſectiones Horizontis ac Meridiani, ita vt eius, & </
s
>
<
s
xml:id
="
echoid-s5429
"
xml:space
="
preserve
">Meridia-
<
lb
/>
ni communis ſectio ſit recta B D, non differet arcus inter planum ipſum, & </
s
>
<
s
xml:id
="
echoid-s5430
"
xml:space
="
preserve
">polum E, ab arcu D E, altitu
<
lb
/>
dinem poli ſupra Horizontem metiente, vt conſtat.</
s
>
<
s
xml:id
="
echoid-s5431
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5432
"
xml:space
="
preserve
">SI verò planum inclinatum rectum fuerit ad Horizontem, hoc eſt, ſi per verticem A, tranſierit, ita vt
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-12
"
xlink:href
="
note-0115-12a
"
xml:space
="
preserve
">Quando planũ
<
lb
/>
recũ eſt ad Ho
<
lb
/>
rizontem.</
note
>
communis ſectio ipſius, ac Meridiani ſit recta A C, non differet arcus inter ipſum planum, & </
s
>
<
s
xml:id
="
echoid-s5433
"
xml:space
="
preserve
">polum E,
<
lb
/>
ab arcu A E, qui complementum altitudinis poli ſupra Horizontem dimetitur, vt manifeſtum eſt.</
s
>
<
s
xml:id
="
echoid-s5434
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5435
"
xml:space
="
preserve
">PARI ratione comperiemus, quantus ſit arcus Meridiani inter planum inclinatum, & </
s
>
<
s
xml:id
="
echoid-s5436
"
xml:space
="
preserve
">verticem ca-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0115-13
"
xlink:href
="
note-0115-13a
"
xml:space
="
preserve
">Quantus ſit ar-
<
lb
/>
cus Meridiani
<
lb
/>
inter planũ in-
<
lb
/>
clinatũ, & ver-
<
lb
/>
ticem capitis.</
note
>
pitis interiectus. </
s
>
<
s
xml:id
="
echoid-s5437
"
xml:space
="
preserve
">Nam ſi arcum Meridiani inter planum & </
s
>
<
s
xml:id
="
echoid-s5438
"
xml:space
="
preserve
">Horizontem auſeramus ex quadrante, reli-
<
lb
/>
quus erit arcus Meridiani inter planum, & </
s
>
<
s
xml:id
="
echoid-s5439
"
xml:space
="
preserve
">verticem capitis; </
s
>
<
s
xml:id
="
echoid-s5440
"
xml:space
="
preserve
">continebiturq́ arcus hic in parte boreali,
<
lb
/>
ſi arcus inter planum, & </
s
>
<
s
xml:id
="
echoid-s5441
"
xml:space
="
preserve
">Horizontem fuerit ſupra Horizontem ex eadem parte boreali; </
s
>
<
s
xml:id
="
echoid-s5442
"
xml:space
="
preserve
">in parte </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>