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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<
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file
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0143
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143
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rhead
="
LIBER PRIMVS.
"/>
tudinis, & </
s
>
<
s
xml:id
="
echoid-s7432
"
xml:space
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">ſinu grad. </
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>
<
s
xml:id
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echoid-s7433
"
xml:space
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">18. </
s
>
<
s
xml:id
="
echoid-s7434
"
xml:space
="
preserve
">compoſita, vt accidit in tertia figura huius propoſ. </
s
>
<
s
xml:id
="
echoid-s7435
"
xml:space
="
preserve
">Subtracto autem arcu ſe-
<
lb
/>
midiurno K Q, ex arcu K R, inuento, perſpicuum eſt, arcum crepuſculi Q R, relinqui. </
s
>
<
s
xml:id
="
echoid-s7436
"
xml:space
="
preserve
">Quòd ſi dicta me-
<
lb
/>
dietas K λ, æqualis fuerit dictæ rectę K O, erit arcus compoſitus ex arcu ſemidiurno, & </
s
>
<
s
xml:id
="
echoid-s7437
"
xml:space
="
preserve
">arcu crepuſcu-
<
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li quadrans, vt in quarta figura huius propoſ. </
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>
<
s
xml:id
="
echoid-s7438
"
xml:space
="
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">apparet.</
s
>
<
s
xml:id
="
echoid-s7439
"
xml:space
="
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"/>
</
p
>
<
p
style
="
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">
<
s
xml:id
="
echoid-s7440
"
xml:space
="
preserve
">QVIN etiam beneficio altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s7441
"
xml:space
="
preserve
">depreſſionis meridianæ, breui admodum calculo
<
lb
/>
arcus ſemidiurnos ſupputabimus, licet eoſdem alio modo in præcedenti propoſ. </
s
>
<
s
xml:id
="
echoid-s7442
"
xml:space
="
preserve
">inuenerimus. </
s
>
<
s
xml:id
="
echoid-s7443
"
xml:space
="
preserve
">Quoniam
<
lb
/>
enim in omnibus figuris huius propoſ. </
s
>
<
s
xml:id
="
echoid-s7444
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7445
"
xml:space
="
preserve
">etiam in priori, quę in ſcholio ponitur, eſt vt K λ, medietas re-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0143-01
"
xlink:href
="
note-0143-01a
"
xml:space
="
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">2. vel 4. ſexti</
note
>
<
note
position
="
right
"
xlink:label
="
note-0143-02
"
xlink:href
="
note-0143-02a
"
xml:space
="
preserve
">Arcus ſemidiur
<
lb
/>
nus qua ratio-
<
lb
/>
ne ſupputandus
<
lb
/>
aliter quàm ſ@-
<
lb
/>
pra.</
note
>
ctæ compoſitæ ex ſinu altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s7446
"
xml:space
="
preserve
">ſinu depreſſionis meridianæ ad λ N, differentiam inter
<
lb
/>
prædictam medietatem, & </
s
>
<
s
xml:id
="
echoid-s7447
"
xml:space
="
preserve
">ſinum altitudinis meridianæ, ita K M, ſinus totus ad M S: </
s
>
<
s
xml:id
="
echoid-s7448
"
xml:space
="
preserve
">Si fiat vt K λ,
<
lb
/>
medietas rectę ex ſinu altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s7449
"
xml:space
="
preserve
">ſinu depreſſionis meridianæ compoſitæ, ad λ N, differen-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0143-03
"
xlink:href
="
note-0143-03a
"
xml:space
="
preserve
">10</
note
>
tiam inter dictam medietatem, & </
s
>
<
s
xml:id
="
echoid-s7450
"
xml:space
="
preserve
">ſinum meridianæ altitudinis, ita K M, ſinus totus ad aliud, inuenietur
<
lb
/>
ſinus rectus M S, cuius arcus P Q, in ſignis borealibus additus quadranti, in auſtralibus verò à qua-
<
lb
/>
drante ſubtractus, dabit arcum ſemidiurnum K Q.</
s
>
<
s
xml:id
="
echoid-s7451
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7452
"
xml:space
="
preserve
">IDEM hac ratione conſequemur. </
s
>
<
s
xml:id
="
echoid-s7453
"
xml:space
="
preserve
">Quoniam in eiſdem figuris eſt, vt K λ, medietas prædicta ad
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0143-04
"
xlink:href
="
note-0143-04a
"
xml:space
="
preserve
">Arcus ſemidiur
<
lb
/>
nus quomodo
<
lb
/>
aliter inueſtige-
<
lb
/>
tur.</
note
>
K N, ſinum altitudinis meridianæ, ita K M, ſinus totus ad K S, ſinum verſum arcus ſemidiurni
<
lb
/>
K Q: </
s
>
<
s
xml:id
="
echoid-s7454
"
xml:space
="
preserve
">Si fiat vt K λ, medietas rectæ compoſitæ ex ſinu altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s7455
"
xml:space
="
preserve
">ſinu depreſſionis meri-
<
lb
/>
dianę ad K N, ſinum altitudinis meridianæ, ita K M, ſinus totus ad aliud, obtinebimus K S, ſinum ver-
<
lb
/>
ſum arcus ſemidiurni K Q. </
s
>
<
s
xml:id
="
echoid-s7456
"
xml:space
="
preserve
">Ex quo ſinu verſo ita adipiſcemur arcum ſemidiurnum K Q. </
s
>
<
s
xml:id
="
echoid-s7457
"
xml:space
="
preserve
">In ſignis borea-
<
lb
/>
libus dematur ex ſinu verſo inuento ſinus totus, & </
s
>
<
s
xml:id
="
echoid-s7458
"
xml:space
="
preserve
">reſidui ſinus recti arcus P Q, ad quadrantem adij-
<
lb
/>
ciatur; </
s
>
<
s
xml:id
="
echoid-s7459
"
xml:space
="
preserve
">In ſignis verò auſtralib{us} contra, ſin{us} verſ{us} inuentus ex ſinu toto auferatur, & </
s
>
<
s
xml:id
="
echoid-s7460
"
xml:space
="
preserve
">reſidui ſinus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0143-05
"
xlink:href
="
note-0143-05a
"
xml:space
="
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">20</
note
>
recti arcus P Q, ex quadrante rurſus ſubtrahatur. </
s
>
<
s
xml:id
="
echoid-s7461
"
xml:space
="
preserve
">Exurget enim ſemper ſiue ex illa additione, ſiue ex
<
lb
/>
hac ſubtractione arcus ſemidiurnus.</
s
>
<
s
xml:id
="
echoid-s7462
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7463
"
xml:space
="
preserve
">HAEC autem omnia intelligenda ſunt, quando complementum altitudinis poli maius eſt declina-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0143-06
"
xlink:href
="
note-0143-06a
"
xml:space
="
preserve
">Arcus diurnus
<
lb
/>
quoniodo ſe ha
<
lb
/>
beat, quando cõ
<
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/>
plementum al-
<
lb
/>
titudinis poli
<
lb
/>
maius non fue-
<
lb
/>
rit declinatione
<
lb
/>
propoſiti paral-
<
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/>
leli.</
note
>
tione paralleli illius, cuius arcus ſemidiurnus inueſtigatur. </
s
>
<
s
xml:id
="
echoid-s7464
"
xml:space
="
preserve
">Nam quando complementum illud non eſt ma-
<
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/>
ius, tanget vel parallelus Horizontem, at que ita eius arcus diurnus, ſi borealis eſt, continebit horas 24.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s7465
"
xml:space
="
preserve
">vel ſi auſiralis, hor. </
s
>
<
s
xml:id
="
echoid-s7466
"
xml:space
="
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">0. </
s
>
<
s
xml:id
="
echoid-s7467
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7468
"
xml:space
="
preserve
">0. </
s
>
<
s
xml:id
="
echoid-s7469
"
xml:space
="
preserve
">Vel totus parallelus borealis ſupra Horizontem extat, & </
s
>
<
s
xml:id
="
echoid-s7470
"
xml:space
="
preserve
">auſtralis infra,
<
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/>
atque ita nullus erit arcus diurnus, ſed continua dies in parallelo boreali, & </
s
>
<
s
xml:id
="
echoid-s7471
"
xml:space
="
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">continua nox in auſtrali erit. </
s
>
<
s
xml:id
="
echoid-s7472
"
xml:space
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">
<
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/>
Quæ omnia in ſecunda figura ſcholij huius propoſ. </
s
>
<
s
xml:id
="
echoid-s7473
"
xml:space
="
preserve
">apparent, vbi complementum altitudinis poli C I, mi-
<
lb
/>
nus eſt declinatione I L, paralleli borealis, & </
s
>
<
s
xml:id
="
echoid-s7474
"
xml:space
="
preserve
">rurſus idem complementum A H, minus declinatione
<
lb
/>
H K, paralleli auſtralis. </
s
>
<
s
xml:id
="
echoid-s7475
"
xml:space
="
preserve
">Quòd ſi complementum illud declinationi foret æquale, tangeret parallelus bo-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0143-07
"
xlink:href
="
note-0143-07a
"
xml:space
="
preserve
">30</
note
>
realis Horizontem in C, & </
s
>
<
s
xml:id
="
echoid-s7476
"
xml:space
="
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">australis in A, vt manifeſtum eſt.</
s
>
<
s
xml:id
="
echoid-s7477
"
xml:space
="
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"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7478
"
xml:space
="
preserve
">VT autem omnibus numeris abſoluta ſit demonſtratio huius propoſ. </
s
>
<
s
xml:id
="
echoid-s7479
"
xml:space
="
preserve
">trademus etiam inuentionem
<
lb
/>
crepuſculorum in ſphærarecta, vbi multo facilius inueniuntur. </
s
>
<
s
xml:id
="
echoid-s7480
"
xml:space
="
preserve
">Sit Meridianus Analemmatis A B C D;
<
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/>
</
s
>
<
s
xml:id
="
echoid-s7481
"
xml:space
="
preserve
">Horizontis recti diameter A C, per polos A, C, tranſiens; </
s
>
<
s
xml:id
="
echoid-s7482
"
xml:space
="
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">Paral-
<
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<
figure
xlink:label
="
fig-0143-01
"
xlink:href
="
fig-0143-01a
"
number
="
103
">
<
image
file
="
0143-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0143-01
"/>
</
figure
>
leli Horizontis, in quo principium, vel terminus crepuſculi ponitur,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0143-08
"
xlink:href
="
note-0143-08a
"
xml:space
="
preserve
">Crepuſculum
<
lb
/>
in ſphæra recta,
<
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/>
quo pacto in-
<
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/>
dagandum.</
note
>
diameter F G; </
s
>
<
s
xml:id
="
echoid-s7483
"
xml:space
="
preserve
">Aequatoris diameter B D, ſecans F G, in H; </
s
>
<
s
xml:id
="
echoid-s7484
"
xml:space
="
preserve
">diame
<
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/>
ter paralleli Solis c
<
unsure
/>
uiuſcunque I K, ſecans A C, F G, in L, & </
s
>
<
s
xml:id
="
echoid-s7485
"
xml:space
="
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">M.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s7486
"
xml:space
="
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">Ex L, centro paralleli deſcribatur ſemicirculus ipſius I N K, exten
<
lb
/>
danturq́, A C, F G, vſque ad N, & </
s
>
<
s
xml:id
="
echoid-s7487
"
xml:space
="
preserve
">O.</
s
>
<
s
xml:id
="
echoid-s7488
"
xml:space
="
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"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7489
"
xml:space
="
preserve
">ERIT igitur A F, vel C G, arcus crepuſculi, Sole in Aequa-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0143-09
"
xlink:href
="
note-0143-09a
"
xml:space
="
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">40</
note
>
tore exiſtente, cuius ſinus eſt recta E H, reſpondens arcui grad. </
s
>
<
s
xml:id
="
echoid-s7490
"
xml:space
="
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">18.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7491
"
xml:space
="
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">Igitur ſi ſumatur arcus grad. </
s
>
<
s
xml:id
="
echoid-s7492
"
xml:space
="
preserve
">18. </
s
>
<
s
xml:id
="
echoid-s7493
"
xml:space
="
preserve
">habebitur arcus crepuſculi in ſphæ-
<
lb
/>
rarecta, Sole in æquinoctijs exiſtente.</
s
>
<
s
xml:id
="
echoid-s7494
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7495
"
xml:space
="
preserve
">SOLE verò in quouis parallelo exiſtente, vt in parallelo INK,
<
lb
/>
erit arcus O N, longitudo crepuſculi. </
s
>
<
s
xml:id
="
echoid-s7496
"
xml:space
="
preserve
">Si igitur fiat, vt I L, quatenus
<
lb
/>
pars eſt ſinus totius B E, maximi circuli, hoc eſt, quatenus ſinus eſt complementi declinationis, (eſt
<
lb
/>
enim arcus I C, vel I A, complementum declinationis) ad L M, ſinum grad. </
s
>
<
s
xml:id
="
echoid-s7497
"
xml:space
="
preserve
">18. </
s
>
<
s
xml:id
="
echoid-s7498
"
xml:space
="
preserve
">eiuſdem circuli maximi,
<
lb
/>
ita I L, quatenus ſinus totus in parallelo I N K, ad aliud, c
<
unsure
/>
ognita erit L M, in partibus ſinus totius I L;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7499
"
xml:space
="
preserve
">atque adeò @ius arcus N O, qui crepuſculum metitur, notus erit. </
s
>
<
s
xml:id
="
echoid-s7500
"
xml:space
="
preserve
">Atque hoc verum eſt, ſiue I K, ſit dia-
<
lb
/>
meter paralleli auſtralis, ſiue borealis, vt ex figura manifeſtum eſt.</
s
>
<
s
xml:id
="
echoid-s7501
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">50</
note
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7502
"
xml:space
="
preserve
">NON eſt autem prætereundum, vno fere nos labore peruestigare poſſe crepuſcula duorum paralle-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0143-11
"
xlink:href
="
note-0143-11a
"
xml:space
="
preserve
">Crepuſcula duo
<
lb
/>
rum parallclo-
<
lb
/>
rum oppoſito-
<
lb
/>
rum, qua ratio-
<
lb
/>
ne vnico labore
<
unsure
/>
<
lb
/>
inueniantur.</
note
>
lorum oppoſitorum, ſi primo modo vtamur. </
s
>
<
s
xml:id
="
echoid-s7503
"
xml:space
="
preserve
">Quoniam enim arcus ſemidiurnus cuiuſuis paralleli æqualis
<
lb
/>
eſt ar cui ſeminocturno, vt in ſcholio antecedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s7504
"
xml:space
="
preserve
">oſtendimus, erit ſinus verſus K S, arcus ſemi-
<
lb
/>
diurni paralleli australis æqualis ſinui verſo L S, arcus ſeminocturni paralleli borealis oppoſiti, vt in
<
lb
/>
ſequẽti prima figura apparet. </
s
>
<
s
xml:id
="
echoid-s7505
"
xml:space
="
preserve
">Est autẽ & </
s
>
<
s
xml:id
="
echoid-s7506
"
xml:space
="
preserve
">S T, portio diametri paralleli auſtralis portioni S T, diametri
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0143-12
"
xlink:href
="
note-0143-12a
"
xml:space
="
preserve
">34. primi.</
note
>
paralleli borealis æqualis. </
s
>
<
s
xml:id
="
echoid-s7507
"
xml:space
="
preserve
">Igitur ſi fiat, vt K N, ſinus altitudinis meridianæ paralleli auſtralis ad
<
lb
/>
N O, ſinum grad. </
s
>
<
s
xml:id
="
echoid-s7508
"
xml:space
="
preserve
">18. </
s
>
<
s
xml:id
="
echoid-s7509
"
xml:space
="
preserve
">ita K S, ſinus verſus arcus ſemidiurni paralleli auſtralis, ad aliud, nota erit re-
<
lb
/>
cta S T; </
s
>
<
s
xml:id
="
echoid-s7510
"
xml:space
="
preserve
">cum eandem proportionem habeat K N, ad N O, quam k S, ad S T. </
s
>
<
s
xml:id
="
echoid-s7511
"
xml:space
="
preserve
">Hæc autem S T, nota,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0143-13
"
xlink:href
="
note-0143-13a
"
xml:space
="
preserve
">2. ſ@nti.</
note
>
(quam fortaſſis facilius inuenies ratione ad finem huius propoſ. </
s
>
<
s
xml:id
="
echoid-s7512
"
xml:space
="
preserve
">præſcripta) ſi adijciatur ad ſinum ver-
<
lb
/>
ſum K S, arcus ſemidiurni paralleli auſtralis, conflabitur K T, ſinus verſus arcus K R, compoſiti ex ar-
<
lb
/>
@u ſemidiurno K Q, & </
s
>
<
s
xml:id
="
echoid-s7513
"
xml:space
="
preserve
">arcu crepuſculi Q R. </
s
>
<
s
xml:id
="
echoid-s7514
"
xml:space
="
preserve
">Dempto ergo ſemidiurno arcu K Q, remanebit </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>