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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0127
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rhead
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LIBER PRIMVS.
"/>
lij ſequentis. </
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>
<
s
xml:id
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echoid-s6452
"
xml:space
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">Sed tamen præſtat inuenire declinationes parallelorum Borealium. </
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>
<
s
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echoid-s6453
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xml:space
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">Nam horũ de-
<
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clinationes æquales ſunt declinationibus reſpondentium parallelorum auſtralium. </
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>
<
s
xml:id
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echoid-s6454
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xml:space
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">Vt declinatio
<
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paralleli borealis, cuius arcus diurnus continet horas 14. </
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>
<
s
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="
echoid-s6455
"
xml:space
="
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">æqualis eſt declinationi paralleli auſtra-
<
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lis, cuius arcus diurnus horas 10. </
s
>
<
s
xml:id
="
echoid-s6456
"
xml:space
="
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">complectitur, nempe qui cum illo horas 24. </
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>
<
s
xml:id
="
echoid-s6457
"
xml:space
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">conſtituit. </
s
>
<
s
xml:id
="
echoid-s6458
"
xml:space
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">Nam ar-
<
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cus nocturnus E D F, paralleli borealis, cuius diameter B D, declinationemq́; </
s
>
<
s
xml:id
="
echoid-s6459
"
xml:space
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">habens D M, æqua-
<
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lis eſt, per propoſ. </
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<
s
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echoid-s6460
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xml:space
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">19. </
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<
s
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xml:space
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">lib. </
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<
s
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"
xml:space
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">2. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Theodoſii, arcui diurno paralleli auſtralis, qui priori ęqnalis eſt, & </
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>
<
s
xml:id
="
echoid-s6464
"
xml:space
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">op-
<
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poſitus, hoc eſt, qui declinationem habet æqualem. </
s
>
<
s
xml:id
="
echoid-s6465
"
xml:space
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">Vnde inuenta declinatione paralleli borealis,
<
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/>
habetur etiam declinatio paralleli auſtralis oppoſiti, & </
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>
<
s
xml:id
="
echoid-s6466
"
xml:space
="
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">æqualis, cuius arcus diurnus cum arcu
<
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diurno illius complet horas 24.</
s
>
<
s
xml:id
="
echoid-s6467
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xml:space
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"/>
</
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<
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<
s
xml:id
="
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"
xml:space
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">QVONIAM verò modus proxime deſcriptus requirit accuratam diuiſionẽ circuli ABCD,
<
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<
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left
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xlink:label
="
note-0127-01
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xlink:href
="
note-0127-01a
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xml:space
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">10</
note
>
in horas, ſemiſſes horarũ, & </
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>
<
s
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xml:space
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">quadrantes, poterimus ex ſinubus idem conſequi ſine vlla diuiſione
<
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circuli, hac arte. </
s
>
<
s
xml:id
="
echoid-s6470
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xml:space
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">Sit Analemma A B C D, cuius centrum E; </
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>
<
s
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="
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xml:space
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">Horizon B D; </
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<
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xml:space
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">Aequator A C; </
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>
<
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xml:space
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">paralle-
<
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<
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xlink:label
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note-0127-02
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xlink:href
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note-0127-02a
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xml:space
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">Declinatio pa-
<
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ralleli, cuius ar-
<
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cus diutnus ſit
<
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notus, qua arte
<
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per ſinus per-
<
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quiratur.</
note
>
lus ſiue boreus, ſiue auſtrinus H I; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">axis mundi F G, ſecans parallelum in K. </
s
>
<
s
xml:id
="
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xml:space
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">Deſcribatur ex K, circa
<
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/>
H I, ſen@icirculus paralleli H M I, cui occurrat axis productus in M. </
s
>
<
s
xml:id
="
echoid-s6476
"
xml:space
="
preserve
">Ducatur quoque ex L, ad H I,
<
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/>
perpendicularis L N, quæ erit communis ſectio paralleli H M I, & </
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>
<
s
xml:id
="
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xml:space
="
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">Horizontis; </
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>
<
s
xml:id
="
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"
xml:space
="
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">(Quoniã enim tam
<
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/>
Horizon, quàm parallelus rectus eſt ad Meridianum, erit quoque cõmunis eorum ſectio ad eun-
<
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/>
<
note
position
="
right
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xlink:label
="
note-0127-03
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xlink:href
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xml:space
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">19. vndec.</
note
>
dem perpendicularis in puncto L,
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<
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number
="
93
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<
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file
="
0127-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0127-01
"/>
</
figure
>
vbi ſe mutuo ſecant, ac proinde & </
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>
<
s
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="
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xml:space
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">ad
<
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rectam H I, per defin. </
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>
<
s
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xml:space
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">3. </
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>
<
s
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xml:space
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">lib. </
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<
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xml:space
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">11. </
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>
<
s
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"
xml:space
="
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">Eucl.
<
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</
s
>
<
s
xml:id
="
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"
xml:space
="
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">Ergo L N, perpendicularis ad H I,
<
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<
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position
="
left
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xlink:label
="
note-0127-04
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xlink:href
="
note-0127-04a
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xml:space
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">20</
note
>
cõmunis ſectio erit Horizontis & </
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>
<
s
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="
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xml:space
="
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">pa
<
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ralleli) atque adeo H N, erit arcus ſe-
<
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/>
midiurnus dicti paralleli, qui poni-
<
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/>
tur notus. </
s
>
<
s
xml:id
="
echoid-s6486
"
xml:space
="
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">Tandem iungatur recta
<
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E H. </
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>
<
s
xml:id
="
echoid-s6487
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xml:space
="
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">Quoniam igitur in triangulo
<
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E
<
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style
="
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">K</
emph
>
L, ſi recta E L, ponatur ſinus to-
<
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tus, recta K L, ſinus eſt anguli K E L,
<
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/>
altitudinis poli, & </
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>
<
s
xml:id
="
echoid-s6488
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xml:space
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">E K, ſinus anguli
<
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/>
E L k, complementi altitudinis poli;
<
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</
s
>
<
s
xml:id
="
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xml:space
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">ſi fiat, vt K L, ſinus altitudinis poli,
<
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<
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position
="
left
"
xlink:label
="
note-0127-05
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xlink:href
="
note-0127-05a
"
xml:space
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">30</
note
>
ad E K, ſinum complementi altitudi-
<
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/>
nis poli, ita K L, quatenus ſinus re-
<
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/>
ctus arcus M N, quo arcus ſemidiur-
<
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/>
nus H N, notus, & </
s
>
<
s
xml:id
="
echoid-s6490
"
xml:space
="
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">quadrans H M,
<
lb
/>
inter ſe differunt, ad aliud, nota fiet
<
lb
/>
recta E k, in partibus ſinus totius
<
lb
/>
K H, reſpectu cuius K L, ſinus rectus
<
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/>
eſt arcus M N. </
s
>
<
s
xml:id
="
echoid-s6491
"
xml:space
="
preserve
">Quia igitur duo qua-
<
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drata rectarum E K, k H, quadrato rectæ E H, æqualia ſunt; </
s
>
<
s
xml:id
="
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"
xml:space
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">ſi ſimul addantur quadratum ſinus to-
<
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<
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position
="
right
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xlink:label
="
note-0127-06
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xlink:href
="
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"
xml:space
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">47. primi.</
note
>
tius K H, & </
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>
<
s
xml:id
="
echoid-s6493
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xml:space
="
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">quadratum rectæ E K, notæ iam factæ in partibus ſinus totius K H, notum erit qua-
<
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<
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position
="
left
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xlink:label
="
note-0127-07
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xlink:href
="
note-0127-07a
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xml:space
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">40</
note
>
dratum rectæ E H, cuius radix quadrata dabit rectam E H, notam in ijſdem partibus ſinus to-
<
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/>
tius k H. </
s
>
<
s
xml:id
="
echoid-s6494
"
xml:space
="
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">Itaque ſi fiat, vt E H, quatenus nota in partibus ſinus totius K H, ad E K, quatenus
<
lb
/>
nota eſt in ijſdem partibus, ita E H, quatenus ſinus totus, ad aliud, nota fiet E K, in partibus
<
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/>
ſinus totius E H. </
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>
<
s
xml:id
="
echoid-s6495
"
xml:space
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">Quare & </
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>
<
s
xml:id
="
echoid-s6496
"
xml:space
="
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">A H, arcus reſpondens ſinui E k, ex tabula ſinuum cognitus
<
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erit, nempe declinatio paralleli, cuius arcus diurnus, ac proinde & </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſemidiurnus H N, no-
<
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tus ponitur.</
s
>
<
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xml:id
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</
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<
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<
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">EXEMPLVM. </
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>
<
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xml:space
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">Sit datus arcus diurnus horarum 14. </
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>
<
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xml:space
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">vel 10. </
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>
<
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xml:space
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">atque adeo ſemidiurnus arcus
<
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<
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="
right
"
xlink:label
="
note-0127-08
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xlink:href
="
note-0127-08a
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xml:space
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">Exemplu@.</
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>
H N, horarum 7. </
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<
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xml:space
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">vel 5. </
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<
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xml:space
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">hoc eſt, grad. </
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<
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xml:space
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">105. </
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<
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xml:space
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">vel 75. </
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>
<
s
xml:id
="
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xml:space
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">ex quo fiet arcus M N, horæ vnius, nempe grad.
<
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</
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<
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="
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xml:space
="
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">15. </
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>
<
s
xml:id
="
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"
xml:space
="
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">cum quadrans H M, contineat horas 6. </
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>
<
s
xml:id
="
echoid-s6510
"
xml:space
="
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">hoc eſt, grad. </
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>
<
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xml:id
="
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"
xml:space
="
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">90. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Si igitur fiat, vt k L, ſinus altitudinis
<
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poli 66913. </
s
>
<
s
xml:id
="
echoid-s6513
"
xml:space
="
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">ad E K, ſinum complementi altitudinis poli 74314. </
s
>
<
s
xml:id
="
echoid-s6514
"
xml:space
="
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">ita K L, ſinus arcus M N, quo
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0127-09
"
xlink:href
="
note-0127-09a
"
xml:space
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">50</
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differt arcus ſemidiurnus à quadrãte, nempe in dato exemplo, ſinus arcus grad. </
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<
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xml:id
="
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xml:space
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">15. </
s
>
<
s
xml:id
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xml:space
="
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">qui eſt 25881.
<
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</
s
>
<
s
xml:id
="
echoid-s6517
"
xml:space
="
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">ad aliud, inuenietur E K, partium ferè 28744, qualium K L, eſt 25881. </
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>
<
s
xml:id
="
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xml:space
="
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">Quia verò K H, ſinus totus
<
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/>
earundem partium eſt 100000. </
s
>
<
s
xml:id
="
echoid-s6519
"
xml:space
="
preserve
">ſi quadrati numeri ſinuum E K, KH, ſimul addantur, fiet quadra-
<
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tum rectę E H, partium ferè 10826217536. </
s
>
<
s
xml:id
="
echoid-s6520
"
xml:space
="
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">atque adeò recta E H, erit quaſi partium 104049. </
s
>
<
s
xml:id
="
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xml:space
="
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">
<
lb
/>
reſpectu ſinus totius K H. </
s
>
<
s
xml:id
="
echoid-s6522
"
xml:space
="
preserve
">Igitur ſi fiat, vt E H, 104049. </
s
>
<
s
xml:id
="
echoid-s6523
"
xml:space
="
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">ad E K, 28744. </
s
>
<
s
xml:id
="
echoid-s6524
"
xml:space
="
preserve
">ita E H, ſinus to-
<
lb
/>
tus 100000. </
s
>
<
s
xml:id
="
echoid-s6525
"
xml:space
="
preserve
">ad aliud, reperietur E K, ſinus declinationis paralleli H I, reſpectu ſinus totius
<
lb
/>
E H, partium ferè 27625. </
s
>
<
s
xml:id
="
echoid-s6526
"
xml:space
="
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">cuius arcus eſt grad. </
s
>
<
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="
echoid-s6527
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xml:space
="
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">16. </
s
>
<
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="
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xml:space
="
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">Min. </
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>
<
s
xml:id
="
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"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s6530
"
xml:space
="
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">Tanta eſt declinatio paralle-
<
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<
note
position
="
right
"
xlink:label
="
note-0127-10
"
xlink:href
="
note-0127-10a
"
xml:space
="
preserve
">Declinatio pa-
<
lb
/>
ralleli, cuius ar-
<
lb
/>
cus. diurnus da-
<
lb
/>
tus ſit, quo pa-
<
lb
/>
cto aliter per ſi-
<
lb
/>
nus ſit inuefti-
<
lb
/>
gandus.</
note
>
li
<
emph
style
="
sc
">H</
emph
>
I, borealis quidem, ſi dies maior eſt 12. </
s
>
<
s
xml:id
="
echoid-s6531
"
xml:space
="
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">horis, auſtralis autem, ſi minor. </
s
>
<
s
xml:id
="
echoid-s6532
"
xml:space
="
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">Eadem ratio eſt
<
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/>
in cæteris.</
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>
<
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="
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"/>
</
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>
<
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>
<
s
xml:id
="
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"
xml:space
="
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">FACILIVS idem obtinebimus per triangula ſphęrica hoc modo. </
s
>
<
s
xml:id
="
echoid-s6535
"
xml:space
="
preserve
">Sit
<
emph
style
="
sc
">H</
emph
>
orizon A B C D;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6536
"
xml:space
="
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">Meridianus A C; </
s
>
<
s
xml:id
="
echoid-s6537
"
xml:space
="
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">Aequator B D, Meridianum ſecans in E; </
s
>
<
s
xml:id
="
echoid-s6538
"
xml:space
="
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">parallelus ſiue borealis, ſiue </
s
>
</
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>
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>
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