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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LIBER PRIMVS.
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gradibus 42. </
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<
s
xml:id
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xml:space
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<
s
xml:id
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xml:space
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">pręcedentem inuẽta grad. </
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<
s
xml:id
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xml:space
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<
s
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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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echoid-s6023
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xml:space
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s
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<
s
xml:id
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xml:space
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">Arcus verò Meridiani inter idem planum, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">polum continebit grad. </
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>
<
s
xml:id
="
echoid-s6026
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xml:space
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">48. </
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>
<
s
xml:id
="
echoid-s6027
"
xml:space
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">quantum nimirũ
<
lb
/>
eſt complementum altitudinis poli ſupra Horizontem. </
s
>
<
s
xml:id
="
echoid-s6028
"
xml:space
="
preserve
">Igitur ſi fiat, vt 76548. </
s
>
<
s
xml:id
="
echoid-s6029
"
xml:space
="
preserve
">ſinus complemen-
<
lb
/>
ti altitudinis poli ſupra planum, ad 66913. </
s
>
<
s
xml:id
="
echoid-s6030
"
xml:space
="
preserve
">ſinum complementi arcus Meridiani inter planum & </
s
>
<
s
xml:id
="
echoid-s6031
"
xml:space
="
preserve
">
<
lb
/>
polum, (quod complementum in huiuſmodi planis inclinatis eſt ipſamet poli altitudo ſupra Ho
<
lb
/>
rizontem,) ita 100000. </
s
>
<
s
xml:id
="
echoid-s6032
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xml:space
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">ſinus totus ad, aliud, rep erietur hic ferè ſinus 87413. </
s
>
<
s
xml:id
="
echoid-s6033
"
xml:space
="
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">cuius arcus continet
<
lb
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gradus 60. </
s
>
<
s
xml:id
="
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"
xml:space
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">Min. </
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>
<
s
xml:id
="
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"
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">57. </
s
>
<
s
xml:id
="
echoid-s6036
"
xml:space
="
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">quo detracto ex quadrante, reliquus erit arcus grad. </
s
>
<
s
xml:id
="
echoid-s6037
"
xml:space
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">29. </
s
>
<
s
xml:id
="
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"
xml:space
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">Min. </
s
>
<
s
xml:id
="
echoid-s6039
"
xml:space
="
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">3. </
s
>
<
s
xml:id
="
echoid-s6040
"
xml:space
="
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">ipſius plani,
<
lb
/>
qui inter Meridianum ipſius, & </
s
>
<
s
xml:id
="
echoid-s6041
"
xml:space
="
preserve
">Meridianum Horizontis interiicitut. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quod eſt primum. </
s
>
<
s
xml:id
="
echoid-s6043
"
xml:space
="
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">Rurſus
<
lb
/>
ſi fiat, vt 74314. </
s
>
<
s
xml:id
="
echoid-s6044
"
xml:space
="
preserve
">ſinus arcus Meridiani inter planum & </
s
>
<
s
xml:id
="
echoid-s6045
"
xml:space
="
preserve
">polum, ad 100000. </
s
>
<
s
xml:id
="
echoid-s6046
"
xml:space
="
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">ſinũ totum, ita 48557. </
s
>
<
s
xml:id
="
echoid-s6047
"
xml:space
="
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">
<
lb
/>
ſinus arcus inter duos Meridianos inuenti ad aliud, inuenietur hic ferè ſinus 65340. </
s
>
<
s
xml:id
="
echoid-s6048
"
xml:space
="
preserve
">cuius arcus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0123-01
"
xlink:href
="
note-0123-01a
"
xml:space
="
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">10</
note
>
complectitur grad. </
s
>
<
s
xml:id
="
echoid-s6049
"
xml:space
="
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">40. </
s
>
<
s
xml:id
="
echoid-s6050
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s6051
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s6052
"
xml:space
="
preserve
">Tanta eſt inclinatio Meridiani ipſius plani ad Meridianum Hori-
<
lb
/>
zontis. </
s
>
<
s
xml:id
="
echoid-s6053
"
xml:space
="
preserve
">quod eſt ſecundum.</
s
>
<
s
xml:id
="
echoid-s6054
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6055
"
xml:space
="
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">PRO figura autem tertia hoc ſume exemplum. </
s
>
<
s
xml:id
="
echoid-s6056
"
xml:space
="
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">Ponatur planum E F, declinare à Meridiano
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0123-02
"
xlink:href
="
note-0123-02a
"
xml:space
="
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">Exemplum ter-
<
lb
/>
tium.</
note
>
grad. </
s
>
<
s
xml:id
="
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xml:space
="
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">60. </
s
>
<
s
xml:id
="
echoid-s6058
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s6059
"
xml:space
="
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">idcirco ab Horizonte grad. </
s
>
<
s
xml:id
="
echoid-s6060
"
xml:space
="
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">30. </
s
>
<
s
xml:id
="
echoid-s6061
"
xml:space
="
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">Erit altitudo poli ſupra ipſum (nempe arcus H I,) per
<
lb
/>
pręcedentem propoſ. </
s
>
<
s
xml:id
="
echoid-s6062
"
xml:space
="
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">inuenta, grad. </
s
>
<
s
xml:id
="
echoid-s6063
"
xml:space
="
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">35. </
s
>
<
s
xml:id
="
echoid-s6064
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s6065
"
xml:space
="
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">25. </
s
>
<
s
xml:id
="
echoid-s6066
"
xml:space
="
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">Itaque ſi fiat, vt 81495. </
s
>
<
s
xml:id
="
echoid-s6067
"
xml:space
="
preserve
">ſinus complementi altitu
<
lb
/>
dinis poli ſupra planum, ad 74314. </
s
>
<
s
xml:id
="
echoid-s6068
"
xml:space
="
preserve
">ſinum complementi arcus Meridiani inter planum, & </
s
>
<
s
xml:id
="
echoid-s6069
"
xml:space
="
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">polũ,
<
lb
/>
hoc eſt, ad ſinum complementi altitudinis poli ſupra Horizontem in hoc exemplo, ita 100000. </
s
>
<
s
xml:id
="
echoid-s6070
"
xml:space
="
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">ſi-
<
lb
/>
nus totus ad aliud, reperietur hic ferè ſinus 91188. </
s
>
<
s
xml:id
="
echoid-s6071
"
xml:space
="
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">cuius arcus continet gradus 65. </
s
>
<
s
xml:id
="
echoid-s6072
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s6073
"
xml:space
="
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">46. </
s
>
<
s
xml:id
="
echoid-s6074
"
xml:space
="
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">quo
<
lb
/>
detracto ex quadrante, reliquus erit arcus grad. </
s
>
<
s
xml:id
="
echoid-s6075
"
xml:space
="
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">24. </
s
>
<
s
xml:id
="
echoid-s6076
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s6077
"
xml:space
="
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">14. </
s
>
<
s
xml:id
="
echoid-s6078
"
xml:space
="
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">ipſius plani inter Meridianum ipſius,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s6079
"
xml:space
="
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">Meridianum Horizontis interiecti, nempe arcus G I. </
s
>
<
s
xml:id
="
echoid-s6080
"
xml:space
="
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">Quod eſt primũ. </
s
>
<
s
xml:id
="
echoid-s6081
"
xml:space
="
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">Rurſus ſi fiat, vt 66913.
<
lb
/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
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">
<
note
position
="
left
"
xlink:label
="
note-0123-03
"
xlink:href
="
note-0123-03a
"
xml:space
="
preserve
">20</
note
>
ſinus arcus Meridiani inter planum & </
s
>
<
s
xml:id
="
echoid-s6083
"
xml:space
="
preserve
">polum, nempe in hoc exemplo, vt ſinus altitudinis poli ſu-
<
lb
/>
pra Horizontem, ad 100000. </
s
>
<
s
xml:id
="
echoid-s6084
"
xml:space
="
preserve
">ſinum totum, ita 41045. </
s
>
<
s
xml:id
="
echoid-s6085
"
xml:space
="
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">ſinus arcus G I, inter duos Meridianos in-
<
lb
/>
uenti ad aliud, inuenietur hic fere ſinus 61341. </
s
>
<
s
xml:id
="
echoid-s6086
"
xml:space
="
preserve
">cuius arcus complectitur grad. </
s
>
<
s
xml:id
="
echoid-s6087
"
xml:space
="
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">37. </
s
>
<
s
xml:id
="
echoid-s6088
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s6089
"
xml:space
="
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">50. </
s
>
<
s
xml:id
="
echoid-s6090
"
xml:space
="
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">Tan-
<
lb
/>
ta eſt inclinatio Meridiani ipſius plani ad Meridianum Horizontis, hoc eſt, tantus eſt angulus
<
lb
/>
G H I, ſeu arcus Aequatoris inter duos Meridianos poſitus. </
s
>
<
s
xml:id
="
echoid-s6091
"
xml:space
="
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">Quod eſt ſecundum.</
s
>
<
s
xml:id
="
echoid-s6092
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6093
"
xml:space
="
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">SI planum inclinatum per polum trãſeat, nullus erit arcus ipſius interpoſitus inter Meridianũ
<
lb
/>
<
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position
="
right
"
xlink:label
="
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xlink:href
="
note-0123-04a
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xml:space
="
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">Quando plan@
<
lb
/>
inclinarum per
<
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/>
polos mundi
<
lb
/>
tranſit.</
note
>
Horizontis, & </
s
>
<
s
xml:id
="
echoid-s6094
"
xml:space
="
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">Meridianum plani inclinati; </
s
>
<
s
xml:id
="
echoid-s6095
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s6096
"
xml:space
="
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">cõplementum inclinationis plani ad Meridianum,
<
lb
/>
erit inclinatio Meridiani ipſius ad Horizontis Meridianum, vt patet in ſphæra materiali. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Dato
<
lb
/>
igitur plano ad Meridianum inclinato, quantus ſit interceptus arcus, &</
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>
<
s
xml:id
="
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"
xml:space
="
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">c. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quod faciendum erat.</
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>
<
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="
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="
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"/>
</
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>
<
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xml:space
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">30</
note
>
</
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<
head
xml:id
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"
xml:space
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">PROBLEMA 10. PROPOSITIO 31.</
head
>
<
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>
<
s
xml:id
="
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"
xml:space
="
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">DATO plano ad Meridianum inclinato, quantus ſit arcus ipſius in-
<
lb
/>
terceptus inter circulum maximum, qui per polos ipſius, & </
s
>
<
s
xml:id
="
echoid-s6102
"
xml:space
="
preserve
">polos Hori-
<
lb
/>
zontis tranſit, metiturq́; </
s
>
<
s
xml:id
="
echoid-s6103
"
xml:space
="
preserve
">eius inclinationem ad Horizontem, & </
s
>
<
s
xml:id
="
echoid-s6104
"
xml:space
="
preserve
">tam Me
<
lb
/>
ridianum proprium ipſius, (nempe circulum maximum, qui per eius
<
lb
/>
polos, & </
s
>
<
s
xml:id
="
echoid-s6105
"
xml:space
="
preserve
">polos mundi ducitur, altitudinemq́; </
s
>
<
s
xml:id
="
echoid-s6106
"
xml:space
="
preserve
">poli ſupra ipſum dimeti-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0123-06
"
xlink:href
="
note-0123-06a
"
xml:space
="
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">40</
note
>
tur, inſtar proprij Meridiani) quàm Meridianum Horizontis, reperire.</
s
>
<
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="
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="
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"/>
</
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>
<
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number
="
89
">
<
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file
="
0123-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123-01
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</
figure
>
<
note
position
="
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"
xml:space
="
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">50</
note
>
<
note
position
="
right
"
xml:space
="
preserve
">Arcus plani in-
<
lb
/>
clinati inter
<
lb
/>
maximum cir-
<
lb
/>
culum per eius
<
lb
/>
polos, & per po-
<
lb
/>
los Horizontis
<
lb
/>
ductum, & Me-
<
lb
/>
ridianum eius
<
lb
/>
proprium in-
<
lb
/>
teriectus, qua
<
lb
/>
uia cognoſca-
<
lb
/>
tur.</
note
>
<
p
>
<
s
xml:id
="
echoid-s6108
"
xml:space
="
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">SIT Horizon A B C D; </
s
>
<
s
xml:id
="
echoid-s6109
"
xml:space
="
preserve
">Meridianus A C; </
s
>
<
s
xml:id
="
echoid-s6110
"
xml:space
="
preserve
">Verticalis k L; </
s
>
<
s
xml:id
="
echoid-s6111
"
xml:space
="
preserve
">planum inclinatum E F, ſecans Me-
<
lb
/>
ridianum in G; </
s
>
<
s
xml:id
="
echoid-s6112
"
xml:space
="
preserve
">eius Meridianus B D, per eius polum P, & </
s
>
<
s
xml:id
="
echoid-s6113
"
xml:space
="
preserve
">per polum mundi H, tranſiens; </
s
>
<
s
xml:id
="
echoid-s6114
"
xml:space
="
preserve
">Cir-
<
lb
/>
culus maximus inclinationem plani ad Horizontem metiens, hoc eſt, per verticem M, ſeu polum
<
lb
/>
Horizontis, & </
s
>
<
s
xml:id
="
echoid-s6115
"
xml:space
="
preserve
">per P, polum plani inclinati deſcriptus N O, ſecans planum inclinatum in Q; </
s
>
<
s
xml:id
="
echoid-s6116
"
xml:space
="
preserve
">opor-
<
lb
/>
teatq́; </
s
>
<
s
xml:id
="
echoid-s6117
"
xml:space
="
preserve
">inuenire tam arcum I Q, quàm arcum G Q. </
s
>
<
s
xml:id
="
echoid-s6118
"
xml:space
="
preserve
">Quoniam arcus M N, P Q, quadrantes </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>