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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0154
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154
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rhead
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GNOMONICES
"/>
<
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>
<
s
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xml:space
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">POSTREMO exiſtat Sol in parallelo quocunq; </
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>
<
s
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"
xml:space
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">auſtrali, vt in principio ♑, habeatq́; </
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>
<
s
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echoid-s8478
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xml:space
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">díſtan-
<
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<
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xlink:label
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note-0154-01
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xlink:href
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note-0154-01a
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xml:space
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">Exemplũ quar-
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tum.</
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tiam à meridie hor. </
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<
s
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xml:space
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">2. </
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>
<
s
xml:id
="
echoid-s8480
"
xml:space
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">hoc eſt, grad. </
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>
<
s
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="
echoid-s8481
"
xml:space
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">30. </
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>
<
s
xml:id
="
echoid-s8482
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xml:space
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">Fiat vt 100000. </
s
>
<
s
xml:id
="
echoid-s8483
"
xml:space
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">ad 50000. </
s
>
<
s
xml:id
="
echoid-s8484
"
xml:space
="
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">ſinum diſtantiæ Solis à meri-
<
lb
/>
die, ita 91706. </
s
>
<
s
xml:id
="
echoid-s8485
"
xml:space
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">ſinus complementi declinationis ad aliud, inuenieturq́; </
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>
<
s
xml:id
="
echoid-s8486
"
xml:space
="
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">hic ſinus 45853. </
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<
s
xml:id
="
echoid-s8487
"
xml:space
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">cuius ar
<
lb
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cus grad. </
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<
s
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echoid-s8488
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">27. </
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<
s
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">Min. </
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<
s
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echoid-s8490
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">18. </
s
>
<
s
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echoid-s8491
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xml:space
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">ablatus ex quadrante relinquet arcũ grad. </
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>
<
s
xml:id
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echoid-s8492
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">62. </
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<
s
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">Min. </
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<
s
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"
xml:space
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">42. </
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>
<
s
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"
xml:space
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">pro Inuẽto primo.</
s
>
<
s
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="
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xml:space
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"/>
</
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<
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>
<
s
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"
xml:space
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">DEINDE fiat, vt 88861. </
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>
<
s
xml:id
="
echoid-s8498
"
xml:space
="
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">ſinus Inuenti primi ad 39874. </
s
>
<
s
xml:id
="
echoid-s8499
"
xml:space
="
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">ſinum declinationis, ita 100000.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8500
"
xml:space
="
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">ſinus totus ad aliud, habebiturq́; </
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>
<
s
xml:id
="
echoid-s8501
"
xml:space
="
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">ferè ſinus hic 44872. </
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>
<
s
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echoid-s8502
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xml:space
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">cuius arcus grad. </
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<
s
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echoid-s8503
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xml:space
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<
s
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">Min. </
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<
s
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<
s
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xml:space
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">ſublatus
<
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ex complemento altitudinis poli grad. </
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>
<
s
xml:id
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xml:space
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">48. </
s
>
<
s
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echoid-s8508
"
xml:space
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">quia ſol auſtralis eſt, relinquet arcum grad. </
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>
<
s
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="
echoid-s8509
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xml:space
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">21. </
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>
<
s
xml:id
="
echoid-s8510
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">Min. </
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>
<
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">
<
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20. </
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>
<
s
xml:id
="
echoid-s8512
"
xml:space
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">pro Inuento ſecundo.</
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>
<
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</
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>
<
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<
s
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">FIAT tandem, vt 100000. </
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>
<
s
xml:id
="
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"
xml:space
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">ſinus totus ad 88861. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſinum Inuenti primi, ita 36379. </
s
>
<
s
xml:id
="
echoid-s8517
"
xml:space
="
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">ſinus In-
<
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uenti ſecundi ad aliud, inuenieturq́; </
s
>
<
s
xml:id
="
echoid-s8518
"
xml:space
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">hic propemodum ſinus 32327. </
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>
<
s
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echoid-s8519
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">cuius arcus grad. </
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>
<
s
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echoid-s8520
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">18. </
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>
<
s
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">Min.
<
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</
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<
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<
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">10</
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52. </
s
>
<
s
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">exhibebit quæſitam Solis altitudinem.</
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>
<
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</
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<
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<
s
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xml:space
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">SOLE exiſtente in Verticali circulo, vt in puncto K, veluti in figura quinta apparet, multo
<
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<
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xlink:label
="
note-0154-03
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="
note-0154-03a
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xml:space
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">Altitudo Solis
<
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in circulo Ver-
<
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/>
ticali quomodo
<
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/>
ex data hora p
<
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/>
triangula ſphæ
<
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/>
tica ſupputetur.</
note
>
<
figure
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fig-0154-01
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xlink:href
="
fig-0154-01a
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number
="
112
">
<
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file
="
0154-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0154-01
"/>
</
figure
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<
note
position
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xlink:label
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xml:space
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">20</
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<
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">30</
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>
expeditius ex diſtantia Solis à meridie cognita altitudinem per ſphęrica triangula venabimur,
<
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hac ratione. </
s
>
<
s
xml:id
="
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"
xml:space
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">Quoniam in triangulo ſphærico A k M, angulus M, rectus eſt, erit per propoſ. </
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>
<
s
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xml:space
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<
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</
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<
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<
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">40</
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>
lib. </
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<
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">4. </
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<
s
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">Ioan. </
s
>
<
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echoid-s8531
"
xml:space
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">Regiom. </
s
>
<
s
xml:id
="
echoid-s8532
"
xml:space
="
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">de triangulis, vel per propoſ. </
s
>
<
s
xml:id
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echoid-s8533
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xml:space
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">15. </
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<
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xml:space
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">lib. </
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<
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">1. </
s
>
<
s
xml:id
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xml:space
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">Gebri, vel per propoſ. </
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>
<
s
xml:id
="
echoid-s8537
"
xml:space
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">43. </
s
>
<
s
xml:id
="
echoid-s8538
"
xml:space
="
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">noſtrorũ
<
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triangulorum ſphæricorum, vt ſinus complementi arcus A M, hoc eſt, vt ſinus diſtantiæ Solis à
<
lb
/>
meridie, id eſt, vt ſinus arcus F M, ad ſinum totum, ita ſinus complementi arcus A
<
emph
style
="
sc
">K</
emph
>
, ad ſinum
<
lb
/>
complementi arcus K M, hoc eſt, ad ſinum complementi declinationis. </
s
>
<
s
xml:id
="
echoid-s8539
"
xml:space
="
preserve
">Conuertendo ergo erit
<
lb
/>
quoque, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complementi declinationis pa-
<
lb
/>
ralleli propoſiti ad ſinum complementi arcus A K, vnde ex prioribus tribus cognitis cognoſce-
<
lb
/>
@ur & </
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>
<
s
xml:id
="
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"
xml:space
="
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">quartum, nempe complementum arcus A K, atque adeò & </
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>
<
s
xml:id
="
echoid-s8541
"
xml:space
="
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">ipſemet arcus A
<
emph
style
="
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">K</
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>
, altitudinem
<
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/>
Solis metiens. </
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>
<
s
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="
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xml:space
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">Itaq; </
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>
<
s
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="
echoid-s8543
"
xml:space
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">Sole in Verticali circulo exiſtente, ſi fiat vt ſinus totus ad ſinum diſtantiæ Solis
<
lb
/>
à meridie, ita ſinus complementi declinationis ad aliud, inuenietur ſinus complementi altitudinis
<
lb
/>
Solis, ac proinde & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ipſa altitudo manifeſta erit.</
s
>
<
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"/>
</
p
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<
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">50</
note
>
<
p
>
<
s
xml:id
="
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xml:space
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">SED ſi diſtantia Solis à meridie ignota fuerit, inueniemus nihilominus altitudinem Solis in
<
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/>
<
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position
="
left
"
xlink:label
="
note-0154-08
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xlink:href
="
note-0154-08a
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xml:space
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">Altitudo Solis
<
lb
/>
in Verticali quo
<
lb
/>
modo ſuppute-
<
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/>
tur per ſphæti-
<
lb
/>
ca triangula,
<
lb
/>
etiãſi hora igno
<
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/>
retur.</
note
>
Verticali exiſtentis hoc modo. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quoniam in triangulo ſphærico E K N, angulus E, rectus eſt; </
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>
<
s
xml:id
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xml:space
="
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">erit
<
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per propoſ. </
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<
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xml:space
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">19. </
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>
<
s
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">l b. </
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<
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">4. </
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>
<
s
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="
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xml:space
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">Ioan. </
s
>
<
s
xml:id
="
echoid-s8553
"
xml:space
="
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">Regiom. </
s
>
<
s
xml:id
="
echoid-s8554
"
xml:space
="
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">de triangulis, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8555
"
xml:space
="
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">15. </
s
>
<
s
xml:id
="
echoid-s8556
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s8557
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s8558
"
xml:space
="
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">Gebri, vel per pro-
<
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/>
poſ. </
s
>
<
s
xml:id
="
echoid-s8559
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s8560
"
xml:space
="
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">noſtrorum triangulorum ſphæricorum, vt ſinus complementi arcus E N, hoc eſt, vt ſi-
<
lb
/>
nus arcus E F, altitudinis poli, ad ſinum totum, ita ſinus complementi arcus N k, id eſt, ita ſinus
<
lb
/>
arcus K M, declinationis paralleli propoſiti, ad ſinum complementi arcus E K, hoc eſt, ad ſinum
<
lb
/>
arcus A K, altitudinis Solis. </
s
>
<
s
xml:id
="
echoid-s8561
"
xml:space
="
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">Igitur ſi fiat, vt ſinus altitudinis poli ad ſinum totum, ita ſinus decli-
<
lb
/>
nationis ad aliud, inuenietur ſinus altitudinis Solis. </
s
>
<
s
xml:id
="
echoid-s8562
"
xml:space
="
preserve
">Quod etiam clarius ita poterit demonſtrari.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8563
"
xml:space
="
preserve
">Quoniam in triangulo ſphærico A K M, eiuſdem figuræ quintę angulus M, rectus eſt, erit per pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s8564
"
xml:space
="
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">16. </
s
>
<
s
xml:id
="
echoid-s8565
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s8566
"
xml:space
="
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">4. </
s
>
<
s
xml:id
="
echoid-s8567
"
xml:space
="
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">Ioan. </
s
>
<
s
xml:id
="
echoid-s8568
"
xml:space
="
preserve
">Regiom. </
s
>
<
s
xml:id
="
echoid-s8569
"
xml:space
="
preserve
">de triangulis, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8570
"
xml:space
="
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">13. </
s
>
<
s
xml:id
="
echoid-s8571
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s8572
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s8573
"
xml:space
="
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">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8574
"
xml:space
="
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">41. </
s
>
<
s
xml:id
="
echoid-s8575
"
xml:space
="
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">
<
lb
/>
noſtrorum triangulorum ſphæricorum, vt ſinus anguli A, altitudinis poli, (eſt enim E F, & </
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>
<
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