Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
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TABVLARVM SINVVM PER PET. APIANVM.
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altitudo Solis in eleuatione poli 48. </
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<
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<
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<
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</
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<
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<
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<
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<
s
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<
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<
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<
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<
s
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<
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<
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<
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mi. </
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<
s
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<
s
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echoid-s6245
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s
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<
s
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echoid-s6246
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xml:space
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">ei addo declinationem Solis, & </
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<
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nient 62. </
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<
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<
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<
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<
s
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">cuius ſinus eſt 88861. </
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<
s
xml:id
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echoid-s6252
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xml:space
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">quem duco in totum, & </
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>
<
s
xml:id
="
echoid-s6253
"
xml:space
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">productum diuido in
<
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ſinum complementi altitudinis poli. </
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<
s
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<
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<
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<
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<
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<
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Duco etiam ſinum altitudinis Solis in totum, & </
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>
<
s
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xml:space
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ti altitudinis poli, quotiens dabit 105405. </
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>
<
s
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xml:space
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">inuentum ſecundum, ſubtraho iam hoc ab in-
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uento primo, & </
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>
<
s
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="
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"
xml:space
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">remanent 27396. </
s
>
<
s
xml:id
="
echoid-s6262
"
xml:space
="
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">id rurſus duco in ſinum totum, & </
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>
<
s
xml:id
="
echoid-s6263
"
xml:space
="
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">diuido in ſinũ com
<
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/>
plemẽti declinationis. </
s
>
<
s
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="
echoid-s6264
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xml:space
="
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<
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">93544. </
s
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<
s
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"
xml:space
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">quotiens eſt 29286. </
s
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<
s
xml:id
="
echoid-s6267
"
xml:space
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">inuentum tertium, hoc quia minus
<
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ſubtraho à toto, & </
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<
s
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="
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"
xml:space
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">remanent 70714. </
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<
s
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="
echoid-s6269
"
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">arcus eius eſt 45. </
s
>
<
s
xml:id
="
echoid-s6270
"
xml:space
="
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">gra, quibus ſubductis à 90. </
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>
<
s
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echoid-s6271
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xml:space
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">reliqui
<
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manent 45. </
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<
s
xml:id
="
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xml:space
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">gra, horæ ſcilicet tres, & </
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>
<
s
xml:id
="
echoid-s6273
"
xml:space
="
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">quando tempus iſtud fuit antemeridianum, numera
<
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tres horas à 12. </
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>
<
s
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="
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"
xml:space
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">retrorſum, at habebis horã 9. </
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<
s
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">eam qua ſolennis & </
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>
<
s
xml:id
="
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"
xml:space
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">fœlix illa optimi Præ
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ſulis facta eſt intronizatio.</
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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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head
>
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<
s
xml:id
="
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xml:space
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">Altitudine poli Borealis ſuper ſemicirculum poſitionis cognita, etiã arcũ
<
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æquatoris inuenire, qui meridiano & </
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>
<
s
xml:id
="
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"
xml:space
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">illo ſemicirculo poſitionis includitur.</
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<
s
xml:id
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</
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<
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<
s
xml:id
="
echoid-s6281
"
xml:space
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">Propone hic tibi ſinum latitudinis tuæ regionis, & </
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>
<
s
xml:id
="
echoid-s6282
"
xml:space
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">ſinum altitudinis poli ſupra ſemi-
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circulum poſitionis, minorem duc in totum, productum in maiorem diuide, quotientis ar
<
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cum ſubtrahe de quadrante, & </
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>
<
s
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="
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xml:space
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">ſinum huius complemẽti, ſimiliter & </
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>
<
s
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echoid-s6284
"
xml:space
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">ſinum complemen
<
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ti altitudinis poli Borealis ſupra ſemicirculum poſitionis ſepone in locum aliquem, mi-
<
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/>
norem duc in totum, & </
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>
<
s
xml:id
="
echoid-s6285
"
xml:space
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">diuide cum maiori, arcus quotientis ex 90. </
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<
s
xml:id
="
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xml:space
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">ſublatus, relinquet ar
<
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cum æ quatoris quæſitũ. </
s
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<
s
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<
s
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xml:space
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">? Iam exemplũ hoc mihi uide, Cupio inuenire arcum æqua
<
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<
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xlink:label
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xlink:href
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xml:space
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">EXEM-
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PLVM
<
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E
<
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style
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emph
>
</
note
>
toris, qui inter meridianum & </
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<
s
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="
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xml:space
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">ſemicirculum poſitionis in ipſa hora intronizationis per
<
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corpus Solis deductum concluſus eſt, ſinum igitur altitudinis poliſuper eundem ſemi-
<
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circulum poſitionis inueni ex ſuperiori pronunc. </
s
>
<
s
xml:id
="
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xml:space
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">51155. </
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<
s
xml:id
="
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"
xml:space
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">eum duco in totum, & </
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>
<
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="
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xml:space
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ctum diuido in ſinum latitudinis regionis, quæ eſt ibi 48. </
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<
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xml:space
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s
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<
s
xml:id
="
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<
s
xml:id
="
echoid-s6295
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xml:space
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">mi. </
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<
s
xml:id
="
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xml:space
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">ſinus eius eſt 74702
<
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quotiens producit 68478. </
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<
s
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<
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<
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<
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="
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<
s
xml:id
="
echoid-s6301
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<
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</
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<
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<
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<
s
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<
s
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"
xml:space
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nis poli ſuper ſemicirculũ poſitionis. </
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<
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<
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<
s
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="
echoid-s6309
"
xml:space
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">proueniunt in quotiente 84814. </
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>
<
s
xml:id
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xml:space
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eſt 58. </
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<
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<
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">1. </
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<
s
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echoid-s6313
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<
s
xml:id
="
echoid-s6314
"
xml:space
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">quibus de 90. </
s
>
<
s
xml:id
="
echoid-s6315
"
xml:space
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">ademptus, remanet 31. </
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<
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echoid-s6316
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xml:space
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s
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<
s
xml:id
="
echoid-s6317
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<
s
xml:id
="
echoid-s6318
"
xml:space
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">mi. </
s
>
<
s
xml:id
="
echoid-s6319
"
xml:space
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">arcus ille æquatoris
<
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quæſitus.</
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>
<
s
xml:id
="
echoid-s6320
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="
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</
p
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</
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<
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xml:id
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type
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="
1
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n
="
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<
head
xml:id
="
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xml:space
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">PRONVNCIATVM LXXXII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s6321
"
xml:space
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">Quum iam altitudo poli ſuper ſemicirculum poſitionis cognitus eſt, de-
<
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/>
hinc arcum circuli uerticalis inter zenith & </
s
>
<
s
xml:id
="
echoid-s6322
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xml:space
="
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">iſtum ſemicirculum poſitionis
<
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concluſum inueſtigare.</
s
>
<
s
xml:id
="
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xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6324
"
xml:space
="
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">Non te deterreat ne moueat pronunciati huius breuitas, nam quo paucioribus uer-
<
lb
/>
bis traditur, eò tam facilius intelligetur, tamen expeditius uſurpari poterit, unde magnũ
<
lb
/>
fructum ex hac re in Aſtrolabio noſtro reportabis. </
s
>
<
s
xml:id
="
echoid-s6325
"
xml:space
="
preserve
">Hic ergo tibi proponeutrun ſinum
<
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/>
altitudinis poli tuæ regionis, & </
s
>
<
s
xml:id
="
echoid-s6326
"
xml:space
="
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">illius quo ſupra ſemicirculum poſitionis, minorẽ duc
<
lb
/>
in totum, productum diuide in maiorem, & </
s
>
<
s
xml:id
="
echoid-s6327
"
xml:space
="
preserve
">arcus quotientis monſtrabit tibi arcum cir-
<
lb
/>
culi uerticalis, ?</
s
>
<
s
xml:id
="
echoid-s6328
"
xml:space
="
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">? Ecce en altitudo poli Auguſtæ eſt 48. </
s
>
<
s
xml:id
="
echoid-s6329
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s6330
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s6331
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6332
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6333
"
xml:space
="
preserve
">ſub horam intro
<
lb
/>
nizationis fuit altitudo poli ſuper ſemicirculum poſitionis, qui per corpus Solis ducitur
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0077-02
"
xlink:href
="
note-0077-02a
"
xml:space
="
preserve
">EXEM-
<
lb
/>
PLVM
<
lb
/>
E
<
emph
style
="
it
">piſcopi.</
emph
>
</
note
>
30. </
s
>
<
s
xml:id
="
echoid-s6334
"
xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s6335
"
xml:space
="
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">46. </
s
>
<
s
xml:id
="
echoid-s6336
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s6337
"
xml:space
="
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">ſinũ eius 51155. </
s
>
<
s
xml:id
="
echoid-s6338
"
xml:space
="
preserve
">duco in totũ, & </
s
>
<
s
xml:id
="
echoid-s6339
"
xml:space
="
preserve
">productum diuido in ſinũ altitudinis po
<
lb
/>
li 74702. </
s
>
<
s
xml:id
="
echoid-s6340
"
xml:space
="
preserve
">q̊tiens erit 68479. </
s
>
<
s
xml:id
="
echoid-s6341
"
xml:space
="
preserve
">ipſe aũt arcus eſt 43. </
s
>
<
s
xml:id
="
echoid-s6342
"
xml:space
="
preserve
">gra. </
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>
<
s
xml:id
="
echoid-s6343
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s6344
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s6345
"
xml:space
="
preserve
">arcus ille quem optabam.</
s
>
<
s
xml:id
="
echoid-s6346
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div183
"
type
="
section
"
level
="
1
"
n
="
95
">
<
head
xml:id
="
echoid-head99
"
xml:space
="
preserve
">PRONVNCIATVM LXXXIII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s6347
"
xml:space
="
preserve
">Si arcus æquatoris à meridiano ſumatur uſ ad ſemicirculum poſitionis,
<
lb
/>
altitudinem per hoc poli ſuper ſemicirculum illum poſitionis perquirere.</
s
>
<
s
xml:id
="
echoid-s6348
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6349
"
xml:space
="
preserve
">Fac age ducas æquatoris ſinum complementi iſtius arcus æquatoris in ſinum latitu-
<
lb
/>
dinis regionis, & </
s
>
<
s
xml:id
="
echoid-s6350
"
xml:space
="
preserve
">dehinc diuide productum in totum, arcum uero quotientis ſubtrahe de
<
lb
/>
90. </
s
>
<
s
xml:id
="
echoid-s6351
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6352
"
xml:space
="
preserve
">ad ſinum reſidui confer ſinum complementi altitudinis poli, minorem duc in totũ
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s6353
"
xml:space
="
preserve
">in maiorem diuide, tunc complementum arcus quotientis dabit altitudinẽ poli </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>