Apian, Petrus
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Instrvmentvm Sinvvm, sev primi mobilis
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♈eſt 35. </
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<
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<
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<
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<
s
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">iam ſi cupiam & </
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<
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echoid-s1852
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xml:space
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">arcum eclypticæ ſibi reſpondentem inuenire in
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ſphæra o bliqua, at adeo eleuato ibi polo ad 48. </
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<
s
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<
s
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"
xml:space
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">ubi talis etiam intronizatio facta
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eſt. </
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<
s
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">Principio quæro per 8. </
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<
s
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xml:space
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">propoſitionem arcum eclypticæ in ſphæra recta cum arcu æ-
<
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quatoris aſcendentem, in hunc modum: </
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<
s
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echoid-s1857
"
xml:space
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">Duco ſinum complementi huius aſcenſionis re-
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ctæ, ſcilicet 35. </
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<
s
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<
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<
s
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echoid-s1860
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<
s
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">qui gradus ſunt 54. </
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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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<
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maximæ declinationis Solis 39874. </
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<
s
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xml:space
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">diuido, deinde quotientem in totum ſinum, qui erit
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32448. </
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<
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">arcus illius 18. </
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<
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<
s
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<
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<
s
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<
s
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">& </
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<
s
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"
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">remanent adhuc 71. </
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<
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<
s
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xml:space
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</
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<
s
xml:id
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xml:space
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">mi. </
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<
s
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"
xml:space
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">ſinum iſtius ſi mihi proponam ſimul cum ſinu aſcenſionis rectæ, ſcilicet 58117. </
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<
s
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rem quo ducam in ſinum totũ, productum uero diuidam in maiorem, proueniet inde
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<
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<
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<
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<
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61441. </
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<
s
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">arcus eius erit 37. </
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<
s
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echoid-s1881
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<
s
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="
echoid-s1882
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">55. </
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>
<
s
xml:id
="
echoid-s1883
"
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">mi. </
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>
<
s
xml:id
="
echoid-s1884
"
xml:space
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">qui etiam arcus eſt eclypticæ à
<
unsure
/>
principio ♈, reſpon
<
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dens arcui æquatoris in ſphæra recta in aſcenſu. </
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>
<
s
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echoid-s1885
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xml:space
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">Ad hæc amplius inquiro per 5. </
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>
<
s
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echoid-s1886
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<
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ciatum iſtius arcus eclypticæ declinationem ab æquatore, & </
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>
<
s
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"
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<
s
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<
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</
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<
s
xml:id
="
echoid-s1890
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">mi. </
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>
<
s
xml:id
="
echoid-s1891
"
xml:space
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">directe pertingit ad 7. </
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<
s
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="
echoid-s1892
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">gra. </
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<
s
xml:id
="
echoid-s1893
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xml:space
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">55. </
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<
s
xml:id
="
echoid-s1894
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xml:space
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">mi. </
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<
s
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">♉. </
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<
s
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">quæro iam adhuc ipſum gradum & </
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<
s
xml:id
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"
xml:space
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">minutũ ♉
<
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declinationem hoc modo. </
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<
s
xml:id
="
echoid-s1898
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xml:space
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">Duco ſinum arcus 37. </
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<
s
xml:id
="
echoid-s1899
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xml:space
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">gra. </
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<
s
xml:id
="
echoid-s1900
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xml:space
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">55. </
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<
s
xml:id
="
echoid-s1901
"
xml:space
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">mi. </
s
>
<
s
xml:id
="
echoid-s1902
"
xml:space
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">in ſinũ maximæ declinatiõis
<
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Solis, ſcilicet 39874. </
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>
<
s
xml:id
="
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"
xml:space
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">productũ diuido in ſinum totum, & </
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>
<
s
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echoid-s1904
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">prodibit 24499. </
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<
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="
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">arcus illius eſt
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<
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<
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14. </
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<
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<
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">11. </
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<
s
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="
echoid-s1908
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">mi. </
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<
s
xml:id
="
echoid-s1909
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">declinatio nimi℞ arcus eclypticæ quæſita. </
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>
<
s
xml:id
="
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xml:space
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">Poſtea adhuc ſinũ arcus aſcenſi
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onis rectæ æquatoris 58117. </
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>
<
s
xml:id
="
echoid-s1911
"
xml:space
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">duxi in ſinũ totũ, productũ diuiſi per ſinũ arcus eclypticæ ei
<
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/>
<
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<
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style
="
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">Arealis.</
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>
</
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in aſcenſione recta reſpondentẽ, & </
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>
<
s
xml:id
="
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">prouenit in quotiente 94589. </
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<
s
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="
echoid-s1913
"
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">arcus ipſius eſt 71. </
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>
<
s
xml:id
="
echoid-s1914
"
xml:space
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">gra.
<
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/>
</
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>
<
s
xml:id
="
echoid-s1915
"
xml:space
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">4. </
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>
<
s
xml:id
="
echoid-s1916
"
xml:space
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">mi. </
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>
<
s
xml:id
="
echoid-s1917
"
xml:space
="
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">qui quia finitur in medietate eclypticæ aſcendente, ſubtraxi iam 71. </
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>
<
s
xml:id
="
echoid-s1918
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xml:space
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">gra. </
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<
s
xml:id
="
echoid-s1919
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xml:space
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<
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="
echoid-s1920
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>
<
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xml:id
="
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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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>
</
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>
micirculo, & </
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<
s
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="
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<
s
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="
echoid-s1923
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xml:space
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>
<
s
xml:id
="
echoid-s1924
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xml:space
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">mi. </
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<
s
xml:id
="
echoid-s1925
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xml:space
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">56. </
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>
<
s
xml:id
="
echoid-s1926
"
xml:space
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">at hoc inuentũ dico primũ. </
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>
<
s
xml:id
="
echoid-s1927
"
xml:space
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altitudinis poli 48. </
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<
s
xml:id
="
echoid-s1928
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xml:space
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>
<
s
xml:id
="
echoid-s1929
"
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">74314. </
s
>
<
s
xml:id
="
echoid-s1930
"
xml:space
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">duxi in ſinũ declinationis extremitatis arcus eclypticæ, ſci
<
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licet 14. </
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>
<
s
xml:id
="
echoid-s1931
"
xml:space
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>
<
s
xml:id
="
echoid-s1932
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>
<
s
xml:id
="
echoid-s1933
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">mi. </
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>
<
s
xml:id
="
echoid-s1934
"
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">24499. </
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>
<
s
xml:id
="
echoid-s1935
"
xml:space
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">ꝓductũ diuiſi in ſinũ totum, & </
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>
<
s
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="
echoid-s1936
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xml:space
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">quotiens eſt 18206. </
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<
s
xml:id
="
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"
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<
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<
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style
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<
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<
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>
<
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/>
<
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style
="
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>
<
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<
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style
="
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">uentum ſe-</
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>
<
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<
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style
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</
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illius 10. </
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<
s
xml:id
="
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xml:space
="
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<
s
xml:id
="
echoid-s1939
"
xml:space
="
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>
<
s
xml:id
="
echoid-s1940
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s1941
"
xml:space
="
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">inuentum illud ſecũdũ. </
s
>
<
s
xml:id
="
echoid-s1942
"
xml:space
="
preserve
">Inſuper etiã ſinũ cõplementi altitudinis poli
<
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/>
66913. </
s
>
<
s
xml:id
="
echoid-s1943
"
xml:space
="
preserve
">tan̈ minorem in ſinũ totũ duxi, diuiſi eundẽ in ſinũ cõplementi ſecundi inuenti,
<
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/>
ſcilicet 79. </
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>
<
s
xml:id
="
echoid-s1944
"
xml:space
="
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">gra. </
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>
<
s
xml:id
="
echoid-s1945
"
xml:space
="
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">31. </
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>
<
s
xml:id
="
echoid-s1946
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s1947
"
xml:space
="
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">98330. </
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>
<
s
xml:id
="
echoid-s1948
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s1949
"
xml:space
="
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">prouenit in quotiente 68049. </
s
>
<
s
xml:id
="
echoid-s1950
"
xml:space
="
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">arcus eius 42. </
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>
<
s
xml:id
="
echoid-s1951
"
xml:space
="
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">gra. </
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>
<
s
xml:id
="
echoid-s1952
"
xml:space
="
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">53. </
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>
<
s
xml:id
="
echoid-s1953
"
xml:space
="
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<
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</
s
>
<
s
xml:id
="
echoid-s1954
"
xml:space
="
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">adpellabitur inuentũ tertiũ, hoc deinde ipſum à primo inuento ſubtraxi, hoc eſt 42. </
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>
<
s
xml:id
="
echoid-s1955
"
xml:space
="
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">gra. </
s
>
<
s
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="
echoid-s1956
"
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="
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">
<
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/>
53. </
s
>
<
s
xml:id
="
echoid-s1957
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s1958
"
xml:space
="
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">à 180. </
s
>
<
s
xml:id
="
echoid-s1959
"
xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s1960
"
xml:space
="
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">56. </
s
>
<
s
xml:id
="
echoid-s1961
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s1962
"
xml:space
="
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">reſiduũ eſt 66. </
s
>
<
s
xml:id
="
echoid-s1963
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1964
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s1965
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1966
"
xml:space
="
preserve
">quo℞ ſinũ 91390. </
s
>
<
s
xml:id
="
echoid-s1967
"
xml:space
="
preserve
">duxi in ſinũ cõplemẽ
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0041-07
"
xlink:href
="
note-0041-07a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Arealis</
emph
>
<
lb
/>
<
emph
style
="
it
">operatio.</
emph
>
<
lb
/>
<
emph
style
="
it
">Inuentum</
emph
>
<
lb
/>
<
emph
style
="
it
">tertium.</
emph
>
</
note
>
tiſecũdi inuẽti 79. </
s
>
<
s
xml:id
="
echoid-s1968
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1969
"
xml:space
="
preserve
">31. </
s
>
<
s
xml:id
="
echoid-s1970
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1971
"
xml:space
="
preserve
">hoc eſt 98330. </
s
>
<
s
xml:id
="
echoid-s1972
"
xml:space
="
preserve
">ꝓductũ diuiſi in ſinũ totũ, & </
s
>
<
s
xml:id
="
echoid-s1973
"
xml:space
="
preserve
">prodijt in quo
<
lb
/>
tienti 89864. </
s
>
<
s
xml:id
="
echoid-s1974
"
xml:space
="
preserve
">arcus illorum ſinuũ eſt 63. </
s
>
<
s
xml:id
="
echoid-s1975
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1976
"
xml:space
="
preserve
">59. </
s
>
<
s
xml:id
="
echoid-s1977
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1978
"
xml:space
="
preserve
">quibus ſubtractis à 90. </
s
>
<
s
xml:id
="
echoid-s1979
"
xml:space
="
preserve
">remanent 26.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1980
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s1981
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1982
"
xml:space
="
preserve
">Poſtremò ꝓpono ſinũ iſtorum 26. </
s
>
<
s
xml:id
="
echoid-s1983
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1984
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1985
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s1986
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1987
"
xml:space
="
preserve
">ſcilicet 43863. </
s
>
<
s
xml:id
="
echoid-s1988
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1989
"
xml:space
="
preserve
">ſinum ſecundi in-
<
lb
/>
uenti 18206. </
s
>
<
s
xml:id
="
echoid-s1990
"
xml:space
="
preserve
">hunc tan̈ minorem duco in totum, productum diuido in 43863. </
s
>
<
s
xml:id
="
echoid-s1991
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1992
"
xml:space
="
preserve
">prode
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0041-08
"
xlink:href
="
note-0041-08a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Lateralis</
emph
>
<
lb
/>
<
emph
style
="
it
">introitus.</
emph
>
</
note
>
unt in quotiente 41506. </
s
>
<
s
xml:id
="
echoid-s1993
"
xml:space
="
preserve
">arcum illius, puta 24. </
s
>
<
s
xml:id
="
echoid-s1994
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1995
"
xml:space
="
preserve
">31. </
s
>
<
s
xml:id
="
echoid-s1996
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1997
"
xml:space
="
preserve
">ſi iuxta regulã ſiue præſcriptũ
<
lb
/>
operationis, propter medietatem eclypticæ aſcendentem addidero ad arcũ eclypticæ 37.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1998
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1999
"
xml:space
="
preserve
">55. </
s
>
<
s
xml:id
="
echoid-s2000
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s2001
"
xml:space
="
preserve
">prouenient uti 62. </
s
>
<
s
xml:id
="
echoid-s2002
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s2003
"
xml:space
="
preserve
">26. </
s
>
<
s
xml:id
="
echoid-s2004
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s2005
"
xml:space
="
preserve
">eclypticæ, quæ cũ illa aſcenſione ſiue arcu æ-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0041-09
"
xlink:href
="
note-0041-09a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Arealis in-</
emph
>
<
lb
/>
<
emph
style
="
it
">greſſus.</
emph
>
</
note
>
quatoris 35. </
s
>
<
s
xml:id
="
echoid-s2006
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s2007
"
xml:space
="
preserve
">32. </
s
>
<
s
xml:id
="
echoid-s2008
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s2009
"
xml:space
="
preserve
">in eleuatione poli 48. </
s
>
<
s
xml:id
="
echoid-s2010
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s2011
"
xml:space
="
preserve
">aſcendũt, ſiue horizontem attingunt
<
lb
/>
planè in 2. </
s
>
<
s
xml:id
="
echoid-s2012
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s2013
"
xml:space
="
preserve
">26. </
s
>
<
s
xml:id
="
echoid-s2014
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s2015
"
xml:space
="
preserve
">II, ubi tunc Solerat in ipſo die intronizationis ornatiſsimi Præ-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0041-10
"
xlink:href
="
note-0041-10a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Locus So-</
emph
>
<
lb
/>
<
emph
style
="
it
">lis die intro</
emph
>
<
lb
/>
<
emph
style
="
it
">nizationis</
emph
>
<
lb
/>
<
emph
style
="
it
">præſulis</
emph
>
<
lb
/>
<
emph
style
="
it
">Auguſtani.</
emph
>
</
note
>
ſulis Auguſtani. </
s
>
<
s
xml:id
="
echoid-s2016
"
xml:space
="
preserve
">Ecce quàm operoſa & </
s
>
<
s
xml:id
="
echoid-s2017
"
xml:space
="
preserve
">prolixa operatione hacidẽ illud adinueni, cuius
<
lb
/>
contrarium ſuperior propoſitio facili & </
s
>
<
s
xml:id
="
echoid-s2018
"
xml:space
="
preserve
">compendiaria uia monſtrauit, quamuis in
<
lb
/>
reliquis tribus quartis zodia ci à ♋ uſ ad ♎, & </
s
>
<
s
xml:id
="
echoid-s2019
"
xml:space
="
preserve
">inde à ♎ ad ♑, at à ♑ ad ♈, aliquan-
<
lb
/>
do alia operatio eſt, attamen mihi conſultum uiſum eſt, illas nullis peculiaribus exem-
<
lb
/>
plis indicare: </
s
>
<
s
xml:id
="
echoid-s2020
"
xml:space
="
preserve
">quiſquis em̃ operationem hanc cũ exemplo adiuncto recte intellexrit, is
<
lb
/>
etiam in reliquis illis nõ aberrabit, ſedubi facile ſe extricabit, nos igitur aliò iam prope
<
lb
/>
rabimus, animum & </
s
>
<
s
xml:id
="
echoid-s2021
"
xml:space
="
preserve
">cogitationem eleuaturi ad altitudinem Solis ſuper horizontem.</
s
>
<
s
xml:id
="
echoid-s2022
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div55
"
type
="
section
"
level
="
1
"
n
="
32
">
<
head
xml:id
="
echoid-head36
"
xml:space
="
preserve
">PRONVNCIATVM XX.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2023
"
xml:space
="
preserve
">Altitudinem Solis in circulo uerticali (dummodo ſit in ſigno aliquo ſe-
<
lb
/>
ptentrionali) inueſtigare.</
s
>
<
s
xml:id
="
echoid-s2024
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2025
"
xml:space
="
preserve
">Iam ſupra pronunciato 12. </
s
>
<
s
xml:id
="
echoid-s2026
"
xml:space
="
preserve
">edoctus es, quidnã ſit ortus æquinoctialis, quamobrẽ ſuꝑ-
<
lb
/>
uacuũ ſuerit idẽ hic denuo cõmemorare, tm̃ ne ignores, quid hic nomine circuli uertica-
<
lb
/>
lis intelligamus, illũ tibi breuiter deſcribemus. </
s
>
<
s
xml:id
="
echoid-s2027
"
xml:space
="
preserve
">Vertex igit̃ ſiue pũctus uerticalis, eſt pun
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0041-11
"
xlink:href
="
note-0041-11a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Vertex ſiue</
emph
>
<
lb
/>
<
emph
style
="
it
">zenith ꝗd.</
emph
>
</
note
>
ctus cœli capiti tuo directe imminens, ſi modo tu ſtes erectus, monſtrat punctũ illũ tibi
<
lb
/>
filũ ſuſpenſum, ex quo plumbimaſſa, aut aliud quiddã graue dependeat, quẽ igitur ſuperi
<
lb
/>
or ſili pars in cœlo locum demonſtrat, ibi ſcias eſſe punctum uerticalem, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>
