Apian, Petrus
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Instrvmentvm Sinvvm, sev primi mobilis
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GENVINVS VSVS
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ducetur inuentum tertium, ſcilicet 105. </
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<
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<
s
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"
xml:space
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">quod ſemper etiam maius eſt 90. </
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<
s
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"
xml:space
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">ſiquidẽ ſe-
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cundum eo eſt maius, ſubduco igitur inuentum hoc de ſemicirculo. </
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>
<
s
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"
xml:space
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">& </
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<
s
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"
xml:space
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">remanent in reſi-
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duo 75. </
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>
<
s
xml:id
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echoid-s6137
"
xml:space
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">gra. </
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>
<
s
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xml:space
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">ſinus eius eſt 96592, qui quia maior etiã diuiſor eſt, iam duco ſinũ primi in-
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uenti. </
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<
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<
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">66145. </
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<
s
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xml:space
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">in totũ, & </
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>
<
s
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xml:space
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">productũ diuido in ipſum diuiſorẽ, ꝓueniẽt in q̊tiente 68479.
<
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</
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>
<
s
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">cuius arcus eſt 43. </
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<
s
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<
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<
s
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">mi. </
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<
s
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">arcus ille circuli uerticalis inter zenith & </
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>
<
s
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xml:space
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">circulum poſitio
<
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/>
nis tranſeuntem per corpus Solis. </
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>
<
s
xml:id
="
echoid-s6149
"
xml:space
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">Verum hæc quæ diximus omnia, de ſtellis & </
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>
<
s
xml:id
="
echoid-s6150
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xml:space
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">punctis
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illis uera ſunt, quæ ſupra horizontem cõſpiciuntur: </
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>
<
s
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"
xml:space
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">ſin a ũt ſub horizonte fuerint, tunc ti
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bi propone punctum diametraliter ei oppoſitum, ut ſi uelim ſcire, quantum circulus poſi
<
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tionũſub terra, qui ꝑ 2. </
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<
s
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<
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<
s
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<
s
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">♐ ducitur, à zenith diſtet, adſumo tũc mihi. </
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mi. </
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<
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">II, & </
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>
<
s
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xml:space
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">cũ eo ꝓcedo per oĩa operando ut ſupra, & </
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>
<
s
xml:id
="
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xml:space
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">ꝓdibit tandem mihi quæſitum.</
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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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">PRONVNCIATVM LXXIX.</
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>
<
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<
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xml:space
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">Altitudinem poli arctici ſuper ſemicirculum poſitionis breuiſsime & </
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<
s
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="
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xml:space
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peditiſsime inueſtigare.</
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>
<
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</
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<
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>
<
s
xml:id
="
echoid-s6167
"
xml:space
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">Altitudo illa poliſuꝑ ſemicirculũ poſitiõis nihil aliud eſt ̈ diſtantia poli arctici ſecun
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<
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<
emph
style
="
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">Quid ſit al</
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>
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<
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style
="
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">titudo poli</
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>
<
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<
emph
style
="
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">ſuper ſemi-</
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>
<
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<
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style
="
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">arculum po</
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>
<
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<
emph
style
="
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">ſitionis.</
emph
>
</
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>
dum circulum maiorẽ à ſemicirculo poſitionis, qui quidẽ circulus maior ſuꝑ ſemicirculũ
<
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/>
poſitionis ducitur ad angulos rectos. </
s
>
<
s
xml:id
="
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"
xml:space
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">Ea altitudo multũ ꝓderit ad dirigendos quin ſi-
<
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/>
gnificatores, ̈uis ita loꝗ Pontanus nõ ꝑmittat, nõ libet tamẽ hic à priſco uocabulo re-
<
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/>
cedere, melius quidẽ diceretur peragratio ſiue permeatio gradus aſcendentis, unde inqui
<
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/>
ritur quicquid accidit in corpore. </
s
>
<
s
xml:id
="
echoid-s6169
"
xml:space
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">Peragratio igitur Solis facit ad quærendũ dignitates,
<
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exaltationes honoris & </
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>
<
s
xml:id
="
echoid-s6170
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xml:space
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">regni ipſius nati, gradus aũt ☽ peragratio fit propter eſſe animæ,
<
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/>
corporis, at coniugij. </
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>
<
s
xml:id
="
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xml:space
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">Quarta dehinc peragratio ſiue directio partis fortunæ, ſiue horo-
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ſcopi gradus ☽ fit propter acquiſitiones & </
s
>
<
s
xml:id
="
echoid-s6172
"
xml:space
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">profectus ſubſtantiæ. </
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<
s
xml:id
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xml:space
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">Vltima aũt quæ & </
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<
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">gra
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dus eſt ipſius medij cœli, fit ꝓpter magiſteriũ & </
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>
<
s
xml:id
="
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"
xml:space
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">reliquas particulares diſpoſitiones. </
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>
<
s
xml:id
="
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xml:space
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">Pro-
<
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<
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xlink:label
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<
emph
style
="
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">Qua ratio</
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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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>
</
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>
pter eiuſmodi directiones ſiue ꝓfectiones inuẽtus eſt circulus poſitionũ, & </
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>
<
s
xml:id
="
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xml:space
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">altitudo eius
<
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reperta. </
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<
s
xml:id
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xml:space
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">Porrò inquiſita iã ex ſuperiori ꝓnunc, diſtantiaà ſemicirculi à uertice capitis ſiue
<
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/>
zenith horizõtis in circulo uerticali, duc ſinum diſtantiæ huius in ſinũ latitudinis regio
<
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/>
nis, ꝓductũ diuide in ſinũ, & </
s
>
<
s
xml:id
="
echoid-s6179
"
xml:space
="
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">arcus quotientis dabit altitudinẽ poliſeptentrionalis
<
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quæſitã ſuꝑ ſemicirculũ poſitiõis. </
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>
<
s
xml:id
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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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">? Exemplũ hoc habe. </
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>
<
s
xml:id
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xml:space
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">Ex ſuꝑiori pronunc, inueni ad
<
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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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">piſcopi.</
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>
</
note
>
horã intronziationis etiã diſtantiã ſemicirculi poſitionis à zenith, qui ductus eſt ꝑ gradũ
<
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ſiue locum Solis 43. </
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>
<
s
xml:id
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xml:space
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">gra. </
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<
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xml:id
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">13. </
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<
s
xml:id
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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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">ſinum eius 68479. </
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>
<
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xml:id
="
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xml:space
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">duco in ſinum altitudinis poli 48. </
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<
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">gra.
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</
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<
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">20. </
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<
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">mi. </
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<
s
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="
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"
xml:space
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">ita ut eſt Auguſtæ, ſinu eius 74702. </
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>
<
s
xml:id
="
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"
xml:space
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">diuiſo in perfectum, produco 51155. </
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>
<
s
xml:id
="
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"
xml:space
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">cuius ar-
<
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cus eſt 30. </
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<
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xml:id
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">gra. </
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<
s
xml:id
="
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">46. </
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<
s
xml:id
="
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"
xml:space
="
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">mi. </
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>
<
s
xml:id
="
echoid-s6197
"
xml:space
="
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">altitudo illa poli ſuper ſemicirculum poſitionis quæſita.</
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>
<
s
xml:id
="
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xml:space
="
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"/>
</
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>
</
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>
<
div
xml:id
="
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"
type
="
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"
level
="
1
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n
="
92
">
<
head
xml:id
="
echoid-head96
"
xml:space
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">PRONVNCIATVM LXXX.</
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>
<
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>
<
s
xml:id
="
echoid-s6199
"
xml:space
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">Horam diurnã ex altitudine Solis ſuꝑ horizõtẽ in omni regione cõijcere.</
s
>
<
s
xml:id
="
echoid-s6200
"
xml:space
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"/>
</
p
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<
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>
<
s
xml:id
="
echoid-s6201
"
xml:space
="
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">Habita altitudine Solis ſuꝑ horizontẽ, q̃re etiã declinationẽ gradus ☉(sun) ꝑ 5. </
s
>
<
s
xml:id
="
echoid-s6202
"
xml:space
="
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">huius, & </
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>
<
s
xml:id
="
echoid-s6203
"
xml:space
="
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">ſi
<
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/>
declinatio fuerit ſeptẽtrionalis, adde eã cõplemẽto altitudinis poli, uiciſsim ſubtrahe eã
<
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/>
ſi ſit Sol in ſigno meridionali, & </
s
>
<
s
xml:id
="
echoid-s6204
"
xml:space
="
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">ꝓueniet altitudo meridiana. </
s
>
<
s
xml:id
="
echoid-s6205
"
xml:space
="
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">Deinde duc ſinũ altitudinis
<
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/>
huius meridianæ in ſinũ totũ, & </
s
>
<
s
xml:id
="
echoid-s6206
"
xml:space
="
preserve
">diuide ꝓductũ in ſinũ cõplementi altitudinis poli, quo-
<
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/>
tientẽ dic inuentũ primũ. </
s
>
<
s
xml:id
="
echoid-s6207
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xml:space
="
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">Poſtea duc etiã ſinũ altitudinis Solis ſupra horizontẽ in ſinum
<
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<
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="
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xlink:label
="
note-0076-04
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xlink:href
="
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<
emph
style
="
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">Inuentum</
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>
<
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<
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="
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>
</
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>
totũ, & </
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>
<
s
xml:id
="
echoid-s6208
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xml:space
="
preserve
">diuide ꝓductũ in ſinũ cõplementi altitudinis poli, quotiens erit inuentũ ſecundũ.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s6209
"
xml:space
="
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">Atqui hoc inuentum ſecundũ inuenire etiã potes hoc modo. </
s
>
<
s
xml:id
="
echoid-s6210
"
xml:space
="
preserve
">Si ſinũ altitudinis Solis du
<
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/>
cas in inuentũ primũ, ꝓductũ uero diuidas in ſinũ altitudinis meridinæ, quotiens ille da-
<
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/>
bit quo inuentũ ſecundũ. </
s
>
<
s
xml:id
="
echoid-s6211
"
xml:space
="
preserve
">Vtro hoc inuẽto habito, ſubtrahe ſecundũ à priori, ſemꝑem̃
<
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<
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position
="
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xlink:label
="
note-0076-05
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xlink:href
="
note-0076-05a
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xml:space
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<
emph
style
="
it
">Inuentum</
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>
<
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<
emph
style
="
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">ſecundum.</
emph
>
</
note
>
illud eſt minus, reliquum rurſus duc in totũ, & </
s
>
<
s
xml:id
="
echoid-s6212
"
xml:space
="
preserve
">ꝓductũ diuide in ſinũ cõplemẽti declina-
<
lb
/>
tionis gradus Solis. </
s
>
<
s
xml:id
="
echoid-s6213
"
xml:space
="
preserve
">q̊tiens uocabit̃ inuentũ tertiũ. </
s
>
<
s
xml:id
="
echoid-s6214
"
xml:space
="
preserve
">q̊d ſi minus fuerit ſinu toto, ſubtrahe
<
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/>
ipſum à toto ſinu, & </
s
>
<
s
xml:id
="
echoid-s6215
"
xml:space
="
preserve
">habebis arcũ tꝑis ante uel poſt meridiẽ. </
s
>
<
s
xml:id
="
echoid-s6216
"
xml:space
="
preserve
">Sed ſi extiterit hoc inuentũ
<
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/>
tertiũ maius toto ſinu, ſubtrahe hinc ſinũ totũ, & </
s
>
<
s
xml:id
="
echoid-s6217
"
xml:space
="
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">arcũ reſidui adde ad 90. </
s
>
<
s
xml:id
="
echoid-s6218
"
xml:space
="
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">ſi´ etiã babebis
<
lb
/>
arcum antemeridianũ uel pomeridianũ, eum ſi diuides per 15. </
s
>
<
s
xml:id
="
echoid-s6219
"
xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s6220
"
xml:space
="
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">iamiã confeceris ho
<
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/>
ras. </
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>
<
s
xml:id
="
echoid-s6221
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="
preserve
">Et ſi tẽpus illud fuerit antemeridiẽ, totidẽ horas cõnumera retrorſum uerſus à 12. </
s
>
<
s
xml:id
="
echoid-s6222
"
xml:space
="
preserve
">ho
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0076-06
"
xlink:href
="
note-0076-06a
"
xml:space
="
preserve
">EXEM-
<
lb
/>
PLVM
<
lb
/>
E
<
emph
style
="
it
">piſcopi.</
emph
>
</
note
>
ra: </
s
>
<
s
xml:id
="
echoid-s6223
"
xml:space
="
preserve
">ſed ſi ſit pomeridianũ, adde tot horas ad 12. </
s
>
<
s
xml:id
="
echoid-s6224
"
xml:space
="
preserve
">hoc eſt meridianã horam, & </
s
>
<
s
xml:id
="
echoid-s6225
"
xml:space
="
preserve
">ꝓueniet ho-
<
lb
/>
ra diei quæſita. </
s
>
<
s
xml:id
="
echoid-s6226
"
xml:space
="
preserve
">?</
s
>
<
s
xml:id
="
echoid-s6227
"
xml:space
="
preserve
">? Exemplũ ni ſit etiã moleſtum tibi, eſto ut hora intronizatiõis </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>