Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
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GENVINVS VSVS
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igitur habes gradũ Solis ex amplitudine ortiua collectũ. </
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<
s
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xml:space
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omnia de occaſu, ſiquidem amplitudo una alteri reſpondet ſaltem unius ꝓpoſiti gradus.</
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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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<
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<
s
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xml:space
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">Altitudinem poli in ſingulos dies examplitudine ortiua uel occidua, So-
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lis ſiue ſtellarum, adpoſite inueſtigare.</
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<
s
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</
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<
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<
s
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echoid-s1528
"
xml:space
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">Vno hoc pronunciato tres ſimul uelut uno faſce cõſtrinximus, 12. </
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<
s
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<
s
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">& </
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<
s
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<
s
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xml:space
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">tria enim
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illa expendenda fuerunt, declinatio, amplitudo, & </
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<
s
xml:id
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"
xml:space
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">altitudo poli, ex ijs: </
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<
s
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echoid-s1534
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xml:space
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">quia priora duo
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<
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<
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<
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<
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</
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iam antea docuimus, reliquum eſt, ut etiã hoc tertium expediamus. </
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<
s
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="
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"
xml:space
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">Si forte altitudinem
<
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poli ex amplitudine ſiue declinatione cognoſcere cupis, propone tibi ſinum amplitudi-
<
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/>
nis ſimul cum ſinu declinationis, minorem duc in ſinum totum, productum diuide in ma
<
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/>
iorem, arcus quotientis oſtendet complementum altitudinis poli, id ſi ſubtrahas à 90. </
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>
<
s
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xml:space
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">re
<
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<
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xml:space
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PLVM
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E
<
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style
="
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<
unsure
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pi.</
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>
</
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>
manebit altitudo poli quam quæſiuiſti. </
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>
<
s
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<
s
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xml:space
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">? Vis & </
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<
s
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xml:space
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">hic exemplum tibi dari@ Enipſo in-
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tronizationis die Sol fuit in 2. </
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<
s
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">gra. </
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<
s
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<
s
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">mi. </
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<
s
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">II. </
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<
s
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">ex 5. </
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<
s
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">ergo pronunciato inueni declinatio
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nem 20. </
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<
s
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">gra. </
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<
s
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<
s
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">mi. </
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<
s
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">ſinus eius eſt 35347. </
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<
s
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="
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xml:space
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">Amplitudinem autem ortiuam Solis in die in-
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tronizationis inueni 31. </
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<
s
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<
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<
s
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">mi. </
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>
<
s
xml:id
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echoid-s1554
"
xml:space
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">iam paro elicere inde altitudinem poli. </
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>
<
s
xml:id
="
echoid-s1555
"
xml:space
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">Sinus igitur
<
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amplitudinis eſt 52825. </
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>
<
s
xml:id
="
echoid-s1556
"
xml:space
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">iam duco minorem iſtam 3534. </
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>
<
s
xml:id
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xml:space
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">à toto ſinu, productum diuido
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in 52825. </
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>
<
s
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xml:space
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">tanquam numerum maiorem, quotientis erit 66913. </
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>
<
s
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">arcus illius 42. </
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>
<
s
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">eum ubi
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ſubtraxeris à 90. </
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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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<
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xml:space
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">PRONVNCIATVM XV.</
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<
s
xml:id
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xml:space
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">In qualibet regione differentiam inquirere aſcenſionalem, per quam lon-
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gitudo dierum & </
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<
s
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<
s
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">unde longitudo diurna per uniuer-
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ſum orbem facile cognoſci poteſt.</
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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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">Differentia aſcenſionalis arcus eſt æquatoris, per quem longitudo diurna agnoſci-
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<
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<
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<
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tur, is autem ſic intelligitur. </
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<
s
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xml:space
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">Quum ab ortu æquinoctiali uſ ad meridianũ 90. </
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<
s
xml:id
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<
s
xml:id
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per interſint, deinde in ſingulas horas gradus 15. </
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<
s
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">emergũt ſuper horizontem, 90. </
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<
s
xml:id
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">illi gra
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dus præciſe horas 6. </
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<
s
xml:id
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xml:space
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">cõficiũt, quo dies medius horis 6. </
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<
s
xml:id
="
echoid-s1575
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xml:space
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">uel longior eſt uel breuior, idip
<
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ſum uocamus differentiam aſcenſionalem, eam inuenire cupiens, propone tibi ſinus utri
<
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/>
uſ complementi, declinationis & </
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>
<
s
xml:id
="
echoid-s1576
"
xml:space
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">amplitudinis, minorem duc in finum totum, produ-
<
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ctum diuide in ſinum maiorem, arcu quotientis dehinc ſubtracto à 90. </
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>
<
s
xml:id
="
echoid-s1577
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xml:space
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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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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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>
rentia aſcenſionalis: </
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>
<
s
xml:id
="
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xml:space
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">quod ſi declinatio fuerit meridionalis, ſubtrahe differentiam illam
<
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aſcenſionalem à 90. </
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>
<
s
xml:id
="
echoid-s1579
"
xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s1580
"
xml:space
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">remanebit arcus ſemidiurnus: </
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>
<
s
xml:id
="
echoid-s1581
"
xml:space
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">ſin autem declinatio ſit ſeptentrio-
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nalis, illam rurſus adde ad 90. </
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<
s
xml:id
="
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xml:space
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">& </
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>
<
s
xml:id
="
echoid-s1583
"
xml:space
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">iterum habebis arcum ſemidiurnum. </
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>
<
s
xml:id
="
echoid-s1584
"
xml:space
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">Tantundem eſt, ſi
<
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arcum quotientis ſubtrahas à ſemicirculo, nam & </
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>
<
s
xml:id
="
echoid-s1585
"
xml:space
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">tunc manebit arcus ſemidiurnus, illo
<
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/>
duplicato, habes arcum diurnum, quem ſi rurſus ſubtrahas à toto circulo, arcus relinque-
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tur nocturnus. </
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>
<
s
xml:id
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xml:space
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<
s
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<
s
xml:id
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<
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<
s
xml:id
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<
s
xml:id
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xml:space
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<
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xml:space
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PLVM
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E
<
emph
style
="
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<
unsure
/>
pi.</
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>
</
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>
plum tibi huiuſmodi: </
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>
<
s
xml:id
="
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"
xml:space
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">Inuenturus longitudinem diei intronizationis, iam antea habeo
<
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perfectam declinationem Solis ex pronunciato 5. </
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>
<
s
xml:id
="
echoid-s1593
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<
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xml:id
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<
s
xml:id
="
echoid-s1595
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>
<
s
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<
s
xml:id
="
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<
s
xml:id
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<
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declinatio eſt 20. </
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<
s
xml:id
="
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>
<
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="
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xml:space
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>
<
s
xml:id
="
echoid-s1601
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xml:space
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">mi. </
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>
<
s
xml:id
="
echoid-s1602
"
xml:space
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">ex 12. </
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>
<
s
xml:id
="
echoid-s1603
"
xml:space
="
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">pronunciato quo inuentam habeo amplitudinem
<
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/>
ad eundem ipſum gradum Solis, puta 31. </
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>
<
s
xml:id
="
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xml:space
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">gra. </
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>
<
s
xml:id
="
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">53. </
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>
<
s
xml:id
="
echoid-s1606
"
xml:space
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">mi. </
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>
<
s
xml:id
="
echoid-s1607
"
xml:space
="
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">Nunc iam colligo complementa,
<
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alterum eſt 58. </
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>
<
s
xml:id
="
echoid-s1608
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xml:space
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">gra. </
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>
<
s
xml:id
="
echoid-s1609
"
xml:space
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">7. </
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>
<
s
xml:id
="
echoid-s1610
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xml:space
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">mi. </
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>
<
s
xml:id
="
echoid-s1611
"
xml:space
="
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">ſinus eius 849 12. </
s
>
<
s
xml:id
="
echoid-s1612
"
xml:space
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">alterum porrò complementum eſt 69. </
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>
<
s
xml:id
="
echoid-s1613
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xml:space
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">gra. </
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>
<
s
xml:id
="
echoid-s1614
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xml:space
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">18.
<
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</
s
>
<
s
xml:id
="
echoid-s1615
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xml:space
="
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">mi. </
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>
<
s
xml:id
="
echoid-s1616
"
xml:space
="
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">arcus ipſius 93544. </
s
>
<
s
xml:id
="
echoid-s1617
"
xml:space
="
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">ſinum minorem multiplica cum toto ſinu, productum diuide in
<
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maximum, & </
s
>
<
s
xml:id
="
echoid-s1618
"
xml:space
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">quotiens erit 90772, arcus eius eſt 65. </
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>
<
s
xml:id
="
echoid-s1619
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xml:space
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">gra. </
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>
<
s
xml:id
="
echoid-s1620
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">12. </
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>
<
s
xml:id
="
echoid-s1621
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s1622
"
xml:space
="
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">Arcũ illum ſi ſubtrahas à
<
lb
/>
90. </
s
>
<
s
xml:id
="
echoid-s1623
"
xml:space
="
preserve
">remanebit differentia aſcenſionalis 24. </
s
>
<
s
xml:id
="
echoid-s1624
"
xml:space
="
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">gra. </
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>
<
s
xml:id
="
echoid-s1625
"
xml:space
="
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">49. </
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>
<
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xml:id
="
echoid-s1626
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1627
"
xml:space
="
preserve
">differentiam hanc adde, & </
s
>
<
s
xml:id
="
echoid-s1628
"
xml:space
="
preserve
">habe-
<
lb
/>
bis arcum ſemidiurnum 114. </
s
>
<
s
xml:id
="
echoid-s1629
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1630
"
xml:space
="
preserve
">49. </
s
>
<
s
xml:id
="
echoid-s1631
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1632
"
xml:space
="
preserve
">Vel ſubtrahe 65. </
s
>
<
s
xml:id
="
echoid-s1633
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1634
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s1635
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1636
"
xml:space
="
preserve
">de ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s1637
"
xml:space
="
preserve
">
<
lb
/>
rurſus manebit arcus ſemidiurnus, eũ ſi reſoluas in horas, habebis horas 7. </
s
>
<
s
xml:id
="
echoid-s1638
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1639
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s1640
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1641
"
xml:space
="
preserve
">Sin
<
lb
/>
autem duplaris numerum, habebis arcũ diurnum 15. </
s
>
<
s
xml:id
="
echoid-s1642
"
xml:space
="
preserve
">horas 36. </
s
>
<
s
xml:id
="
echoid-s1643
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1644
"
xml:space
="
preserve
">Ad extremum ſi ſub-
<
lb
/>
trahas arcum diurnum à 24. </
s
>
<
s
xml:id
="
echoid-s1645
"
xml:space
="
preserve
">horis, reliquæ tibi manebunt horæ 8. </
s
>
<
s
xml:id
="
echoid-s1646
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1647
"
xml:space
="
preserve
">24. </
s
>
<
s
xml:id
="
echoid-s1648
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1649
"
xml:space
="
preserve
">tempus ſcili-
<
lb
/>
cet nocturnum. </
s
>
<
s
xml:id
="
echoid-s1650
"
xml:space
="
preserve
">At hoc modo cuiuslibet puncti uel ſtellæ fixæ potes arcum inuenire
<
lb
/>
diurnum, hoc eſt, quot horis & </
s
>
<
s
xml:id
="
echoid-s1651
"
xml:space
="
preserve
">minutis maneat ſuper horizontem, ſiue interdiu tandem
<
lb
/>
ſiue noctu id fiat. </
s
>
<
s
xml:id
="
echoid-s1652
"
xml:space
="
preserve
">Quod autem ad puncta eclypticæ tantum pertinet, ſequenti pronun
<
lb
/>
ciato explicabimus.</
s
>
<
s
xml:id
="
echoid-s1653
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>
