Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
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<
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0065
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65
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rhead
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TABVLARVM SINVVM PER PET. APIANVM.
"/>
adde reſiduũ ad iſtud q̊d paulo ante ſe poſuiſti reliquũ aſcenſionũrecta℞. </
s
>
<
s
xml:id
="
echoid-s4601
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xml:space
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">Sed ſi declina
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tio finis arcus ꝓpoſiti, ſecundũ ordinẽ ſignorũ numerãdo, minor extiterit declinatiõe ini
<
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tij huius arcus, tũc ſubtrahe reſiduũ hoc â reſiduo aſcenſionũ rectarũ, ꝓ utrã hanc rationẽ
<
lb
/>
q̊d ꝓducitur tempus ipſum eſt (ſi ſemper 15. </
s
>
<
s
xml:id
="
echoid-s4602
"
xml:space
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preserve
">gradus ꝓ una hora ſupputentur) in quo ar-
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cus ꝓpoſitus ꝓcurrit ultra circulũ uerticalẽ. </
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>
<
s
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xml:space
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">ld omne ſic intelligendũ eſt, ꝙ ambo termi-
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ni iſtius arcus ſint in medietate ſeptentrionali, fœlicius iſta oia intelliges ex adiũcto exẽ-
<
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<
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xlink:label
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note-0065-01
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PLVM
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<
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unsure
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pi.</
emph
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</
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plo. </
s
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<
s
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xml:space
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<
s
xml:id
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xml:space
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">?Volo ſcire quanto tꝑe arcus iſte à 2. </
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>
<
s
xml:id
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echoid-s4606
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xml:space
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<
s
xml:id
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xml:space
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<
s
xml:id
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echoid-s4608
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xml:space
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<
s
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xml:space
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">II, ubi Sol fuit in die & </
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<
s
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echoid-s4610
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xml:space
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">hora in-
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tronizatiõis uſ ad 16. </
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<
s
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<
s
xml:id
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xml:space
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<
s
xml:id
="
echoid-s4613
"
xml:space
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">mi. </
s
>
<
s
xml:id
="
echoid-s4614
"
xml:space
="
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">II, circulũ uerticalẽ trãſcendat, aſcenſionẽ igitur re-
<
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ctaminueni ad 2. </
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>
<
s
xml:id
="
echoid-s4615
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xml:space
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<
s
xml:id
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echoid-s4616
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xml:space
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">26. </
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<
s
xml:id
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echoid-s4617
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xml:space
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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
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<
s
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xml:space
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<
s
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echoid-s4625
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xml:space
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</
s
>
<
s
xml:id
="
echoid-s4626
"
xml:space
="
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">49. </
s
>
<
s
xml:id
="
echoid-s4627
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4628
"
xml:space
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">II eſt 75. </
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>
<
s
xml:id
="
echoid-s4629
"
xml:space
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s
>
<
s
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="
echoid-s4630
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xml:space
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">37. </
s
>
<
s
xml:id
="
echoid-s4631
"
xml:space
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">mi. </
s
>
<
s
xml:id
="
echoid-s4632
"
xml:space
="
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">differentia earũ 15. </
s
>
<
s
xml:id
="
echoid-s4633
"
xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s4634
"
xml:space
="
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">16. </
s
>
<
s
xml:id
="
echoid-s4635
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4636
"
xml:space
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">reſiduũ ſepono ſeorſim, mox
<
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ex præcedenti ꝓnunciato quæro tempus ab hora 6. </
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>
<
s
xml:id
="
echoid-s4637
"
xml:space
="
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">uſ dum 2. </
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>
<
s
xml:id
="
echoid-s4638
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<
s
xml:id
="
echoid-s4639
"
xml:space
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">26. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">mi (qui Solipſe
<
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/>
eſt) ad circulũ perueniat uerticalem, inuenio ergo 19. </
s
>
<
s
xml:id
="
echoid-s4641
"
xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s4642
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xml:space
="
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">53. </
s
>
<
s
xml:id
="
echoid-s4643
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4644
"
xml:space
="
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">At hoc ita ſeruo, non
<
lb
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immutans in horas. </
s
>
<
s
xml:id
="
echoid-s4645
"
xml:space
="
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">Comperio etiam tempus illud ad 16. </
s
>
<
s
xml:id
="
echoid-s4646
"
xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s4647
"
xml:space
="
preserve
">49. </
s
>
<
s
xml:id
="
echoid-s4648
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4649
"
xml:space
="
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">II, a b hora 6. </
s
>
<
s
xml:id
="
echoid-s4650
"
xml:space
="
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">do-
<
lb
/>
nec attingat circulum uerticalem habere 29. </
s
>
<
s
xml:id
="
echoid-s4651
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xml:space
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">gra. </
s
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<
s
xml:id
="
echoid-s4652
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xml:space
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">10. </
s
>
<
s
xml:id
="
echoid-s4653
"
xml:space
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">mi. </
s
>
<
s
xml:id
="
echoid-s4654
"
xml:space
="
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">Nunc igitur ſubtraho 19. </
s
>
<
s
xml:id
="
echoid-s4655
"
xml:space
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<
s
xml:id
="
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<
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53. </
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>
<
s
xml:id
="
echoid-s4657
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4658
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">à 39. </
s
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<
s
xml:id
="
echoid-s4659
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xml:space
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">gra. </
s
>
<
s
xml:id
="
echoid-s4660
"
xml:space
="
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">10, mi. </
s
>
<
s
xml:id
="
echoid-s4661
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xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s4662
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xml:space
="
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">remanent 9. </
s
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<
s
xml:id
="
echoid-s4663
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xml:space
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s
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<
s
xml:id
="
echoid-s4664
"
xml:space
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s
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<
s
xml:id
="
echoid-s4665
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xml:space
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<
s
xml:id
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echoid-s4666
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xml:space
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s
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<
s
xml:id
="
echoid-s4667
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xml:space
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">49. </
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>
<
s
xml:id
="
echoid-s4668
"
xml:space
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s
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<
s
xml:id
="
echoid-s4669
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xml:space
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<
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II, maiorem 22. </
s
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<
s
xml:id
="
echoid-s4670
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xml:space
="
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">gra. </
s
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<
s
xml:id
="
echoid-s4671
"
xml:space
="
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">50. </
s
>
<
s
xml:id
="
echoid-s4672
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4673
"
xml:space
="
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">quàm declinatio hæc 2. </
s
>
<
s
xml:id
="
echoid-s4674
"
xml:space
="
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s
>
<
s
xml:id
="
echoid-s4675
"
xml:space
="
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s
>
<
s
xml:id
="
echoid-s4676
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4677
"
xml:space
="
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">II, quamper 5. </
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>
<
s
xml:id
="
echoid-s4678
"
xml:space
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">pronuncia
<
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tum inueni eſſe 20. </
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<
s
xml:id
="
echoid-s4679
"
xml:space
="
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s
>
<
s
xml:id
="
echoid-s4680
"
xml:space
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">42. </
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>
<
s
xml:id
="
echoid-s4681
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xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4682
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xml:space
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<
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echoid-s4683
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<
s
xml:id
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echoid-s4684
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xml:space
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>
<
s
xml:id
="
echoid-s4685
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xml:space
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s
>
<
s
xml:id
="
echoid-s4686
"
xml:space
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">ad reſiduũ ſiue differẽtiam aſcen-
<
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ſionum rectarum, ſcilicet 15. </
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>
<
s
xml:id
="
echoid-s4687
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xml:space
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<
s
xml:id
="
echoid-s4688
"
xml:space
="
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">16. </
s
>
<
s
xml:id
="
echoid-s4689
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4690
"
xml:space
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">inde & </
s
>
<
s
xml:id
="
echoid-s4691
"
xml:space
="
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">prouenient 24 gra. </
s
>
<
s
xml:id
="
echoid-s4692
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xml:space
="
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">33. </
s
>
<
s
xml:id
="
echoid-s4693
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4694
"
xml:space
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uerſis in horas & </
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>
<
s
xml:id
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echoid-s4695
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xml:space
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">horarum minuta, habebo horã 1. </
s
>
<
s
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="
echoid-s4696
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">& </
s
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<
s
xml:id
="
echoid-s4697
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xml:space
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">minuta ferè 38. </
s
>
<
s
xml:id
="
echoid-s4698
"
xml:space
="
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">Quanto tꝓe arcus
<
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ille à 2. </
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>
<
s
xml:id
="
echoid-s4699
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xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s4700
"
xml:space
="
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">26. </
s
>
<
s
xml:id
="
echoid-s4701
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4702
"
xml:space
="
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">II decurrit uſ ad 16. </
s
>
<
s
xml:id
="
echoid-s4703
"
xml:space
="
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">gra. </
s
>
<
s
xml:id
="
echoid-s4704
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xml:space
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">49. </
s
>
<
s
xml:id
="
echoid-s4705
"
xml:space
="
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">mi. </
s
>
<
s
xml:id
="
echoid-s4706
"
xml:space
="
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">II, ſuper circulum uerticalem.</
s
>
<
s
xml:id
="
echoid-s4707
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xml:space
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"/>
</
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>
</
div
>
<
div
xml:id
="
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type
="
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level
="
1
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<
head
xml:id
="
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xml:space
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preserve
">PRONVNCIATVM LXIIII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4708
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xml:space
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">Idem hoctempus adhucalio modo perquirere, at ea ueluti generalis eſt
<
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regula ad totam eclypticam.</
s
>
<
s
xml:id
="
echoid-s4709
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xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4710
"
xml:space
="
preserve
">Quum in hac operatione arcus datus ſit ſemicirculus, is ſanè uerticalem tranſcendit
<
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in 12. </
s
>
<
s
xml:id
="
echoid-s4711
"
xml:space
="
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">horis, at ideo nulla peculiari animaduerſione hic opus eſt. </
s
>
<
s
xml:id
="
echoid-s4712
"
xml:space
="
preserve
">Si autem arcus datus
<
lb
/>
eclypticæ fuerit ſemicirculo minor, eius´ termini à principio ♋ æquales habuerint re-
<
lb
/>
motiones, & </
s
>
<
s
xml:id
="
echoid-s4713
"
xml:space
="
preserve
">ideo etiam neceſſario ab æquinoctiali ſcilicet â 90. </
s
>
<
s
xml:id
="
echoid-s4714
"
xml:space
="
preserve
">gradu, qui cum principio
<
lb
/>
cancri ſemper iacet in medio cœli, æquales diſtantias tunc differentia aſcenſionum, quæ
<
lb
/>
aliàs aſcenſio dati arcus recta diciſolet, eſtarcus huius temporis quem inquiris, non eſt
<
lb
/>
igitur quòd amplius labores ſolicitus, ſiquidem eo temporearcus datus percurrit circu-
<
lb
/>
lum uerticalem. </
s
>
<
s
xml:id
="
echoid-s4715
"
xml:space
="
preserve
">Cæterum ſi termini arcus dati inæquales habuerint diſtantias à princi-
<
lb
/>
pio Cancri, oportebit te amborum illorum aſcenſionem quærere rectam, ſimiliter & </
s
>
<
s
xml:id
="
echoid-s4716
"
xml:space
="
preserve
">utri
<
lb
/>
uſ declinationem ab æquatore. </
s
>
<
s
xml:id
="
echoid-s4717
"
xml:space
="
preserve
">Deinde inquire etiam cuiuslibet termiui altitudinem
<
lb
/>
ſupra horizontem in circulo uerticali per 20. </
s
>
<
s
xml:id
="
echoid-s4718
"
xml:space
="
preserve
">pronunciatum, poſtea tibi propone ſinus
<
lb
/>
primi termini complementi altitudinis & </
s
>
<
s
xml:id
="
echoid-s4719
"
xml:space
="
preserve
">complementi declinationis, minorem ex ijs
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0065-02
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xlink:href
="
note-0065-02a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Aredlis in-</
emph
>
<
lb
/>
<
emph
style
="
it
">greſſus.</
emph
>
</
note
>
duc in totum, productum diuide in maiorem, & </
s
>
<
s
xml:id
="
echoid-s4720
"
xml:space
="
preserve
">arcus quotientis uocabitur inuentũ
<
lb
/>
primum. </
s
>
<
s
xml:id
="
echoid-s4721
"
xml:space
="
preserve
">Simili modo operaberis etiam cum finali complemento termini & </
s
>
<
s
xml:id
="
echoid-s4722
"
xml:space
="
preserve
">ſinum cõ-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0065-03
"
xlink:href
="
note-0065-03a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Inuentum</
emph
>
<
lb
/>
<
emph
style
="
it
">primum-</
emph
>
<
lb
/>
<
emph
style
="
it
">Inuentum</
emph
>
<
lb
/>
<
emph
style
="
it
">ſecundum.</
emph
>
</
note
>
plementi declinationis eius, at ſic arcus quotientis dabit inuentum ſecundũ. </
s
>
<
s
xml:id
="
echoid-s4723
"
xml:space
="
preserve
">Porrò de-
<
lb
/>
inceps ſubtrabe inuentũ minus à maiori, & </
s
>
<
s
xml:id
="
echoid-s4724
"
xml:space
="
preserve
">remanebit differentia inuentorũ eã adde ad
<
lb
/>
aſcenſionem rectã arcus propoſiti, quam paulo ante dixi differentiã inter aſcenſiones re
<
lb
/>
ctas duorũ terminorũ, ſi modo terminus finalis Borealior extiterit ̈ initialis, uel ſubtra
<
lb
/>
he differentiam iſtam, ſi terminus finalis meridionalior fuerit puncto initiali. </
s
>
<
s
xml:id
="
echoid-s4725
"
xml:space
="
preserve
">Ex hac ſiue
<
lb
/>
additione ſiue ſubtra ctione, quicquid reſultabit, arcus erit æquatoris ſimul oriens cũ ar-
<
lb
/>
cu ꝓpoſito eclypticæ circulum uerticalem ſupergreditur, tantũ ut gradus iſtos in horas
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s4726
"
xml:space
="
preserve
">horarũ minuta cõuertas. </
s
>
<
s
xml:id
="
echoid-s4727
"
xml:space
="
preserve
">Adhuc tamen, ſi arcus datus eclypticæ incipiat in principio
<
lb
/>
♈, & </
s
>
<
s
xml:id
="
echoid-s4728
"
xml:space
="
preserve
">deſinat citra princi piũ ♎, tunc ſanè ipſum inuentum primum ſine illa ulterioriſup
<
lb
/>
putatione erit 90. </
s
>
<
s
xml:id
="
echoid-s4729
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4730
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4731
"
xml:space
="
preserve
">ſi finis arcus propoſiti, deſinat in principium ♎ præciſe, princi
<
lb
/>
pium autem ſuum habeat poſt principium ♈, tunc obmiſſo inuento altero, operatio fi
<
lb
/>
et ut prius. </
s
>
<
s
xml:id
="
echoid-s4732
"
xml:space
="
preserve
">?</
s
>
<
s
xml:id
="
echoid-s4733
"
xml:space
="
preserve
">? Exemplum ſit hoc tibi, ne difficultatem cauſſari nimiam queas. </
s
>
<
s
xml:id
="
echoid-s4734
"
xml:space
="
preserve
">Ipſo die
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0065-04
"
xlink:href
="
note-0065-04a
"
xml:space
="
preserve
">EXEM-
<
lb
/>
PLVM
<
lb
/>
<
emph
style
="
it
">Epiſoo
<
unsure
/>
pi.</
emph
>
</
note
>
intronizationis fuit locus ☉(sun) 2. </
s
>
<
s
xml:id
="
echoid-s4735
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4736
"
xml:space
="
preserve
">26. </
s
>
<
s
xml:id
="
echoid-s4737
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4738
"
xml:space
="
preserve
">II, nunc ergo cupio ſcire à gradu ☉(sun) uſ ad
<
lb
/>
16. </
s
>
<
s
xml:id
="
echoid-s4739
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4740
"
xml:space
="
preserve
">49. </
s
>
<
s
xml:id
="
echoid-s4741
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4742
"
xml:space
="
preserve
">Gemini, tempus iſtud, in q̊ arcus hic circulũ uerticalem ſupergreditur </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>