Clavius, Christoph
,
Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur
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LIBER SECVNDVS.
"/>
trabamus, initio facto à maioribus, ſiue poſterioribus, reliquę erunt aſcenſiones rectę omnium punctorum
<
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ſecundi quadrantis Eclipticę. </
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>
<
s
xml:id
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xml:space
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">Rurſus ſi eaſdem ſemicir culo apponamus, facto initio à minoribus, ſiue prio
<
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ribus, conficientur aſcenſiones rectæ omnium punctorum tertij quadrantis Eclipticę. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Si denique eaſdem
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auferamus ex toto circulo, initio rurſus facto à maioribus, ſiue poſterioribus, remanebunt aſcenſiones re-
<
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/>
ctę omnium punctorum vltimi quadrantis Eclipticę. </
s
>
<
s
xml:id
="
echoid-s12503
"
xml:space
="
preserve
">Itaque totus labor poſitus eſt in perueſtigatione
<
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/>
aſcenſionum rectarum omnium punctorum primi quadrantis Eclipticæ inchoati à principio ♈, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">in fi-
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ne ♊, terminati.</
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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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<
s
xml:id
="
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"
xml:space
="
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">SIT rurſum Horizon obliquus A B C D; </
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>
<
s
xml:id
="
echoid-s12507
"
xml:space
="
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">Aequator B D; </
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>
<
s
xml:id
="
echoid-s12508
"
xml:space
="
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">Ecliptica E F; </
s
>
<
s
xml:id
="
echoid-s12509
"
xml:space
="
preserve
">principium ♈, in ſecunda
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0211-01
"
xlink:href
="
note-0211-01a
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xml:space
="
preserve
">Differentia in-
<
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ter aſcẽſionem
<
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rectam & obli-
<
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quam cuiusli
<
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bet puncti Ecli
<
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pticæ qua via
<
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exploranda. ad
<
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datam altitudi-
<
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nem poli.</
note
>
figura G; </
s
>
<
s
xml:id
="
echoid-s12510
"
xml:space
="
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">in tertia verò principium ♎, idem punctum G; </
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>
<
s
xml:id
="
echoid-s12511
"
xml:space
="
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">Meridianus A C; </
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>
<
s
xml:id
="
echoid-s12512
"
xml:space
="
preserve
">arcus Eclipticæ G E, à prin
<
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/>
cipio ♈, vel ♎, inchoatus qua drante minor, ita vt eius aſcenſio obliqua, hoc est, in obliqua ſphæra, ſit ar
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0211-02
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xlink:href
="
note-0211-02a
"
xml:space
="
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">10</
note
>
cus Aequatoris G B, quem inueſtigare oportet. </
s
>
<
s
xml:id
="
echoid-s12513
"
xml:space
="
preserve
">Ducatur ex polo mundi H, per E, circulus maximus ſe-
<
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/>
cans Aequatorem in I, ita vt G I, ſit aſcenſio recta eiuſdem arcus Eclipticæ G E. </
s
>
<
s
xml:id
="
echoid-s12514
"
xml:space
="
preserve
">Quoniam ergo in trian-
<
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/>
gulo ſphęrico C E H, in quo angulus C, rectus est, est per propoſ. </
s
>
<
s
xml:id
="
echoid-s12515
"
xml:space
="
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">16. </
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>
<
s
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="
echoid-s12516
"
xml:space
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">lib. </
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>
<
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="
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xml:space
="
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">4. </
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>
<
s
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="
echoid-s12518
"
xml:space
="
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">Ioan. </
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>
<
s
xml:id
="
echoid-s12519
"
xml:space
="
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">Regiom. </
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>
<
s
xml:id
="
echoid-s12520
"
xml:space
="
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">de triangulis, vel
<
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/>
per propoſ. </
s
>
<
s
xml:id
="
echoid-s12521
"
xml:space
="
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">16. </
s
>
<
s
xml:id
="
echoid-s12522
"
xml:space
="
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">lib. </
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>
<
s
xml:id
="
echoid-s12523
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s12524
"
xml:space
="
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">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s12525
"
xml:space
="
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">41. </
s
>
<
s
xml:id
="
echoid-s12526
"
xml:space
="
preserve
">noſtrorum triangulorum ſphæricorum, vt ſinus arcus H E,
<
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/>
hoc eſt, vt ſinus complementi declinationis puncti Eclipticæ arcum G E, @terminantis (In tertia namque
<
lb
/>
figura idem ſinus eſt arcus H E, & </
s
>
<
s
xml:id
="
echoid-s12527
"
xml:space
="
preserve
">complementi declinationis E I, propterea quòd arcus H E, cum com-
<
lb
/>
plemento declinationis E I, ſemicir culum conficit) ad ſinum anguli C, hoc eſt, ad ſinum totum, ita ſinus
<
lb
/>
arcus C H, altitudinis poli, ad ſinum anguli C E H, qui in ſecunda figura æqualis eſt angulo B E I. </
s
>
<
s
xml:id
="
echoid-s12528
"
xml:space
="
preserve
">Rurſus
<
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eadem ratione, & </
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>
<
s
xml:id
="
echoid-s12529
"
xml:space
="
preserve
">conuertendo, intriangulo ſphærico B E I, eſt vt ſinus anguli E B I, complementi altitu
<
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/>
dinis poli, quem nimirum Aequator cum Horizonte conſtituit, ad ſinum arcus E I, declinationis, ita ſinus
<
lb
/>
<
note
position
="
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"
xlink:label
="
note-0211-03
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xlink:href
="
note-0211-03a
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xml:space
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">20</
note
>
anguli B E I, proximè inuenti ad ſinum arcus B I, quo aſcenſio recta G I, ab aſcenſione obliqua G B, dif-
<
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/>
fert: </
s
>
<
s
xml:id
="
echoid-s12530
"
xml:space
="
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">Si fiat, vt ſinus complementi declinationis puncti arcum Eclipticæ terminantis ad ſinum totum, ita
<
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/>
ſinus altitudinis poli ad aliud, inuenietur ſinus anguli B E I: </
s
>
<
s
xml:id
="
echoid-s12531
"
xml:space
="
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">Et ſi rurſus fiat, vt ſinus complementi al-
<
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/>
titudinis poli ad ſinum declinationis eiuſdem arcus Eclipticę, ita ſinus anguli B E I, proximè inuentus ad
<
lb
/>
aliud, inuenietur ſinus arcus B I, differentiæ aſcenſionis rectę, & </
s
>
<
s
xml:id
="
echoid-s12532
"
xml:space
="
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">obliquę arcui Eelipticę G E, reſponden-
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/>
tis. </
s
>
<
s
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="
echoid-s12533
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xml:space
="
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">Exemplum. </
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>
<
s
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="
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xml:space
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">Ponatur punctum E, in ſecunda figura grad. </
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>
<
s
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xml:space
="
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">29. </
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>
<
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="
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xml:space
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">♉, & </
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>
<
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"
xml:space
="
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">in tertia grad. </
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>
<
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xml:space
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">29. </
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<
s
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="
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xml:space
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">♏, ita vt
<
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arcus G E, contineat grad. </
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>
<
s
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">59. </
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<
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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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">arcus E I, declinationis grad. </
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>
<
s
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="
echoid-s12543
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xml:space
="
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">19. </
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>
<
s
xml:id
="
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xml:space
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">Min. </
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>
<
s
xml:id
="
echoid-s12545
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xml:space
="
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">59. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Si igitur fiat, vt 93979.
<
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</
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>
<
s
xml:id
="
echoid-s12547
"
xml:space
="
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">ſinus complementi declinationis ad 100000. </
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>
<
s
xml:id
="
echoid-s12548
"
xml:space
="
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">ſinum totum, ita 66913. </
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>
<
s
xml:id
="
echoid-s12549
"
xml:space
="
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">ſinus altitudinis poli ad aliud, re-
<
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perietur hic ferè ſinus 71199. </
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>
<
s
xml:id
="
echoid-s12550
"
xml:space
="
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">anguli E, qui ſeruetur. </
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>
<
s
xml:id
="
echoid-s12551
"
xml:space
="
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">Deinde ſi fiat, vt 74314. </
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>
<
s
xml:id
="
echoid-s12552
"
xml:space
="
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">ſinus complementi altitu
<
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dinis poli ad 34174. </
s
>
<
s
xml:id
="
echoid-s12553
"
xml:space
="
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">ſinum declinationis, ita 71199. </
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>
<
s
xml:id
="
echoid-s12554
"
xml:space
="
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">ſinus ſeruatus ad aliud, proueniet ferè hic ſinus
<
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<
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position
="
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xlink:label
="
note-0211-04
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xlink:href
="
note-0211-04a
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xml:space
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">30</
note
>
32741. </
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>
<
s
xml:id
="
echoid-s12555
"
xml:space
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">cuius arcus continet grad. </
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>
<
s
xml:id
="
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xml:space
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">19. </
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>
<
s
xml:id
="
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xml:space
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">Min. </
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<
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="
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xml:space
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">7. </
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>
<
s
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xml:space
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">pro differentia aſcenſionis rectę, & </
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>
<
s
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="
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xml:space
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">obliquę arcus G E.
<
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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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="
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xlink:label
="
note-0211-05
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xlink:href
="
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xml:space
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">Aſcenſio obli-
<
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qua cuiusuis pũ
<
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cti Eclipticæ
<
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qua ratione in-
<
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ueniatur ex dif
<
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/>
ferentia aſcen-
<
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ſionali.</
note
>
Quę differentia ſi in ſecunda figura dematur ex aſcenſione recta G I, iam antea inuenta, (quia circulus ma
<
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/>
ximus H E, qui vices gerit recti Horizontis, Aequatorem ſecat infra Horizontem, cum medietas Zo-
<
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diaci ab ♈, vſque ad ♎, ſit borealis) remanebit aſcenſio obliqua G B, grad. </
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>
<
s
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="
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xml:space
="
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">37. </
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<
s
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xml:space
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">Min. </
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<
s
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="
echoid-s12564
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xml:space
="
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">39. </
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<
s
xml:id
="
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"
xml:space
="
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">arcui Eclipticę
<
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boreali G E, debita: </
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>
<
s
xml:id
="
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"
xml:space
="
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">Si verò eadem differentia in tertia figura rectæ aſcenſioni G I, addatur (quia
<
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/>
circulus maximus H E, ſecat Aequatorem ſupra Horizontem, propterea quòd medietas Zodiaci à ♎,
<
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/>
vſque ad ♈, australis eſt) conficietur aſcenſio obliqua G B, grad. </
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>
<
s
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="
echoid-s12567
"
xml:space
="
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">75. </
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>
<
s
xml:id
="
echoid-s12568
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xml:space
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">Min. </
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<
s
xml:id
="
echoid-s12569
"
xml:space
="
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">53. </
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>
<
s
xml:id
="
echoid-s12570
"
xml:space
="
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">conueniens arcui Eclipticæ
<
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auſtrali G E, à principio ♎, computato; </
s
>
<
s
xml:id
="
echoid-s12571
"
xml:space
="
preserve
">cui ſi apponatur ſemicirculus, conflabitur aſcenſio obliqua grad.
<
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</
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>
<
s
xml:id
="
echoid-s12572
"
xml:space
="
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">255. </
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>
<
s
xml:id
="
echoid-s12573
"
xml:space
="
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">Min. </
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>
<
s
xml:id
="
echoid-s12574
"
xml:space
="
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">53. </
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>
<
s
xml:id
="
echoid-s12575
"
xml:space
="
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">arcui Eclipticæ à principio ♈, vſque ad grad. </
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>
<
s
xml:id
="
echoid-s12576
"
xml:space
="
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">29. </
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>
<
s
xml:id
="
echoid-s12577
"
xml:space
="
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">♏, inchoato debita.</
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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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style
="
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<
s
xml:id
="
echoid-s12579
"
xml:space
="
preserve
">ALITER quoque eadem differentia B I, inter aſcenſionem rectam, & </
s
>
<
s
xml:id
="
echoid-s12580
"
xml:space
="
preserve
">obliquam inuenietur hac
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0211-06
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xlink:href
="
note-0211-06a
"
xml:space
="
preserve
">40</
note
>
<
note
position
="
right
"
xlink:label
="
note-0211-07
"
xlink:href
="
note-0211-07a
"
xml:space
="
preserve
">Quomodo ea-
<
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/>
dem differẽtia
<
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/>
inter aſcenſio-
<
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/>
nem rectam &
<
lb
/>
obliquam cu-
<
lb
/>
iuſuis puncti
<
lb
/>
Eclipticæ, ad da
<
lb
/>
tam latitudinẽ
<
lb
/>
loci aliter inue-
<
lb
/>
ſtigetur.</
note
>
ratione. </
s
>
<
s
xml:id
="
echoid-s12581
"
xml:space
="
preserve
">Quoniam in triangulo ſphęrico B E I, angulus I, rectus eſt, erit per propoſ. </
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>
<
s
xml:id
="
echoid-s12582
"
xml:space
="
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">19. </
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>
<
s
xml:id
="
echoid-s12583
"
xml:space
="
preserve
">lib. </
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>
<
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xml:id
="
echoid-s12584
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s12585
"
xml:space
="
preserve
">Ioan. </
s
>
<
s
xml:id
="
echoid-s12586
"
xml:space
="
preserve
">Re-
<
lb
/>
giom. </
s
>
<
s
xml:id
="
echoid-s12587
"
xml:space
="
preserve
">de triangulis, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s12588
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s12589
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s12590
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s12591
"
xml:space
="
preserve
">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s12592
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s12593
"
xml:space
="
preserve
">noſtrorum triangulorum ſphęrico-
<
lb
/>
rum, vt ſinus complementi arcus B E, latitudinis ortiuę, cuius inuentionem in priori diſcurſu propoſ. </
s
>
<
s
xml:id
="
echoid-s12594
"
xml:space
="
preserve
">34.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12595
"
xml:space
="
preserve
">pręcedentis libri tradidimus, ad ſinum complementi arcus E I, declinationis puncti Eclipticæ propoſiti,
<
lb
/>
ita ſinus complementi arcus B I, differentię quęſitæ ad ſinum totum: </
s
>
<
s
xml:id
="
echoid-s12596
"
xml:space
="
preserve
">Et conuertendo vt ſinus complemen
<
lb
/>
ti declinationis puncti Eclipticæ propoſiti ad ſinum complementi latitudinis ortiuæ eiuſdem puncti, ita
<
lb
/>
ſinus totus ad ſinum complementi differentiæ aſcenſionum. </
s
>
<
s
xml:id
="
echoid-s12597
"
xml:space
="
preserve
">Quamobrem ſi fiat, vt ſinus complementi de-
<
lb
/>
clinationis ad ſinum complementi latitudinis ortiuę, ita ſinus totus ad aliud, reperietur ſinus complemen-
<
lb
/>
ti differentię aſcenſionum quęſitę.</
s
>
<
s
xml:id
="
echoid-s12598
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s12599
"
xml:space
="
preserve
">QVONIAM autem declinationes omnium punctorum Eclipticę à principio ♈, vſque ad princi-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0211-08
"
xlink:href
="
note-0211-08a
"
xml:space
="
preserve
">50</
note
>
<
note
position
="
right
"
xlink:label
="
note-0211-09
"
xlink:href
="
note-0211-09a
"
xml:space
="
preserve
">Differentiæ a-
<
lb
/>
ſcenſionales pũ
<
lb
/>
ctorum prioris
<
lb
/>
quadrantis Ecli
<
lb
/>
pticæ ab A riet
<
unsure
/>
e
<
lb
/>
vſque ad Can-
<
lb
/>
crũ æquales sũt
<
lb
/>
differentijs aſcẽ
<
lb
/>
ſionalibus poſte
<
lb
/>
riorum trium
<
lb
/>
quadrantum
<
lb
/>
Eclipticæ.</
note
>
pium ♋, ęquales ſunt declinationibus omnium punctorum Eclipticę à principio ♎, vſque ad principium
<
lb
/>
♋, contra ſucceſſionem ſignorum progrediendo, ſingulę ſingulis, cum huiuſmodi puncta eoſdem parallelos
<
lb
/>
deſcribant, bina nimirum ſingulos: </
s
>
<
s
xml:id
="
echoid-s12600
"
xml:space
="
preserve
">Rurſus declinationes omnium punctorum Eclipticę ab ♈, vſque ad
<
lb
/>
♎, æquales ſunt declinationibus omnium punctorum Eclipticæ à ♎, vſque ad ♈, ſecundum ſignorum ſe-
<
lb
/>
riem procedendo, ſingulæ ſingulis, cum hæc puncta illis ſint oppoſita, ac proinde æquales parallelos deſcri-
<
lb
/>
bant: </
s
>
<
s
xml:id
="
echoid-s12601
"
xml:space
="
preserve
">Fit, vt declinationes prioris quadrantis Eclipticæ ab ♈, vſque ad ♋, ęquales ſint declinationibus
<
lb
/>
poſteriorum trium quadrantum, vt in tabula declinationum apparet. </
s
>
<
s
xml:id
="
echoid-s12602
"
xml:space
="
preserve
">Quare cum latitudines ortiuæ in-
<
lb
/>
ueſtigentur beneficio declinationum, & </
s
>
<
s
xml:id
="
echoid-s12603
"
xml:space
="
preserve
">altitudinis poli, vt ex propoſ. </
s
>
<
s
xml:id
="
echoid-s12604
"
xml:space
="
preserve
">34. </
s
>
<
s
xml:id
="
echoid-s12605
"
xml:space
="
preserve
">ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s12606
"
xml:space
="
preserve
">liquet, manife-
<
lb
/>
ſtum eſt, latitudines ortiuas punctorum prioris quadrantis Eclipticæ ad quamcunque latitudinem inuen-
<
lb
/>
tas, æquales eſſe latitudinibus ortiuis poſteriorum trium quadrantum in eadem latitudine. </
s
>
<
s
xml:id
="
echoid-s12607
"
xml:space
="
preserve
">Ac proinde
<
lb
/>
eum differentiæ inter aſcenſiones rectas, & </
s
>
<
s
xml:id
="
echoid-s12608
"
xml:space
="
preserve
">obliquas inquirantur, vt proximè demonſtrauimus, per </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>