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.
"/>
ordinatim applicatæ ex dictis punctis tropicorum ſint ad diametrum, perpendiculares) deſcripta
<
lb
/>
erunt aſcendentia ſigna.</
s
>
<
s
xml:id
="
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xml:space
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</
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>
<
p
>
<
s
xml:id
="
echoid-s11848
"
xml:space
="
preserve
">ALITER deſcribentur aſcendentia ſigna hoc pacto. </
s
>
<
s
xml:id
="
echoid-s11849
"
xml:space
="
preserve
">Primum quęrantur puncta Eclipticæ in
<
lb
/>
circulo Meridiano exiſtentia, hoc eſt, mediationes cœli, cum principia ſignorum Zodiaci oriun-
<
lb
/>
tur, & </
s
>
<
s
xml:id
="
echoid-s11850
"
xml:space
="
preserve
">eorundem punctorum declinationes. </
s
>
<
s
xml:id
="
echoid-s11851
"
xml:space
="
preserve
">Deindeiiſdem ſignorum initiis aſcen dentibus, inue-
<
lb
/>
ſtigentur puncta Eclipticæ in circulo horæ 6. </
s
>
<
s
xml:id
="
echoid-s11852
"
xml:space
="
preserve
">à meridie, vel media nocte conſtituta, vna cum eo-
<
lb
/>
rundem declinationibus. </
s
>
<
s
xml:id
="
echoid-s11853
"
xml:space
="
preserve
">Quæ omnia ita abſoluemus. </
s
>
<
s
xml:id
="
echoid-s11854
"
xml:space
="
preserve
">Ex aſcenſione obliqua principii cuiusli-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0201-01
"
xlink:href
="
note-0201-01a
"
xml:space
="
preserve
">Quomodo me-
<
lb
/>
diationes cœli,
<
lb
/>
cũ initia ſigno-
<
lb
/>
rum oriuntur,
<
lb
/>
inue ſtigandę
<
lb
/>
ſint.</
note
>
bet ſigni (quę vel ex tabulis aſcenſionum obliquarum, quæ in tabulis Directionum Ioan. </
s
>
<
s
xml:id
="
echoid-s11855
"
xml:space
="
preserve
">Regiom.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s11856
"
xml:space
="
preserve
">vel in commentariis noſtris in ſphæram continentur, ſumenda eſt, vel certè ex doctrina ſinuum, vt
<
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/>
in cap. </
s
>
<
s
xml:id
="
echoid-s11857
"
xml:space
="
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">3. </
s
>
<
s
xml:id
="
echoid-s11858
"
xml:space
="
preserve
">ſphęræ præcepimus, & </
s
>
<
s
xml:id
="
echoid-s11859
"
xml:space
="
preserve
">ad finem ſcholii huius propoſ. </
s
>
<
s
xml:id
="
echoid-s11860
"
xml:space
="
preserve
">oſtendemus, eruenda) quadrans
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0201-02
"
xlink:href
="
note-0201-02a
"
xml:space
="
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">10</
note
>
circuli auferatur, hoceſt, grad. </
s
>
<
s
xml:id
="
echoid-s11861
"
xml:space
="
preserve
">90. </
s
>
<
s
xml:id
="
echoid-s11862
"
xml:space
="
preserve
">adiecto prius integro circulo ad aſcenſionem obliquam, ſi de-
<
lb
/>
tractio fieri nequit, vt in calculo Aſtronomico ſieri ſolet. </
s
>
<
s
xml:id
="
echoid-s11863
"
xml:space
="
preserve
">Numerus en im reliquus erit aſcenſio
<
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/>
recta puncti Eclipticæ, quod tunc in Meridiano ſupra Horizontem reperitur, quodq́; </
s
>
<
s
xml:id
="
echoid-s11864
"
xml:space
="
preserve
">Mediatio-
<
lb
/>
nem cœli dicunt Aſtronomi. </
s
>
<
s
xml:id
="
echoid-s11865
"
xml:space
="
preserve
">Quare ex tabula aſcenſionum rectarum, vel ex doctrina, quam in
<
lb
/>
ſcholio ſequenti trademus, punctum illud Eclipticæ notum fiet, cuius punctum oppoſitum in eo-
<
lb
/>
dem Meridiano exiſter infra Horizontem, quod angulum terræ dicere poſſumus cum Aſtrono-
<
lb
/>
mis. </
s
>
<
s
xml:id
="
echoid-s11866
"
xml:space
="
preserve
">Huius operationis demonſtratio difficilis non eſt, ſi poſitio Horizontis, Meridiani, Zodiaci,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s11867
"
xml:space
="
preserve
">Æ quatoris in ſphæra rectè concipiatur. </
s
>
<
s
xml:id
="
echoid-s11868
"
xml:space
="
preserve
">Nam quando aſcenſio obliqua maior fuerit quadran-
<
lb
/>
te, vel quadranti æqualis, perſpicuum eſt, ſi quadransÆ quatoris inter orientem, & </
s
>
<
s
xml:id
="
echoid-s11869
"
xml:space
="
preserve
">meridiem poſi-
<
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/>
tus ex ea auferatur, relinqui aſcenſionem rectam puncti Eclipticæ cœlum mediantis, nempe di-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0201-03
"
xlink:href
="
note-0201-03a
"
xml:space
="
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">20</
note
>
ſtantiam principii ♈, à Meridiano circulo ſecundum ſignorum ſucceſſionem: </
s
>
<
s
xml:id
="
echoid-s11870
"
xml:space
="
preserve
">Quando vero aſcẽ-
<
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/>
ſio obliqua quadrante fuerit minor, liquido etiam conſtat, ſi quadrans Aequatoris inter orien-
<
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/>
tem, & </
s
>
<
s
xml:id
="
echoid-s11871
"
xml:space
="
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">meridiem conſtitutus ab integro circulo dematur, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">reliquis tribus quadrantibus aſcen-
<
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/>
ſio obliqua apponatur, (quod perinde eſt, ac ſi quadrans ab aggregato, quod ex aſcenſione obli-
<
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/>
qua, & </
s
>
<
s
xml:id
="
echoid-s11873
"
xml:space
="
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">circulo integro fit, detrahatur) conflari aſcenſionem rectam puncti Eclipticæ cœlum me-
<
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diantis. </
s
>
<
s
xml:id
="
echoid-s11874
"
xml:space
="
preserve
">In ſphæra quoquerecta eadem operatio locum habet, ſi loco aſcenſionis obliquæ aſcen-
<
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/>
dentis ſigni accipiatur aſcenſio recta eiuſdem.</
s
>
<
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xml:id
="
echoid-s11875
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</
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>
<
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>
<
s
xml:id
="
echoid-s11876
"
xml:space
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">EXEMPLVM. </
s
>
<
s
xml:id
="
echoid-s11877
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xml:space
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">Ad latitudinem grad. </
s
>
<
s
xml:id
="
echoid-s11878
"
xml:space
="
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">42. </
s
>
<
s
xml:id
="
echoid-s11879
"
xml:space
="
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">qualis ferè eſt Romæ, aſcenſio obliqua prine
<
unsure
/>
i-
<
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/>
<
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position
="
right
"
xlink:label
="
note-0201-04
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xlink:href
="
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xml:space
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">Exemplum.</
note
>
pii ♍, eſt grad. </
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>
<
s
xml:id
="
echoid-s11880
"
xml:space
="
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">141. </
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>
<
s
xml:id
="
echoid-s11881
"
xml:space
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">Min. </
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>
<
s
xml:id
="
echoid-s11882
"
xml:space
="
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">33. </
s
>
<
s
xml:id
="
echoid-s11883
"
xml:space
="
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">ex qua ſi dematur quadrans, hoc eſt, grad. </
s
>
<
s
xml:id
="
echoid-s11884
"
xml:space
="
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">90. </
s
>
<
s
xml:id
="
echoid-s11885
"
xml:space
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">remanent grad. </
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>
<
s
xml:id
="
echoid-s11886
"
xml:space
="
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">51.
<
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</
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>
<
s
xml:id
="
echoid-s11887
"
xml:space
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">Min. </
s
>
<
s
xml:id
="
echoid-s11888
"
xml:space
="
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">33. </
s
>
<
s
xml:id
="
echoid-s11889
"
xml:space
="
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">pro aſcenſione recta puncti Eclipticæ cœlum mediantis, cum principium ♍, oritur. </
s
>
<
s
xml:id
="
echoid-s11890
"
xml:space
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">
<
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/>
<
note
position
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xlink:label
="
note-0201-05
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xlink:href
="
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xml:space
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">30</
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>
Huic autem aſcenſioni rectæ reſpondet in tabula aſcenſionum rectarum (adhibita tamen parte
<
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proportionali, vt fieri conſuea
<
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/>
it, quando numerus non præcisè in tabula aliqua continetur)
<
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/>
gradus 23. </
s
>
<
s
xml:id
="
echoid-s11891
"
xml:space
="
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">Min. </
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>
<
s
xml:id
="
echoid-s11892
"
xml:space
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">57. </
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>
<
s
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="
echoid-s11893
"
xml:space
="
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">♉. </
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>
<
s
xml:id
="
echoid-s11894
"
xml:space
="
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">Hoc ergo punctum Eclipticæ in Meridiano tunc reperietur ſupra Ho-
<
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rizontem, infra vero Horizontem in eodem Meridiano exiſtet gradus 23. </
s
>
<
s
xml:id
="
echoid-s11895
"
xml:space
="
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">Min. </
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>
<
s
xml:id
="
echoid-s11896
"
xml:space
="
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">57. </
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>
<
s
xml:id
="
echoid-s11897
"
xml:space
="
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">♏. </
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>
<
s
xml:id
="
echoid-s11898
"
xml:space
="
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">Rurſus
<
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/>
obliqua aſcenſio principii ♋, continet grad. </
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>
<
s
xml:id
="
echoid-s11899
"
xml:space
="
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">66. </
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>
<
s
xml:id
="
echoid-s11900
"
xml:space
="
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">Min. </
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>
<
s
xml:id
="
echoid-s11901
"
xml:space
="
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">57. </
s
>
<
s
xml:id
="
echoid-s11902
"
xml:space
="
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">Cui ſi addatur integer circulus, hoc
<
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/>
eſt, grad. </
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>
<
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xml:id
="
echoid-s11903
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xml:space
="
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">360. </
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>
<
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xml:id
="
echoid-s11904
"
xml:space
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">fiunt grad. </
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>
<
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="
echoid-s11905
"
xml:space
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">426. </
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>
<
s
xml:id
="
echoid-s11906
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xml:space
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">Min. </
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>
<
s
xml:id
="
echoid-s11907
"
xml:space
="
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">57. </
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>
<
s
xml:id
="
echoid-s11908
"
xml:space
="
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">à quibus ſi deducantur grad. </
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>
<
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="
echoid-s11909
"
xml:space
="
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">90. </
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>
<
s
xml:id
="
echoid-s11910
"
xml:space
="
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">relinquuntur grad. </
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>
<
s
xml:id
="
echoid-s11911
"
xml:space
="
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">336.
<
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</
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>
<
s
xml:id
="
echoid-s11912
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s11913
"
xml:space
="
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">57. </
s
>
<
s
xml:id
="
echoid-s11914
"
xml:space
="
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">pro aſcenſione recta puncti Eclipticæ mediantis tunc cœlum, cum initium ♋, aſcendit
<
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/>
ſupra Horizontem. </
s
>
<
s
xml:id
="
echoid-s11915
"
xml:space
="
preserve
">Huic rectæ aſcenſioni reſpondet in tabula aſcenſionum rectarum gradus
<
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5. </
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>
<
s
xml:id
="
echoid-s11916
"
xml:space
="
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">Min. </
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>
<
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xml:id
="
echoid-s11917
"
xml:space
="
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">6. </
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>
<
s
xml:id
="
echoid-s11918
"
xml:space
="
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">♓. </
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>
<
s
xml:id
="
echoid-s11919
"
xml:space
="
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">Quare hoc punctum eo tempore in Meridiano ſupra Horizontem exiſtet, angulus
<
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/>
autem terræ erit gradus 5. </
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>
<
s
xml:id
="
echoid-s11920
"
xml:space
="
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">
<
emph
style
="
sc
">M</
emph
>
in. </
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>
<
s
xml:id
="
echoid-s11921
"
xml:space
="
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">6. </
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>
<
s
xml:id
="
echoid-s11922
"
xml:space
="
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">♍. </
s
>
<
s
xml:id
="
echoid-s11923
"
xml:space
="
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">Poſtremo in ſphera recta, (vt de hac exemplum etiam af-
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0201-06
"
xlink:href
="
note-0201-06a
"
xml:space
="
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">40</
note
>
feramus) aſcenſio recta ♐, complectitur grad. </
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>
<
s
xml:id
="
echoid-s11924
"
xml:space
="
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">237. </
s
>
<
s
xml:id
="
echoid-s11925
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s11926
"
xml:space
="
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">48. </
s
>
<
s
xml:id
="
echoid-s11927
"
xml:space
="
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">Ex hac dempto quadrante, ſuper-
<
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/>
ſunt grad. </
s
>
<
s
xml:id
="
echoid-s11928
"
xml:space
="
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">147. </
s
>
<
s
xml:id
="
echoid-s11929
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s11930
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s11931
"
xml:space
="
preserve
">pro aſcenſione recta illius puncti Eclipticæ, quod tunc cœlum mediat.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s11932
"
xml:space
="
preserve
">Cui aſcenſioni conuenit gradus 25. </
s
>
<
s
xml:id
="
echoid-s11933
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s11934
"
xml:space
="
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">31. </
s
>
<
s
xml:id
="
echoid-s11935
"
xml:space
="
preserve
">♌, atque hoc punctum tuncin Meridiano exiſtet
<
lb
/>
ſupra Horizontem, & </
s
>
<
s
xml:id
="
echoid-s11936
"
xml:space
="
preserve
">in angulo propterea terræ erit gradus 25. </
s
>
<
s
xml:id
="
echoid-s11937
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s11938
"
xml:space
="
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">31. </
s
>
<
s
xml:id
="
echoid-s11939
"
xml:space
="
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">♒. </
s
>
<
s
xml:id
="
echoid-s11940
"
xml:space
="
preserve
">Hac arte compo-
<
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/>
ſuimus ſequentem tabellam mediationum cœli, & </
s
>
<
s
xml:id
="
echoid-s11941
"
xml:space
="
preserve
">angulorum terræ, oriente principio cuiuſuis
<
lb
/>
ſigni Zodiaci, ad latitudinem grad. </
s
>
<
s
xml:id
="
echoid-s11942
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s11943
"
xml:space
="
preserve
">in qua etiam adſcripſimus earundem mediationum, & </
s
>
<
s
xml:id
="
echoid-s11944
"
xml:space
="
preserve
">
<
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angulorum terræ declinationes per doctrinam ſinuum inuentas, vt in coroll. </
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<
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<
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<
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dentis libri tradidimus, licet eædem ex tabula declinationum, habita ratione partis proportiona-
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lis, elici poſſint. </
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<
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">Perſpicuum autem eſt, declinationes punctorum ſeptentrionalium Eclipticæ
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eſſe ſeptentrionales, auſtralium verò auſtrales. </
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<
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">Vnde facile iudicabis, quorumnam puncto-
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rum declinatio in dicta tabula ſit borealis, & </
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<
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<
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">quod quidem noſſe, magni re-
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fert, vt ſigna aſcendentia deſcribantur.</
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<
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">VI. Mediationes cœli, & anguli terræ, eorumq́; declinationes, orientibus 12.
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ſignorum Zodiaci initiis, ad latitudinem grad. 42.</
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Signa aſcen- # ♈ # ♉ # ♊ # ♋ # dentia
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Gradus & # G. M. # G. M. # G. M. # G. M. # Minuta
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Mediationes # 0. 0. ♑. # 15. 59. ♑. # 6. 3. ♒. # 5. 6. ♓. # cœli
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Anguli # 0. 0. ♋ # 15. 59. ♋. # 6. 3. ♌. # 5. 6. ♍. # terræ
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Declina- # 23. 30. # 22. 32. # 18. 48. # 9. 40. # tiones
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