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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421 - 432
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LIBER SEXTVS.
"/>
li, ita ſinus complementi diſtantiæ Solis à meridie ad aliud, inuenietur ſinus circunferentiæ hori-
<
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zontalis; </
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<
s
xml:id
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"
xml:space
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">atque adeo circunferentia horizontalis ignota non erit. </
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<
s
xml:id
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"
xml:space
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">Sed prior modus videtur eſſe
<
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commodior, cum vtatur ſinu toto, vt patet.</
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<
s
xml:id
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xml:space
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</
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<
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<
s
xml:id
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"
xml:space
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">RVRSVS, quia in triangulo B F G, angulus F, rectus eſt, erit per propoſ. </
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>
<
s
xml:id
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"
xml:space
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">19. </
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<
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xml:id
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xml:space
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">lib. </
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<
s
xml:id
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"
xml:space
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">4. </
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<
s
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xml:space
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">Ioan. </
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>
<
s
xml:id
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"
xml:space
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">Re-
<
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giom. </
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<
s
xml:id
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xml:space
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">de triang. </
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>
<
s
xml:id
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xml:space
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">vel per propoſ. </
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>
<
s
xml:id
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xml:space
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">15. </
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<
s
xml:id
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xml:space
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">lib. </
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<
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xml:space
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">1. </
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<
s
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xml:space
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">Gebri, vel per propoſ. </
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<
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xml:space
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<
s
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xml:space
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">noſtrorum triang. </
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<
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<
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">vt
<
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ſinus complementi arcus F G, diſtantiæ Solis à meridie ad ſinum totum, ita ſinus complementi
<
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/>
circunferentiæ horariæ B G, ad ſinum complementi arcus B F, hoc eſt, ad ſinum arcus E F, altitu
<
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/>
dinis poli: </
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<
s
xml:id
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"
xml:space
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">Et conuertendo, vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita ſi-
<
lb
/>
nus altitudinis poli ad ſinum complementi circunferentiæ horariæ. </
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>
<
s
xml:id
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xml:space
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">Quare ſi fiat, vt ſinus totus ad
<
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ſinum complementi diſtantiæ Solis à meridie, ita ſinus altitudinis poli ad aliud, reperietur ſinus
<
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<
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xlink:label
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xml:space
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xlink:label
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xml:space
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">Horatia.</
note
>
complementi circunferentię horariæ; </
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<
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xml:id
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xml:space
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">ac proinde hoc complementum, vna cum horaria circun-
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ferentia, notum erit.</
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<
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xml:space
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</
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<
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<
s
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xml:space
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">POSTREMO, quoniam in triangulo A G K, angulus K, rectus eſt, erit per propoſ. </
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<
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xml:space
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">19. </
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<
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xml:space
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">lib.
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</
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<
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">4. </
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<
s
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xml:space
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">Ioan. </
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>
<
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xml:space
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">Regiom. </
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>
<
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xml:space
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">de triang. </
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>
<
s
xml:id
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xml:space
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">vel per propoſ. </
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>
<
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xml:space
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">15. </
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>
<
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xml:space
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">lib. </
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<
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xml:space
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">1. </
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>
<
s
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xml:space
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">Gebri, vel per propoſ. </
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>
<
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xml:space
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">43. </
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>
<
s
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xml:space
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">noſtrorum triang. </
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<
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xml:space
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">
<
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ſphær. </
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<
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xml:space
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">vt ſinus complementi arcus A G, hoc eſt, vt ſinus arcus F G, diſtantiæ Solis à meridie, ad
<
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/>
ſinum complementi arcus G K, hoc eſt, ad ſinum circunferentiæ horariæ B G, ita ſinus comple-
<
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menti arcus A K, id eſt, ſinus circunferentiæ Verticalis E K, ad ſinum totum: </
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<
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xml:id
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xml:space
="
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">Et conuertendo, vt
<
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/>
ſinus horatię circunferentiæ ad ſinum diſtantiæ Solis à meridie, ita ſinus totus ad ſinum circun-
<
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/>
ferentiæ Verticalis. </
s
>
<
s
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xml:space
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">Quamobrem ſi fiat, vt ſinus circunferentiæ horariæ ad ſinum diſtantiæ Solis
<
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<
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">Verticalis.</
note
>
à meridie, ita ſinus totus ad aliud, inuenietur ſinus circunferentiæ Verticalis; </
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>
<
s
xml:id
="
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xml:space
="
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">ideoq́ue circunfe-
<
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<
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">20</
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>
rentia Verticalis nota erit.</
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<
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style
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">INVENTIO SVPRADICT ARVM SEX CIRCVNFEREN-
<
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tiarum in ſphæra recta tam Geometrice ex Analemmate, quàm per numeros
<
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/>
ex doctrina ſinuum, ſiue Sol exiſtat in Aequatore, ſiue in alio
<
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quouis parallelo. CAP. VIII.</
head
>
<
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<
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xml:space
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">ETSI omnia præcepta, quæ hactenus pro inueſtigandis dictis ſex circunferentijs tradidimus,
<
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<
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xlink:label
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xlink:href
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xml:space
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">Præcepta ſupe-
<
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riota accommo
<
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dantur etiam
<
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ſphærę obliquę,
<
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/>
quę polum an-
<
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/>
t
<
unsure
/>
a@cticum con-
<
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ſpicuum habet
<
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ſupra Horizon-
<
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tem.</
note
>
intelligenda ſunt in ſphæra obliqua, in qua polus arcticus ſupra Horizontem extollitur, cum
<
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de hac Ptolemæus ſolum loquatur in ſuo Analemmate: </
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>
<
s
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xml:space
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">eadem tamen locum etiam habent in il-
<
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<
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xlink:href
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">30</
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la ſphęrę obliquitate, vbi polus antarcticus ſupra Horizontem eſt eleuatus, ſi ea, quæ de paralle-
<
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lis borealibus, & </
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>
<
s
xml:id
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"
xml:space
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">polo arctico dicta ſunt, accommodentur parallelis auſtralibus, & </
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>
<
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xml:space
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">polo antarctico,
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& </
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>
<
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">contra. </
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>
<
s
xml:id
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"
xml:space
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">Immo vero eiſdem præceptis dictas ſex circunferentias indagabimus in ſphæra recta,
<
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& </
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>
<
s
xml:id
="
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xml:space
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">multo quidem facilius, quàm in obliqua. </
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>
<
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xml:id
="
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xml:space
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">Quod vt planius fiat; </
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>
<
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xml:id
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xml:space
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">Sit Meridianus A B C D, cu-
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ius centrum E; </
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>
<
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="
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">communis ſectio ipſius, & </
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>
<
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xml:id
="
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xml:space
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">Horizontis recti B D, quæ etiam axem mundi referet;
<
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</
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>
<
s
xml:id
="
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"
xml:space
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">communis ſectio eiuſdem, ac Verticalis, Aequatorisve (Æquator enim & </
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>
<
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xml:space
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">Verticalis in ſphęra re-
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<
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cta nõ differunt) recta A C,
<
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ſecans B D, ad angulos re-
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ctos; </
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<
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xml:space
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">communis ſectio deni
<
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que eiuſdẽ, & </
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>
<
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xml:space
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">paralleli ſiue
<
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<
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borealis, ſiue auſtralis a b,
<
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circa quam ſemicirculus
<
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a e b, deſcribatur. </
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>
<
s
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xml:space
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">Quòd
<
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ſi ſemicirculus A B C, circa
<
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A C, moueri intelligatur,
<
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donec rectus ſit ad Meridia-
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num, repræſentabit is ſemi-
<
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circulum Æquatoris orien-
<
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talem, occidentalemve, ita
<
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vt E B, ſit communis ſectio
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<
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Æquatoris, & </
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<
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">Horizontis
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recti, & </
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<
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xml:id
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xml:space
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">A B, portio Æquato
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ris ſupra terram, & </
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<
s
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xml:space
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<
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tio infra terram, vt ſupra in
<
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ſphęra obliqua oſtẽdimus.
<
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</
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<
s
xml:id
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xml:space
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">Diuiſio Aequatoris in ho-
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ras inchoanda eſt à puncto
<
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A, vel B, ita vt in A, ſtatua-
<
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tur hora 12. </
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>
<
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xml:id
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xml:space
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">à med. </
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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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">in B, hora 6. </
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<
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xml:space
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">à mer. </
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>
<
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xml:id
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xml:space
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">vel med. </
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<
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xml:id
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xml:space
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">noc. </
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>
<
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xml:id
="
echoid-s36103
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xml:space
="
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">Item in A, hora 6. </
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>
<
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xml:space
="
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">ab or. </
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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:id
="
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">18. </
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>
<
s
xml:id
="
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">ab occ. </
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<
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& </
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<
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xml:space
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">6. </
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>
<
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="
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xml:space
="
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">inæqualis: </
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>
<
s
xml:id
="
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xml:space
="
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">In puncto autem B, hora 12. </
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>
<
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xml:space
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">& </
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<
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xml:id
="
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xml:space
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">24. </
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>
<
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">ab or. </
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>
<
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="
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xml:space
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">Item 24. </
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>
<
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xml:space
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">& </
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<
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">12. </
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>
<
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xml:id
="
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"
xml:space
="
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">ab occ. </
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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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">12. </
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<
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xml:space
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">inæqualis. </
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<
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<
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Eodem modo erit d c, ad a b, perpendicularis, hoc eſt, d B, producta, communis ſectio </
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