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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gulo E k N, figuræ quintæ angulus E, rectus eſt, erit per propoſ. </
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>
<
s
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<
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<
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<
s
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">Ioan. </
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<
s
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">Regiom. </
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<
s
xml:id
="
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xml:space
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">de triangu
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lis, vel per Propoſ. </
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<
s
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xml:space
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">13. </
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<
s
xml:id
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xml:space
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<
s
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echoid-s8907
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xml:space
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">1. </
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<
s
xml:id
="
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"
xml:space
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">Gebri, vel per propoſ. </
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>
<
s
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="
echoid-s8909
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xml:space
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">41. </
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<
s
xml:id
="
echoid-s8910
"
xml:space
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">noſtrorum triangulorum ſphæricorum, vt
<
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ſinusarcus N k, complementi declinationis ad ſinum anguli recti E, id eſt, ad ſinum totum, ita ſi-
<
lb
/>
nus arcus E K, complementi altitudinis Solis ad ſinum anguli N, diſtantiæ Solis à meridie. </
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>
<
s
xml:id
="
echoid-s8911
"
xml:space
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">Itaque
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ſi fiat, vt ſinus complementi declinationis ad ſinum to@um, ita ſinus complementi altitudinis So-
<
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lis in Verticali circulo ad aliud, inueniet ur ſinus diſtantiæ Solis à meridie.</
s
>
<
s
xml:id
="
echoid-s8912
"
xml:space
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"/>
</
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<
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<
s
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echoid-s8913
"
xml:space
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">VNDE ſi quæratur, qua hora Sol in Verticali circulo reperiatur, inuenienda primum erit al-
<
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<
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xlink:label
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note-0158-01
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xlink:href
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xml:space
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">Qua hora Sol
<
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in Verticali cir
<
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culo exiſtat.</
note
>
titudo Solis in Verticali circulo, vt ſupra docuimus, etiamſi ignota ſit diſtantia Solis à meridie:
<
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</
s
>
<
s
xml:id
="
echoid-s8914
"
xml:space
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preserve
">Deinde ex hac altitudine exploranda diſtantia Solis à meridie, vt proxime oſtendimus.</
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>
<
s
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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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">SOLE in Aequatore exiſtente, facili etiam negotio ex altitudine Solis horam inquiremus.
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</
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>
<
s
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xml:space
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<
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position
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xlink:label
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note-0158-02
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xlink:href
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note-0158-02a
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xml:space
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">Hora qua via
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in æquinoctijs
<
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ex altiuidine
<
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Solis nota explo
<
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ianda.</
note
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<
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="
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xlink:label
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Quoniam enim in ſphærico triangulo E H K, quintæ figurę, ſi intelligatur Aequator eſſe G H I, & </
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Sol in K, vt ſupra diximus, angulus H, rectus eſt, erit per propoſ. </
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<
s
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="
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xml:space
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">19. </
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<
s
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xml:space
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">lib. </
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<
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">4. </
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<
s
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="
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xml:space
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">Ioan. </
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>
<
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="
echoid-s8923
"
xml:space
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">Regiom. </
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>
<
s
xml:id
="
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xml:space
="
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">de trian-
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gulis, vel per propoſ. </
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<
s
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="
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">15. </
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<
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xml:space
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">hb. </
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<
s
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xml:space
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">1. </
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>
<
s
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="
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xml:space
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">Gebri, vel per propoſ. </
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>
<
s
xml:id
="
echoid-s8929
"
xml:space
="
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">43. </
s
>
<
s
xml:id
="
echoid-s8930
"
xml:space
="
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">noſtrorum triangulorum ſphæricorum, vt
<
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/>
ſmus complementi arcus EH, altitudinis poli, ad ſinum totum, ita ſinus complementi arcus E K,
<
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/>
hoc eſt, ita ſinus arcus A K, altitudinis Solis, ad ſinum complementi arcus H K, diſtantię Solis à
<
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/>
meridie. </
s
>
<
s
xml:id
="
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xml:space
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">Quare ſi hat, vt ſinus complementi altitudinis poli ad ſinum totum, ita ſinus altitudinis
<
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Solis ad aliud, inuenietur ſinus complementi diſtantię Solis à meridie.</
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<
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</
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<
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<
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<
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xml:space
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">Quia enim in triangulo ſphærico A G K, angulus A,
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rectus eſt, per propoſ. </
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<
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">15. </
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<
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xml:space
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">lib. </
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>
<
s
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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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">Theodoſii, quòd circulus maximus E A, per polum Horizontis E,
<
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ductus ſit, erit per propoſ. </
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>
<
s
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="
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xml:space
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">16. </
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<
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">lib. </
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<
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<
s
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">Ioan. </
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<
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xml:space
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">Regiom. </
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>
<
s
xml:id
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"
xml:space
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">de triangulis, vel per propoſ. </
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<
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">13. </
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<
s
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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
xml:id
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xml:space
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">Gebri,
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<
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">20</
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vel per propoſ. </
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<
s
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xml:space
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">41. </
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<
s
xml:id
="
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xml:space
="
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">noſtrorum triangulorum ſphæricorum, vt ſinus anguli G, complementi altitu-
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dinis poli, (Si enim Aequator ponatur G H I, erit angulus G, reſpondens arcui H B, altitudinis
<
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Aequatoris, ſeu complementi altitudinis poli) ad ſinum arcus A k, altitudinis Solis, ita ſinus an-
<
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guli A, recti, id eſt, ita ſinus totus, ad ſinum arcus Gk, altitudinis Solis, ita ſinus an-
<
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Si igitur fiat, vt ſinus complementi altitudinis poli, ad ſinum altitudinis Solis, ita ſinus totusad
<
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aliud, notus fiet ſinus complementi diſtantiæ Solis à meridie.</
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>
<
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</
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<
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<
s
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xml:space
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">POSTREMO in ſphæra recta ita procedemus. </
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<
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xml:space
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">Sole exiſtente in æquinoctiis, accipiemus
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<
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xlink:label
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">Quo pacto in
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ſphæra recta rẽ-
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pore ęquinoctio
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rum reperienda
<
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ſit hora ex alti-
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dine Solis.</
note
>
<
figure
xlink:label
="
fig-0158-01
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xlink:href
="
fig-0158-01a
"
number
="
115
">
<
image
file
="
0158-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0158-01
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</
figure
>
cõplementum altitudinis Solis pro diſtantia eiuſdẽ
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à meridie. </
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>
<
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="
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xml:space
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">Nã in appoſita figura, quam pro ſphæra
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recta conſtruximus, arcus EI, diſtantiæ Solis à meri
<
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<
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="
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xlink:label
="
note-0158-06
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="
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">30</
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>
die, complementũ eſt arcus A I, altitudinis Solis.</
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<
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</
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<
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<
s
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xml:space
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">QVANDO verò Sol in aliquo alio parallelo
<
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<
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xlink:label
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">Qua ratione in
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ſphæra recta ſit
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indaganda ho-
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ra ex al titudine
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Solis in quocũ-
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que parallelo
<
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exiſtentis.</
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>
exiſtit, vt in K; </
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>
<
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="
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xml:space
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">quoniã in triangulo ſphærico E I K,
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angulus I, rectus eſt, erit per propoſ. </
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<
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="
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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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">lib. </
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>
<
s
xml:id
="
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xml:space
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">4. </
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>
<
s
xml:id
="
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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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">Regiom. </
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>
<
s
xml:id
="
echoid-s8963
"
xml:space
="
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">de triangulis, vel per propoſ. </
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>
<
s
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xml:space
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">15. </
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<
s
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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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">1. </
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>
<
s
xml:id
="
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xml:space
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">Ge-
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bri, vel per propoſ. </
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>
<
s
xml:id
="
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xml:space
="
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">43. </
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>
<
s
xml:id
="
echoid-s8969
"
xml:space
="
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">noſtrorum triangulorũ ſphæ
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ricorum, vt ſinus complemẽti arcus Ik, declinatio-
<
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/>
nis paralleli propoſiti, ad ſinum totum, ita ſinus cõ-
<
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/>
plementi arcus E K, hoc eſt, ita ſinus arcus K L, alti
<
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/>
tudinis Solis, ad ſinum complementi arcus E I, di-
<
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/>
<
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">40</
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ſtantiæ Solis à meridie. </
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>
<
s
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xml:space
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">Quamobrem ſi fiat, vt ſinus
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complementi declinationis Solis ad ſinum totum,
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/>
ita ſinus altitudinis Solis ad aliud, notus fiet ſinus
<
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cõplementi diſtantiæ Solis à meridie. </
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>
<
s
xml:id
="
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xml:space
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">Igitur ex co-
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gnita diei hora altitudinem Solis ſupra Horizontem: </
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>
<
s
xml:id
="
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xml:space
="
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">Et contra ex altitudine Solis nota horam dioi
<
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cognouimus. </
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>
<
s
xml:id
="
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xml:space
="
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">Quod erar faciendum.</
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>
<
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="
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</
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>
</
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type
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<
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style
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">SCHOLIVM.</
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<
s
xml:id
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xml:space
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">QVANDO inueniendæ ſunt altitudines Solis pro ſingulis horis duorum parallelorum oppoſito-
<
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<
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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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">50</
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>
rum, quales ſunt v. </
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>
<
s
xml:id
="
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xml:space
="
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">g. </
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>
<
s
xml:id
="
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"
xml:space
="
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">duo tropici à principijs ♋, & </
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>
<
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xml:id
="
echoid-s8978
"
xml:space
="
preserve
">♑, deſcripti, quod non rarò vſu venit in conſtruen-
<
lb
/>
dis inſtrumentis horarijs, & </
s
>
<
s
xml:id
="
echoid-s8979
"
xml:space
="
preserve
">in deſcriptionibus horologiorum, perfacile reddetur totum negotium, ſi ea,
<
lb
/>
quæ iamiam explicabimus, attentè conſiderentur.</
s
>
<
s
xml:id
="
echoid-s8980
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s8981
"
xml:space
="
preserve
">NAM ſi primo velimus modo vti, permanebit pro ſingulis horis vtriuſque paralleli eadem medietas
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0158-10
"
xlink:href
="
note-0158-10a
"
xml:space
="
preserve
">Qui numeti nõ
<
lb
/>
mutentur un-
<
lb
/>
quam, ſi per pri
<
lb
/>
mum modum
<
lb
/>
traditum inue-
<
lb
/>
ſtigentur altitu
<
lb
/>
dines S olis pro
<
lb
/>
ſingulis. horis
<
lb
/>
duorum paralle
<
lb
/>
lotum oppoſito
<
lb
/>
rum.</
note
>
rectæ compoſitæ ex ſinu altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s8982
"
xml:space
="
preserve
">ſinu depreſſionis meridianæ, ita vt ſemel inuenta huiuſ-
<
lb
/>
modi medietas adbibeatur ad omnium horarum altitudines perueſtigandas in duobus parallelis oppoſi-
<
lb
/>
tis. </
s
>
<
s
xml:id
="
echoid-s8983
"
xml:space
="
preserve
">Quia enim, vt in ſcholio antecedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s8984
"
xml:space
="
preserve
">oſtendimus, depreſſio meridiana cuiuſcunque paralleli
<
lb
/>
æqualis eſt altitudini meridianæ paralleli oppoſiti, fit vt recta compoſita ex ſinu altitudinis meridianæ, et
<
lb
/>
ſinu depreſſionis meridianæ vnius paralleli, ſit æqualis rectæ compoſitæ ex ſinu altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s8985
"
xml:space
="
preserve
">
<
lb
/>
ſinu depreſſionis meridianæ alterius paralleli oppoſiti, quandoquidem depreſſio meridiana illius æqualis
<
lb
/>
eſt altitudini meridianæ huius, & </
s
>
<
s
xml:id
="
echoid-s8986
"
xml:space
="
preserve
">huius meridiana depreſſio ęqualis illius altitudini meridianæ. </
s
>
<
s
xml:id
="
echoid-s8987
"
xml:space
="
preserve
">Vnde &</
s
>
<
s
xml:id
="
echoid-s8988
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>