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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GNOMONICES
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altitudinis Solis, & </
s
>
<
s
xml:id
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xml:space
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">differẽtia inter dictam medietatem, & </
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>
<
s
xml:id
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xml:space
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">ſinum altitudinis meridianę
<
unsure
/>
, ita ſinus
<
lb
/>
totus ad aliud, habebitur ſinus complementi diſtantię Solis à meridie, atq; </
s
>
<
s
xml:id
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xml:space
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">adeo & </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">ipſum comple
<
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/>
mentum diſtantię Solis à meridie notum erit, beneficio cuius diſtantiam Solis à meridie, ac proin
<
lb
/>
de & </
s
>
<
s
xml:id
="
echoid-s7908
"
xml:space
="
preserve
">horam tempore obſeruationis cognoſcemus hoc modo. </
s
>
<
s
xml:id
="
echoid-s7909
"
xml:space
="
preserve
">Quando Sol ſeptentrionalis eſt, & </
s
>
<
s
xml:id
="
echoid-s7910
"
xml:space
="
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">
<
lb
/>
ſinus altitudinis Solis ſuperat differentiam inter medietatem dictam, & </
s
>
<
s
xml:id
="
echoid-s7911
"
xml:space
="
preserve
">ſinum altitudinis meri-
<
lb
/>
dianę, vt in figura prima & </
s
>
<
s
xml:id
="
echoid-s7912
"
xml:space
="
preserve
">tertia apparet, ſubtrahatur complementum diſtautię Solis à meridie
<
lb
/>
inuentum ex quadrante, reman ebitq́; </
s
>
<
s
xml:id
="
echoid-s7913
"
xml:space
="
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">Solis diſtan
<
unsure
/>
tia à meridie, quo ad gradus.</
s
>
<
s
xml:id
="
echoid-s7914
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xml:space
="
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"/>
</
p
>
<
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>
<
s
xml:id
="
echoid-s7915
"
xml:space
="
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">QVOD ſi ſinus altitudinis Solis fuerit ęqualis differentię inter prędictam medietatem, & </
s
>
<
s
xml:id
="
echoid-s7916
"
xml:space
="
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">ſi-
<
lb
/>
num altitudinis meridianę, diſtabit Sol quadrante i
<
unsure
/>
ntegro, ſiue ſex horis à meridie, vt in tribus
<
lb
/>
figuris prioribus manifeſtum eſſe poteſt. </
s
>
<
s
xml:id
="
echoid-s7917
"
xml:space
="
preserve
">Si enim λ N, differentia inter K N, ſinum altitudinis
<
lb
/>
<
note
position
="
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xlink:label
="
note-0148-01
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xlink:href
="
note-0148-01a
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xml:space
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">10</
note
>
meridianæ, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">K λ, medietatem prædictam, ponatur ſinus altitudinis Solis, ita vt λ M, ſit por-
<
lb
/>
tio diametri paralleli Horizontis per Solem tranſeuntis, dabit quadrans K P, diſtantiam Solis
<
lb
/>
à meridie.</
s
>
<
s
xml:id
="
echoid-s7919
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7920
"
xml:space
="
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">SI vero Sole exiſtente boreali, ſinus altitudinis ſolis minor extiterit, quam differentia inter me
<
lb
/>
dietatem prędictam, & </
s
>
<
s
xml:id
="
echoid-s7921
"
xml:space
="
preserve
">ſinum altitudinis meridianæ, vt in ſecun da figura cõtingit, adiungatur cõ-
<
lb
/>
plementum diſtantię Solis à meridie inuentum quadranti, conflabiturq́; </
s
>
<
s
xml:id
="
echoid-s7922
"
xml:space
="
preserve
">diſtantia Solis à meri-
<
lb
/>
die, quo ad gradus.</
s
>
<
s
xml:id
="
echoid-s7923
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7924
"
xml:space
="
preserve
">SOLE deniq; </
s
>
<
s
xml:id
="
echoid-s7925
"
xml:space
="
preserve
">auſtrali exiſtente, complementum diſtantiæ Solis à meridie inuentum perpe-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0148-02
"
xlink:href
="
note-0148-02a
"
xml:space
="
preserve
">Qua ratione tẽ
<
lb
/>
pore æquinoctii
<
lb
/>
hora ex altitu-
<
lb
/>
dine Solis ſu-
<
lb
/>
pra Horizontẽ
<
lb
/>
cognita depre-
<
lb
/>
hendatur.</
note
>
tuo ex quadrante deducendum eſt, vt diſtantia Solis à meridie quoad gradus remaneat, vt ex figu-
<
lb
/>
ra quarta & </
s
>
<
s
xml:id
="
echoid-s7926
"
xml:space
="
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">quinta conſtat. </
s
>
<
s
xml:id
="
echoid-s7927
"
xml:space
="
preserve
">Nam ſi ex quadrante K P, ſubtrahatur O P, complementum diſtantiæ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0148-03
"
xlink:href
="
note-0148-03a
"
xml:space
="
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">20</
note
>
Solis à meridie, relinquetur K O, diſtantia Solis à meridie.</
s
>
<
s
xml:id
="
echoid-s7928
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xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7929
"
xml:space
="
preserve
">HANC autem diſtãtiam Solis à meridie ex altitudine Solis cognita facilius comperiemus,
<
lb
/>
Sole Æquatorem percurrente. </
s
>
<
s
xml:id
="
echoid-s7930
"
xml:space
="
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">Vt enim ex ſexta figura liquet, eſt vt H N, ſinus complementi alti-
<
lb
/>
<
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position
="
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"
xlink:label
="
note-0148-04
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xlink:href
="
note-0148-04a
"
xml:space
="
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">2. vel 4. ſexti</
note
>
tudinis poli ad T N, ſinum altitudinis Solis tempore obſeruationis, ita H E, ſinus totus ad R E, ſi-
<
lb
/>
num complementi diſtantiæ Solis à meridie. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Quapropter ſi fiat, vt ſinus complementi altitudi-
<
lb
/>
nis poli ad ſinum altitudinis Solis tempore obſeruationis inuentæ, ita ſinus totus ad aliud,
<
lb
/>
inuenietur ſinus complementi diſtantiæ Solis à meridie, ac proinde & </
s
>
<
s
xml:id
="
echoid-s7932
"
xml:space
="
preserve
">ipſamet diſtantia latere
<
lb
/>
non poterit.</
s
>
<
s
xml:id
="
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xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7934
"
xml:space
="
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">VNO exemplo rem explicemus. </
s
>
<
s
xml:id
="
echoid-s7935
"
xml:space
="
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">Ponamus Sole exiſtente in principio ♊, vel ♌ nos ante meri-
<
lb
/>
<
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position
="
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xlink:label
="
note-0148-05
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xlink:href
="
note-0148-05a
"
xml:space
="
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">Exemplum.</
note
>
diem inueniſſe altitudinem Solis grad, 43. </
s
>
<
s
xml:id
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echoid-s7936
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7937
"
xml:space
="
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">20. </
s
>
<
s
xml:id
="
echoid-s7938
"
xml:space
="
preserve
">ex quo exploranda ſit hora tempore illius ob-
<
lb
/>
<
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xlink:label
="
note-0148-06
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xlink:href
="
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"
xml:space
="
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">30</
note
>
ſeruationis. </
s
>
<
s
xml:id
="
echoid-s7939
"
xml:space
="
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">Fiat vt 69743. </
s
>
<
s
xml:id
="
echoid-s7940
"
xml:space
="
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">medietas rectæ cõpoſitæ ex ſinu altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s7941
"
xml:space
="
preserve
">ſinu depreſ-
<
lb
/>
ſionis meridianæ, ad 45519 differentiam inter ſinum altitudinis Solis, & </
s
>
<
s
xml:id
="
echoid-s7942
"
xml:space
="
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">inter differentiam præ-
<
lb
/>
dictæ medietatis, & </
s
>
<
s
xml:id
="
echoid-s7943
"
xml:space
="
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">ſinus altitudinis meridianæ, ita 100000. </
s
>
<
s
xml:id
="
echoid-s7944
"
xml:space
="
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">ſinus totus ad aliud. </
s
>
<
s
xml:id
="
echoid-s7945
"
xml:space
="
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">Prodibit enim
<
lb
/>
ſinus ferè hic 65267. </
s
>
<
s
xml:id
="
echoid-s7946
"
xml:space
="
preserve
">complementi diſtantiæ Solis à meridie, cuius arcus grad. </
s
>
<
s
xml:id
="
echoid-s7947
"
xml:space
="
preserve
">40. </
s
>
<
s
xml:id
="
echoid-s7948
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7949
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7950
"
xml:space
="
preserve
">ſubtra
<
lb
/>
tractus ex quadrante, (quia Sol borealis eſt, & </
s
>
<
s
xml:id
="
echoid-s7951
"
xml:space
="
preserve
">ſinus altitudinis Solis, nempe 68624. </
s
>
<
s
xml:id
="
echoid-s7952
"
xml:space
="
preserve
">ſuperat diffe-
<
lb
/>
rentiã, quæ inter medietatem ſæpius dictam, & </
s
>
<
s
xml:id
="
echoid-s7953
"
xml:space
="
preserve
">ſinum altitudinis meridianæ reperitur, nimirum
<
lb
/>
23105.) </
s
>
<
s
xml:id
="
echoid-s7954
"
xml:space
="
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">relinquet grad. </
s
>
<
s
xml:id
="
echoid-s7955
"
xml:space
="
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">49. </
s
>
<
s
xml:id
="
echoid-s7956
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7957
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s7958
"
xml:space
="
preserve
">pro diſtantia Solis à meridie, quæ complectitur horas 3.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7959
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7960
"
xml:space
="
preserve
">17. </
s
>
<
s
xml:id
="
echoid-s7961
"
xml:space
="
preserve
">Cum igitur obſeruatio fiat ante meridiem, inſtabit tunc hora 8. </
s
>
<
s
xml:id
="
echoid-s7962
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7963
"
xml:space
="
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">43. </
s
>
<
s
xml:id
="
echoid-s7964
"
xml:space
="
preserve
">poſt mediam
<
lb
/>
noctem, more Aſtronomorum. </
s
>
<
s
xml:id
="
echoid-s7965
"
xml:space
="
preserve
">Et ſi poſt meridiem facta eſſet obſeruatio, inſtaret hora 3. </
s
>
<
s
xml:id
="
echoid-s7966
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7967
"
xml:space
="
preserve
">17. </
s
>
<
s
xml:id
="
echoid-s7968
"
xml:space
="
preserve
">
<
lb
/>
à meridie. </
s
>
<
s
xml:id
="
echoid-s7969
"
xml:space
="
preserve
">At ſecundum Italos erit hora 13. </
s
>
<
s
xml:id
="
echoid-s7970
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7971
"
xml:space
="
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">26. </
s
>
<
s
xml:id
="
echoid-s7972
"
xml:space
="
preserve
">ab occaſu, quia illo die meridies fit hora 16. </
s
>
<
s
xml:id
="
echoid-s7973
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
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xlink:label
="
note-0148-07
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xlink:href
="
note-0148-07a
"
xml:space
="
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">40</
note
>
Min. </
s
>
<
s
xml:id
="
echoid-s7974
"
xml:space
="
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">43. </
s
>
<
s
xml:id
="
echoid-s7975
"
xml:space
="
preserve
">à quo meridie ſi auferatur diſtantia Solis à meridie proximè inuenta, nempe hor. </
s
>
<
s
xml:id
="
echoid-s7976
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s7977
"
xml:space
="
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">Min.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7978
"
xml:space
="
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">17. </
s
>
<
s
xml:id
="
echoid-s7979
"
xml:space
="
preserve
">remanebunt horæ 13. </
s
>
<
s
xml:id
="
echoid-s7980
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7981
"
xml:space
="
preserve
">26. </
s
>
<
s
xml:id
="
echoid-s7982
"
xml:space
="
preserve
">Si vero obſeruatio fieret poſt meridiem, addenda eſſet hęc di-
<
lb
/>
ſtantia, vt hora ab occaſu Solis nota euaderet. </
s
>
<
s
xml:id
="
echoid-s7983
"
xml:space
="
preserve
">Inueniretur autem hora 20. </
s
>
<
s
xml:id
="
echoid-s7984
"
xml:space
="
preserve
">ab occaſu. </
s
>
<
s
xml:id
="
echoid-s7985
"
xml:space
="
preserve
">Secundum
<
lb
/>
denique Babylonios erit hora 4. </
s
>
<
s
xml:id
="
echoid-s7986
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7987
"
xml:space
="
preserve
">o. </
s
>
<
s
xml:id
="
echoid-s7988
"
xml:space
="
preserve
">ab ortu Solis. </
s
>
<
s
xml:id
="
echoid-s7989
"
xml:space
="
preserve
">Cum enim illo die meridies fiat ſecundum
<
lb
/>
has horas, hora 7. </
s
>
<
s
xml:id
="
echoid-s7990
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7991
"
xml:space
="
preserve
">17. </
s
>
<
s
xml:id
="
echoid-s7992
"
xml:space
="
preserve
">ſi ex hoc meridiano tempore detrahatur diſtantia Solis à meridie in-
<
lb
/>
uenta, nempe hor. </
s
>
<
s
xml:id
="
echoid-s7993
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s7994
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7995
"
xml:space
="
preserve
">17. </
s
>
<
s
xml:id
="
echoid-s7996
"
xml:space
="
preserve
">remanet hora 4. </
s
>
<
s
xml:id
="
echoid-s7997
"
xml:space
="
preserve
">Quòd ſi obſeruatio poſt meridiem fieret, addenda
<
lb
/>
eſſet hęc diſtantia, atq; </
s
>
<
s
xml:id
="
echoid-s7998
"
xml:space
="
preserve
">ita inueniretur hora 10. </
s
>
<
s
xml:id
="
echoid-s7999
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8000
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s8001
"
xml:space
="
preserve
">ab ortu Solis. </
s
>
<
s
xml:id
="
echoid-s8002
"
xml:space
="
preserve
">Ex hoc exemplo cętera ſine
<
lb
/>
labore intelligentur.</
s
>
<
s
xml:id
="
echoid-s8003
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8004
"
xml:space
="
preserve
">IN Verticali ci@culo Sole exiſtente, ita quoque pręter artem hactenus traditam ex eius altitu-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0148-08
"
xlink:href
="
note-0148-08a
"
xml:space
="
preserve
">Hora quanta
<
lb
/>
ſit, cum @ol in
<
lb
/>
Verticali circu
<
lb
/>
lo @xiſtit, qua
<
lb
/>
ratione explorã
<
lb
/>
dum.</
note
>
dine horam offendemus. </
s
>
<
s
xml:id
="
echoid-s8005
"
xml:space
="
preserve
">Ducta in quarta figura ex puncto Z, vbi parallelus Solis Verticalẽ inter-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0148-09
"
xlink:href
="
note-0148-09a
"
xml:space
="
preserve
">50</
note
>
ſecat, ad V X, perpendiculari Z β, vſque ad circunferentiam paralleli Solis ex centro Y, deſcripti
<
lb
/>
circa diametrum V X, erit Z β, cõmunis ſectio paralleli Solis, & </
s
>
<
s
xml:id
="
echoid-s8006
"
xml:space
="
preserve
">paralleli Horizontis, cuius dia-
<
lb
/>
meter μ Z: </
s
>
<
s
xml:id
="
echoid-s8007
"
xml:space
="
preserve
">quod ita perſpicuũ fiet. </
s
>
<
s
xml:id
="
echoid-s8008
"
xml:space
="
preserve
">Quoniã vterq; </
s
>
<
s
xml:id
="
echoid-s8009
"
xml:space
="
preserve
">parallelus ad Meridianũ rectus eſt, erit & </
s
>
<
s
xml:id
="
echoid-s8010
"
xml:space
="
preserve
">eorũ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0148-10
"
xlink:href
="
note-0148-10a
"
xml:space
="
preserve
">19. vndec.</
note
>
cõmunis ſectio ad eandẽ recta, ac proinde per defin. </
s
>
<
s
xml:id
="
echoid-s8011
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s8012
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s8013
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s8014
"
xml:space
="
preserve
">Euclidis, ad V X, perpendicularis in
<
lb
/>
Z, puncto, vbi ſe mutuo ſecant dicti paralleli in Meridiano. </
s
>
<
s
xml:id
="
echoid-s8015
"
xml:space
="
preserve
">Igitur Z β, perpendicularis ad V X, in
<
lb
/>
Z, communis ſectio erit illorum parallelorum. </
s
>
<
s
xml:id
="
echoid-s8016
"
xml:space
="
preserve
">Ex quo ſequitur, cum Z, ſit centrum paralleli Ho
<
lb
/>
rizontis, cuius diameter μ Z, rectam Z β, ę
<
unsure
/>
qualem eſſe ſemidiametro μ Z, quan
<
unsure
/>
doquidem om-
<
lb
/>
nes lineæ ductæ ex Z, ad circunferentiam paralleli, cuius diameter μ Z, (qualis etiam eſt Z β,
<
lb
/>
communis eius ſectio cum parallelo Solis, vt oſtenſum eſt) ęquales ſunt ſemidiametro μ Z. </
s
>
<
s
xml:id
="
echoid-s8017
"
xml:space
="
preserve
">Quo-
<
lb
/>
niam verò μ Z, ſinus eſt complementi altitudinis Solis in Verticali circulo exiſtentis, nempe ſi-
<
lb
/>
nus arcus B μ, erit vt V Y, ſinus complementi declinationis paralleli V X, (quatenus </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>