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
"/>
ſinus cõplementi arcus I F, declinationis paralleli propoſiti ad ſinũ totum, ita ſinus cõplementiar-
<
lb
/>
cus BF, latitudinis ortiuæ, occiduęve proximè inuentæ ad ſinũ cõplemẽti arcus B I, hoc eſt, ad ſinũ
<
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arcus ſemidiurni I E, in parallelo aultrali, vel arcus ſeminocturni in parallelo boreali. </
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>
<
s
xml:id
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xml:space
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">Nam arcus
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<
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number
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98
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<
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file
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0136-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0136-01
"/>
</
figure
>
Aequatoris inter I, & </
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>
<
s
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="
echoid-s6973
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xml:space
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">Meridianum ſub Horizonte
<
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complementũ eſt arcus B I, in triangulo boreali, cũ
<
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arcus Aequatoris ex B, per I, vſque ad Meridianum
<
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/>
infra Horizontem porrectus ſit quadrans. </
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>
<
s
xml:id
="
echoid-s6974
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xml:space
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">Igitur
<
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ſi fiat, vt ſinus complementi declinationis propoſi-
<
lb
/>
ti paralleli ad ſinum totum, ita ſinus compleinen-
<
lb
/>
ti latitudinis ortiuæ proxime inuentæ in priori di-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0136-01
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xlink:href
="
note-0136-01a
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xml:space
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">10</
note
>
ſcurſu, ad aliud, inuenietur ſinus arcus ſemidiur-
<
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ni auſtralis, vel ſeminocturni borealis. </
s
>
<
s
xml:id
="
echoid-s6975
"
xml:space
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">Dempto au-
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tem arcu ſeminocturno boreali ex ſemicirculo Ae-
<
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/>
quatoris, qui inter Meridianum ſupra, & </
s
>
<
s
xml:id
="
echoid-s6976
"
xml:space
="
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">infra Ho-
<
lb
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rizontem interijcitur, re@iquus erit arcus diurnus
<
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borealis I B E.</
s
>
<
s
xml:id
="
echoid-s6977
"
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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">PONATVR exempli gratia inquirendus ar-
<
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<
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left
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xlink:label
="
note-0136-02
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xlink:href
="
note-0136-02a
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xml:space
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">Exemplum.</
note
>
cus ſemidiurnus ad latitudinem grad. </
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>
<
s
xml:id
="
echoid-s6979
"
xml:space
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">42. </
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>
<
s
xml:id
="
echoid-s6980
"
xml:space
="
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">Sole exi-
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ſtente in principio ♊, vel ♐, vbi declinationem
<
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habet grad. </
s
>
<
s
xml:id
="
echoid-s6981
"
xml:space
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">20. </
s
>
<
s
xml:id
="
echoid-s6982
"
xml:space
="
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">Min. </
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>
<
s
xml:id
="
echoid-s6983
"
xml:space
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">12. </
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>
<
s
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="
echoid-s6984
"
xml:space
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">Fiat vt 74314. </
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>
<
s
xml:id
="
echoid-s6985
"
xml:space
="
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">ſinus com
<
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/>
<
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="
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xlink:label
="
note-0136-03
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xlink:href
="
note-0136-03a
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xml:space
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">20</
note
>
plementi altitudinis poli, ad 34529. </
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>
<
s
xml:id
="
echoid-s6986
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xml:space
="
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">ſinũ declinationis paralleli ♊, vel ♐, ita 100000. </
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>
<
s
xml:id
="
echoid-s6987
"
xml:space
="
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">ſinus to-
<
lb
/>
tus ad aliud, inuenieturq́ hic ferè ſinus 46464. </
s
>
<
s
xml:id
="
echoid-s6988
"
xml:space
="
preserve
">cuius arcus grad. </
s
>
<
s
xml:id
="
echoid-s6989
"
xml:space
="
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">27. </
s
>
<
s
xml:id
="
echoid-s6990
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s6991
"
xml:space
="
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">41. </
s
>
<
s
xml:id
="
echoid-s6992
"
xml:space
="
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">dabit latitudinem
<
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/>
ortiuam, occiduamve, borealem quidem paralleli ♊, auſtralem verò paralleli ♐. </
s
>
<
s
xml:id
="
echoid-s6993
"
xml:space
="
preserve
">Rurſus fiat, vt
<
lb
/>
93849. </
s
>
<
s
xml:id
="
echoid-s6994
"
xml:space
="
preserve
">ſinus complementi declinationis eiuſdem paralleli ♊, vel ♐, ad 100000, ſinum totum,
<
lb
/>
ita 88552. </
s
>
<
s
xml:id
="
echoid-s6995
"
xml:space
="
preserve
">ſinus complementi latitudinis ortiuæ proximè inuentæ ad aliud, conſurgetq́; </
s
>
<
s
xml:id
="
echoid-s6996
"
xml:space
="
preserve
">quaſi hic
<
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ſinus 94355. </
s
>
<
s
xml:id
="
echoid-s6997
"
xml:space
="
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">cuius arcus grad. </
s
>
<
s
xml:id
="
echoid-s6998
"
xml:space
="
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">70. </
s
>
<
s
xml:id
="
echoid-s6999
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7000
"
xml:space
="
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">39. </
s
>
<
s
xml:id
="
echoid-s7001
"
xml:space
="
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">exhibebit arcum ſemidiurnum paralleli ♐, & </
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>
<
s
xml:id
="
echoid-s7002
"
xml:space
="
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">ſemi-
<
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nocturnum paralleli ♊, quo dempto ex ſemicirculo, id eſt, ex grad. </
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>
<
s
xml:id
="
echoid-s7003
"
xml:space
="
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">180. </
s
>
<
s
xml:id
="
echoid-s7004
"
xml:space
="
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">reliquus erit arcus ſemi-
<
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/>
diurnus paralleli ♊, grad. </
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>
<
s
xml:id
="
echoid-s7005
"
xml:space
="
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">109. </
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>
<
s
xml:id
="
echoid-s7006
"
xml:space
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">Min. </
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<
s
xml:id
="
echoid-s7007
"
xml:space
="
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">21. </
s
>
<
s
xml:id
="
echoid-s7008
"
xml:space
="
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">Quòd ſi gradus horum arcuum reducantur ad horas, tri
<
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/>
buendo ſingulis horis grad. </
s
>
<
s
xml:id
="
echoid-s7009
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xml:space
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">15. </
s
>
<
s
xml:id
="
echoid-s7010
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s7011
"
xml:space
="
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">quaternis minutis horæ ſingulos gradus, continebit arcus ſemi-
<
lb
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diurnus paralleli ♐, Hor. </
s
>
<
s
xml:id
="
echoid-s7012
"
xml:space
="
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">4. </
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>
<
s
xml:id
="
echoid-s7013
"
xml:space
="
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">Min. </
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>
<
s
xml:id
="
echoid-s7014
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xml:space
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">43. </
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<
s
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="
echoid-s7015
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xml:space
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">paralleli autem ♊, Hor. </
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<
s
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echoid-s7016
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xml:space
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">7. </
s
>
<
s
xml:id
="
echoid-s7017
"
xml:space
="
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">Min. </
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>
<
s
xml:id
="
echoid-s7018
"
xml:space
="
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">17. </
s
>
<
s
xml:id
="
echoid-s7019
"
xml:space
="
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">paulo amplius. </
s
>
<
s
xml:id
="
echoid-s7020
"
xml:space
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">Si au-
<
lb
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<
note
position
="
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xlink:label
="
note-0136-04
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xlink:href
="
note-0136-04a
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xml:space
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tem eoſdem arcus ſemidiutnos duplicemus, habebimus totos arcus diurnos, nempe arcum diur-
<
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num paralleli ♐, grad. </
s
>
<
s
xml:id
="
echoid-s7021
"
xml:space
="
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">141. </
s
>
<
s
xml:id
="
echoid-s7022
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7023
"
xml:space
="
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">18. </
s
>
<
s
xml:id
="
echoid-s7024
"
xml:space
="
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">vel Hor. </
s
>
<
s
xml:id
="
echoid-s7025
"
xml:space
="
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">9. </
s
>
<
s
xml:id
="
echoid-s7026
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7027
"
xml:space
="
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">26. </
s
>
<
s
xml:id
="
echoid-s7028
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s7029
"
xml:space
="
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">arcum diurnum paralleli ♊, grad.
<
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</
s
>
<
s
xml:id
="
echoid-s7030
"
xml:space
="
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">21 8, Min. </
s
>
<
s
xml:id
="
echoid-s7031
"
xml:space
="
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">42. </
s
>
<
s
xml:id
="
echoid-s7032
"
xml:space
="
preserve
">vel Hor. </
s
>
<
s
xml:id
="
echoid-s7033
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s7034
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7035
"
xml:space
="
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">35. </
s
>
<
s
xml:id
="
echoid-s7036
"
xml:space
="
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">paulo minus.</
s
>
<
s
xml:id
="
echoid-s7037
"
xml:space
="
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"/>
</
p
>
<
note
position
="
left
"
xml:space
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">Arcus ſemidiur
<
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/>
nus, qua ratio-
<
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ne aliter inue-
<
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/>
ſtigetur per triã
<
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gula ſphærica.</
note
>
<
p
>
<
s
xml:id
="
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xml:space
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">POSSVMVS autem arcum ſemidiurnum cuiuſuis paralleli per eadem triangula ſphærica
<
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inuenire etiam hoc modo. </
s
>
<
s
xml:id
="
echoid-s7039
"
xml:space
="
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">Quoniam in triangulo ſphærico C F H, angulus C, rectus eſt, erit per
<
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propoſ. </
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<
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xml:space
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">16 lib. </
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>
<
s
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xml:space
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">4. </
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>
<
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="
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xml:space
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">Ioan. </
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>
<
s
xml:id
="
echoid-s7043
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xml:space
="
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">Regiom. </
s
>
<
s
xml:id
="
echoid-s7044
"
xml:space
="
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">de triangulis, vel per propoſ. </
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>
<
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xml:id
="
echoid-s7045
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xml:space
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">13 lib. </
s
>
<
s
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="
echoid-s7046
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xml:space
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">1. </
s
>
<
s
xml:id
="
echoid-s7047
"
xml:space
="
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">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s7048
"
xml:space
="
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">41.
<
lb
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</
s
>
<
s
xml:id
="
echoid-s7049
"
xml:space
="
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">noſtrorum triangulorum ſphæricorum, vt ſinus arcus F H, complementi declinationis paralleli
<
lb
/>
propoſiti (Nam F H, in parallelo boreali complementum eſt declinationis F I, in auſtrali verò
<
lb
/>
arcus F H, eundem ſinum habet, quem complementum arcus F I, declinationis cum eo ſemicir-
<
lb
/>
culum conſtituens, quod quidem complementum interijcitur inter F, & </
s
>
<
s
xml:id
="
echoid-s7050
"
xml:space
="
preserve
">alterum polum, cum ar-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0136-06
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xlink:href
="
note-0136-06a
"
xml:space
="
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">40</
note
>
cus ex I, per F, vſque ad alterum polum tendens ſit quadrans) ad ſinum anguli recti C, id eſt, ad ſi-
<
lb
/>
num totum, ita ſinus arcus C H, altitudinis poli, ad ſinum anguli F. </
s
>
<
s
xml:id
="
echoid-s7051
"
xml:space
="
preserve
">Ex tribus ergo prioribus co-
<
lb
/>
gnitis cognoſcetur & </
s
>
<
s
xml:id
="
echoid-s7052
"
xml:space
="
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">angulus F. </
s
>
<
s
xml:id
="
echoid-s7053
"
xml:space
="
preserve
">Rurſus quia in triangulo ſphærico B I F, angulus I, rectus eſt, erit
<
lb
/>
per eaſdem propoſitiones, vt ſinus anguli B, complementi altitudinis poli, quem Aequator facit
<
lb
/>
cum Horizonte, ad ſinum arcus F I, declinationis dati paralleli, ita ſinus anguli F, proxime co-
<
lb
/>
gniti ad ſinum arcus B I. </
s
>
<
s
xml:id
="
echoid-s7054
"
xml:space
="
preserve
">Igitur ex tribus notis cognitus fiet arcus B I, qui in ſignis borealibus ad-
<
lb
/>
ditus quadranti conficit arcum ſemidiurnum E I, in ſignis autem auſtralibus ex quadrante ſub-
<
lb
/>
latus relinquit arcum ſemidiurnum E I. </
s
>
<
s
xml:id
="
echoid-s7055
"
xml:space
="
preserve
">Itaque ſi fiat, vt ſinus complementi declinationis paral-
<
lb
/>
leli propoſiti ad ſinum totum, ita ſinus altitudinis poli ad aliud, habebitur ſinus quidam, quem
<
lb
/>
Primum Inuentum licebit appellare. </
s
>
<
s
xml:id
="
echoid-s7056
"
xml:space
="
preserve
">Deinde ſi fiat, vt ſinus complementi altitudinis poli ad ſi-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0136-07
"
xlink:href
="
note-0136-07a
"
xml:space
="
preserve
">50</
note
>
num declinationis, ita ſinus, quem diximus Primum Inuentum, ad aliud, inuenietur ſinus, cuius
<
lb
/>
arcus, Sole exiſtente boreali, additus quadranti, vel Sole auſtrali exiſtente, ex quadrante demptus,
<
lb
/>
dabit arcum ſemidiurnum.</
s
>
<
s
xml:id
="
echoid-s7057
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7058
"
xml:space
="
preserve
">COMMODISSIME etiam ſine triangulis ſphæricis latitudines ortiuas, occiduasue, atq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7059
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0136-08
"
xlink:href
="
note-0136-08a
"
xml:space
="
preserve
">Amplitudo or.
<
lb
/>
tiua uel occi-
<
lb
/>
dua, quo modo
<
lb
/>
ſuppu@etur pe@
<
lb
/>
ſinus ex Ana-
<
lb
/>
@emmate.</
note
>
arcus ſemidiurnos reperiemus hac ratione. </
s
>
<
s
xml:id
="
echoid-s7060
"
xml:space
="
preserve
">Repetatur Analemma, hoc eſt, figura ſecunda præ-
<
lb
/>
cedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s7061
"
xml:space
="
preserve
">vbi H N, tam in parallelo boreali, quàm in auſtrali oſtenſus eſt eſſe arcus ſemi-
<
lb
/>
diurnus; </
s
>
<
s
xml:id
="
echoid-s7062
"
xml:space
="
preserve
">Item E L, ſinus rectus eſt amplitudinis ortiuæ, occiduæue: </
s
>
<
s
xml:id
="
echoid-s7063
"
xml:space
="
preserve
">Nam vt in ſcholio propoſ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7064
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s7065
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s7066
"
xml:space
="
preserve
">demonſtrauimus recta, ex L, ducta ad B D, perpendicularis, cum ſit commu-
<
lb
/>
nis ſectio Horizontis & </
s
>
<
s
xml:id
="
echoid-s7067
"
xml:space
="
preserve
">paralleli, aufert ex circulo A B C D, arcum latitudinis ortiuæ, ſiue occi-
<
lb
/>
duæ, cuius quidem ſinus eſt E L. </
s
>
<
s
xml:id
="
echoid-s7068
"
xml:space
="
preserve
">Quoniam igitur in triangulo rectangulo E k L, ſi E L, ponatur
<
lb
/>
ſinus totus, recta E K, eſt ſinus anguli E L
<
emph
style
="
sc
">K</
emph
>
, complementi altitudinis poli, vt in tractatione </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>