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.
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horologii, vel horæ 12. </
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>
<
s
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xml:space
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<
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xml:space
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">vt ibi. </
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<
s
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xml:space
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">Pari ratione in figura tertia eiuſdem propoſ. </
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<
s
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echoid-s17569
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xml:space
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">26.
<
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</
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<
s
xml:id
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echoid-s17570
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xml:space
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">lineam α β, quæ in horologio Meridiano pertinebat ad horam 6. </
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>
<
s
xml:id
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xml:space
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">à mer. </
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>
<
s
xml:id
="
echoid-s17572
"
xml:space
="
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">eſſe lineam meridianam,
<
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/>
ſeu horæ 12 in horologio polari; </
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>
<
s
xml:id
="
echoid-s17573
"
xml:space
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">proximam verò illi parallelam pertinere ad horam 1. </
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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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">11. </
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>
<
s
xml:id
="
echoid-s17576
"
xml:space
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">à me
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ridie, & </
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>
<
s
xml:id
="
echoid-s17577
"
xml:space
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">media nocte, &</
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>
<
s
xml:id
="
echoid-s17578
"
xml:space
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">c. </
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>
<
s
xml:id
="
echoid-s17579
"
xml:space
="
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">In vtroque porrò horologio polari ſigna Borealia infra lineam æquino-
<
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<
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xlink:label
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note-0275-01
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xlink:href
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xml:space
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">In horologio
<
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polati tam Su-
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periori, quàm
<
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Inferioti ſigna
<
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borealia ſunt
<
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inſra lineã ęqui
<
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noctialem, & au
<
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ſiralia ſupra.</
note
>
ctialem verſus auſtrum, & </
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>
<
s
xml:id
="
echoid-s17580
"
xml:space
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">ſupra eandem verſus boream auſtralia continentur, vt ex Analemmate,
<
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ſeu figura prima propoſ. </
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>
<
s
xml:id
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xml:space
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">26. </
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>
<
s
xml:id
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xml:space
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">huius libri colligi poteſt. </
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>
<
s
xml:id
="
echoid-s17583
"
xml:space
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">Nam Sole exiſtente in ♋, vmbra ſtyli proii-
<
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citur in partes inferiores lineæ meridianæ in vtroque horologio, nempe in punctum N, verſus au-
<
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/>
ſtrum tempore meridiei; </
s
>
<
s
xml:id
="
echoid-s17584
"
xml:space
="
preserve
">exiſtente verò eodem in ♑, in ſuperiores partes, vt in punctum Q, ver-
<
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ſus boream.</
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>
<
s
xml:id
="
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</
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>
<
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xml:space
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">Linea hor@zon-
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talis in horolo-
<
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g@o Polari quo
<
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modo deſcriba-
<
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@ur.</
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>
<
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>
<
s
xml:id
="
echoid-s17586
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xml:space
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">QVONIAM verò planum horologii polaris ab Horizonte ſecatur, cum ei non ſit parallelũ,
<
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<
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">10</
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>
quemadmodum & </
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>
<
s
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="
echoid-s17587
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xml:space
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">circulus horæ 6. </
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>
<
s
xml:id
="
echoid-s17588
"
xml:space
="
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">à meridie, vel media nocte, cui horologium æquidiſtat, ab eo-
<
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/>
dem Horizonte ſecatur, deſcribemus communem ſectionem Horizontis, ac plani horologii, nem
<
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/>
pe lineam horizontalem, in quam vmbra ſtyli proiicitur, cum Soloritur, vel occidit, vt ex propoſ.
<
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/>
</
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>
<
s
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="
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xml:space
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">11. </
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>
<
s
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="
echoid-s17590
"
xml:space
="
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">ſuperioris lib. </
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>
<
s
xml:id
="
echoid-s17591
"
xml:space
="
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">conſtat, hac ratione. </
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>
<
s
xml:id
="
echoid-s17592
"
xml:space
="
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">Ad punctum B, vbi hora 3. </
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>
<
s
xml:id
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echoid-s17593
"
xml:space
="
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">vel 9. </
s
>
<
s
xml:id
="
echoid-s17594
"
xml:space
="
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">lineam æquinoctialem ſe-
<
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/>
cat, fiat angulus A B D, complemento altitudinis poli æqualis, ſecetq́ue recta B D, lineam meri-
<
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/>
dianam in D, ſupra quidem locum ſtyli in horologio ſuperiori, infra verò eundẽ in inferiori; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quod
<
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/>
facile fiet, ſi ex B, deſcribatur arcus circuli vltra lineam meridianam, in quo à recta C S, comple-
<
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/>
mentum altitudinis poli ſupputetur, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ex ſine ſupputationis ad B, recta ducatur, &</
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>
<
s
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="
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xml:space
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">c. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Si enim per
<
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/>
D, lineæ æquinoctiali C S, parallela ducatur, erit hæc, linea horizontalis. </
s
>
<
s
xml:id
="
echoid-s17599
"
xml:space
="
preserve
">Nam quia recta A B,
<
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/>
longitudini ſtyli A E, eſt æqualis, vt in ſcholio propoſ. </
s
>
<
s
xml:id
="
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xml:space
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">25. </
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>
<
s
xml:id
="
echoid-s17601
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xml:space
="
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">huius libri oſtendimus, ſi triangulum
<
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/>
<
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">20</
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D B A, circa rectam A D, intelligatur conuerti, donec ad planum horologii rectum ſit, & </
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>
<
s
xml:id
="
echoid-s17602
"
xml:space
="
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">in plano
<
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/>
Meridiani circuli exiſtat, tranſibit Horizon per punctum B, nempe per verticem ſtyli, ſeu centrum
<
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/>
mundi; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Nam recta A B, in illo ſitu, quem in illa conuerſione trianguli acquiſiuit, perpendicularis
<
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/>
eſt ad planum horologii, & </
s
>
<
s
xml:id
="
echoid-s17604
"
xml:space
="
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">in plano Æ quatoris exiſtit, atque adeo B, erit vertex ſtyli, ſeu centrum
<
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/>
mundi. </
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>
<
s
xml:id
="
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xml:space
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">Cum ergo angulus D B A, conſtitutus ſit æqualis complemento altitudinis poli, qualem
<
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/>
nimirum Horizon facit cum plano Æ quatoris, atque adeo reliquus B D A, altitudini poli æqualis
<
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/>
ſit, nempe inclinationi plani horologii ad Horizontem, tranſibit Horizon per rectam B D, occur-
<
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/>
retq́ue plano horologii in D; </
s
>
<
s
xml:id
="
echoid-s17606
"
xml:space
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">quandoquidem hac ratione in plano Meridiani circuli cum A B, cõ-
<
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muni ſectione Aequatoris, & </
s
>
<
s
xml:id
="
echoid-s17607
"
xml:space
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">Meridiani conſtituit angulum complemento altitudinis poli æqua-
<
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lem, cum recta verò A E, communi ſectione plani horologii, ac Meridiani angulum æqualem alti-
<
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/>
<
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position
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">30</
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tudini poli, vt res exigit. </
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>
<
s
xml:id
="
echoid-s17608
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xml:space
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">Quare per D, ducenda erit linea horizontalis. </
s
>
<
s
xml:id
="
echoid-s17609
"
xml:space
="
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">Quia verò Aequator, Ho-
<
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rizon, & </
s
>
<
s
xml:id
="
echoid-s17610
"
xml:space
="
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">circulus horæ ſextæ habent vnam communem ſectionem, æquidiſtatq́ue plannm horolo
<
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/>
gij vni illorum, nempe circulo horæ 6. </
s
>
<
s
xml:id
="
echoid-s17611
"
xml:space
="
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">erunt communes ſectiones factæ à plano horologii in aliis
<
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duobus circulis, nempe linea æquinoctialis, & </
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>
<
s
xml:id
="
echoid-s17612
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xml:space
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">horizontalis, parallelæ inter ſe, vt in ſcholio propoſ.
<
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</
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>
<
s
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="
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xml:space
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">22. </
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>
<
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xml:space
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">ſuperioris lib. </
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>
<
s
xml:id
="
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"
xml:space
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">demonſtratum eſt. </
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>
<
s
xml:id
="
echoid-s17616
"
xml:space
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">Recta igitur per D, lineæ æquinoctiali parallela ducta, ho-
<
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/>
rizon talis linea eſt, quod eſt propoſitum.</
s
>
<
s
xml:id
="
echoid-s17617
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="
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"/>
</
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>
<
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>
<
s
xml:id
="
echoid-s17618
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xml:space
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">INVENIEMVS quoque punctum D, per quod horizontalis linea ducenda eſt, hoc mo-
<
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/>
<
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="
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xlink:label
="
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xlink:href
="
note-0275-06a
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xml:space
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">Alia deſcriptio
<
unsure
/>
<
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/>
lineæ horizon-
<
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talis in eodem
<
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/>
horologio Po.
<
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/>
lari.</
note
>
do. </
s
>
<
s
xml:id
="
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xml:space
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">In Analemmate, ex quo arcus ſignorũ deſcripti ſunt, notentur puncta l, m, vbi diameter Hori-
<
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zontis B D, parallelas L M, L M, per quas ducũtur horologiorum plana, interſecat, & </
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>
<
s
xml:id
="
echoid-s17620
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xml:space
="
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">recta K l, vel
<
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K m, trãsferatur in lineã meridianã ex loco ſtyli A, ſurſum verſus vſq; </
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>
<
s
xml:id
="
echoid-s17621
"
xml:space
="
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">ad D, in horologio ſuperio-
<
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/>
<
note
position
="
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xlink:label
="
note-0275-07
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xlink:href
="
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xml:space
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">40</
note
>
ri, deorſum autẽ verſus in inferiori. </
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>
<
s
xml:id
="
echoid-s17622
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xml:space
="
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">Nam per D, ducenda eſt linea horizontalis, vt prius. </
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>
<
s
xml:id
="
echoid-s17623
"
xml:space
="
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">quoniã in
<
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punctis l, & </
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>
<
s
xml:id
="
echoid-s17624
"
xml:space
="
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">m, planum Horizontis per B D, ductum occurrit planis horologiorum per L M, L M,
<
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/>
rectas ductis, ſupra K, quidem locũ ſtyli in horologio ſuperiori, infra verò in inferiori, &</
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>
<
s
xml:id
="
echoid-s17625
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xml:space
="
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">c. </
s
>
<
s
xml:id
="
echoid-s17626
"
xml:space
="
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">Et quo-
<
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/>
niam recta K l, rectæ K m, æqualis eſt; </
s
>
<
s
xml:id
="
echoid-s17627
"
xml:space
="
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">(Nam in triangulis E K l, E K m, anguli ad K, recti ſunt,
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0275-08
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xlink:href
="
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xml:space
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">15. primi.</
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>
& </
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>
<
s
xml:id
="
echoid-s17628
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xml:space
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">anguli ad verticem E, æquales; </
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>
<
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xml:id
="
echoid-s17629
"
xml:space
="
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">Item & </
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>
<
s
xml:id
="
echoid-s17630
"
xml:space
="
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">latera E K, E K, ęqualia. </
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>
<
s
xml:id
="
echoid-s17631
"
xml:space
="
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">Igitur & </
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>
<
s
xml:id
="
echoid-s17632
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xml:space
="
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">latera K l, K m, æqualia
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0275-09
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xlink:href
="
note-0275-09a
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xml:space
="
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">26. primi.</
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>
erunt) propterea diximus eandẽ K l, vel K m, transferendã in lineam meridianam ſupra vel infra
<
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/>
locum ſtyli in vtroque horologio, vt punctum reperiatur, per quod horizontalis linea ducatur.</
s
>
<
s
xml:id
="
echoid-s17633
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s17634
"
xml:space
="
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">PORRO ſi horologium polare ſuperius inuertatur, ita vt ſuperiora fiant inferiora, & </
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>
<
s
xml:id
="
echoid-s17635
"
xml:space
="
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">quæ
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0275-10
"
xlink:href
="
note-0275-10a
"
xml:space
="
preserve
">Si omnes par-
<
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/>
tes Superioris
<
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/>
horologii Pola-
<
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/>
ris inuertantur,
<
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/>
vt ſuperior fiat
<
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/>
inferior, & dex-
<
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/>
t@a ſiniſtra, fa-
<
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/>
ctum erit horo-
<
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/>
logiũ Inferius;
<
lb
/>
ſed horæ, quæ
<
lb
/>
prius numera-
<
lb
/>
bantur à n@er@
<
lb
/>
numerande sũt
<
lb
/>
à med. noc. &
<
lb
/>
contra.</
note
>
dextra ſunt poſt eam inuerſionem, fiant ſiniſtra, & </
s
>
<
s
xml:id
="
echoid-s17636
"
xml:space
="
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">contra, vt in ſcholio propoſ. </
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>
<
s
xml:id
="
echoid-s17637
"
xml:space
="
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">14. </
s
>
<
s
xml:id
="
echoid-s17638
"
xml:space
="
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">huius libri ſcri-
<
lb
/>
pſimus, indicabit idem horas in facie oppoſita plani, hoc eſt, in inferiori, quæ ad Nadir ſpectat, vt
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0275-11
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xlink:href
="
note-0275-11a
"
xml:space
="
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">50</
note
>
in dicto ſcholio demonſtrauimus. </
s
>
<
s
xml:id
="
echoid-s17639
"
xml:space
="
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">Sed linea meridiana monſtrabit tunc horam 12. </
s
>
<
s
xml:id
="
echoid-s17640
"
xml:space
="
preserve
">mediæ noctis,
<
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/>
cum in ſuperiori hologio horam 12. </
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>
<
s
xml:id
="
echoid-s17641
"
xml:space
="
preserve
">meridiei indicet: </
s
>
<
s
xml:id
="
echoid-s17642
"
xml:space
="
preserve
">reliquæ verò horæ, quæ in eodem ſuperio-
<
lb
/>
ri horologio à meridie numerantur, à media nocte ſupputandæ erunt in inferiori, & </
s
>
<
s
xml:id
="
echoid-s17643
"
xml:space
="
preserve
">contra. </
s
>
<
s
xml:id
="
echoid-s17644
"
xml:space
="
preserve
">Quo-
<
lb
/>
niam enim Sol in alio ſemicirculo eiuſdem circuli horarij exiſtat neceſſe eſt, cum vmbra ſtyli in
<
lb
/>
ſuperius horologium cadit, & </
s
>
<
s
xml:id
="
echoid-s17645
"
xml:space
="
preserve
">in alio, cum in inferius, vt patet; </
s
>
<
s
xml:id
="
echoid-s17646
"
xml:space
="
preserve
">efficitur, vt linea, quæ in ſuperiori
<
lb
/>
horologio indicat horam à meridie, monſtret in inferiori eandem horam à media nocte, & </
s
>
<
s
xml:id
="
echoid-s17647
"
xml:space
="
preserve
">con-
<
lb
/>
tra; </
s
>
<
s
xml:id
="
echoid-s17648
"
xml:space
="
preserve
">quandoquidem vnus ſemicirculus ad horas à meridie, & </
s
>
<
s
xml:id
="
echoid-s17649
"
xml:space
="
preserve
">alter ad horas à media nocte perti-
<
lb
/>
net, vt in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s17650
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s17651
"
xml:space
="
preserve
">ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s17652
"
xml:space
="
preserve
">docuimus. </
s
>
<
s
xml:id
="
echoid-s17653
"
xml:space
="
preserve
">Arcus quoque vel paralleli ſignorum au-
<
lb
/>
ſtralium ſuperioris horologii mutantur in arcus borealium ſignorum in inferiori, & </
s
>
<
s
xml:id
="
echoid-s17654
"
xml:space
="
preserve
">contra; </
s
>
<
s
xml:id
="
echoid-s17655
"
xml:space
="
preserve
">vt
<
lb
/>
parallelus ♑, in parallelum ♋, parallelus ♐, & </
s
>
<
s
xml:id
="
echoid-s17656
"
xml:space
="
preserve
">♒, in parallelum ♊, & </
s
>
<
s
xml:id
="
echoid-s17657
"
xml:space
="
preserve
">♌, &</
s
>
<
s
xml:id
="
echoid-s17658
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s17659
"
xml:space
="
preserve
">Quod oſtendemus,
<
lb
/>
vt in propoſ, 26. </
s
>
<
s
xml:id
="
echoid-s17660
"
xml:space
="
preserve
">huius libri idem demonſtrauimus in Meridiano horologio, hoc ſolum </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>