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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cet & </
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<
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">arcus auſtrales horologii auſtralis mutantur in boreali horologio in arcus boreales, & </
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tra, vt ſupra dictum eſt.</
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</
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<
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<
s
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xml:space
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">DEMONSTRATIO autem huius rei non differt ab ea, quam in horologio horizontali
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adduximus propoſ. </
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>
<
s
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="
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xml:space
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">2. </
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<
s
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">huius libri. </
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>
<
s
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xml:space
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">Eſtenim & </
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>
<
s
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">Verticalis circulus Horizon quidam, & </
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>
<
s
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="
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xml:space
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">angulus
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D H I, æqualis altitudini poli ſupra ipſum, vt conſtat. </
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>
<
s
xml:id
="
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"
xml:space
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">Quare eadem erit demonſtratio in vtro-
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que horologio.</
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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
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xml:space
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">CÆTERVM in horologio Auſtrali arcus ſignorum auſtralium continentur inter centrũ
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<
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xlink:label
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note-0237-01
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xlink:href
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xml:space
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">Qni arcus ad
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ſigna auſtralia,
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& qui ad borea
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lia pertineant.</
note
>
horologii, & </
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>
<
s
xml:id
="
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xml:space
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">lineam æquinoctialem, borealium vero vltra lineam æquinoctialem: </
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>
<
s
xml:id
="
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xml:space
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">In boreali au-
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tem horologio contrario modo ſe res habet; </
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>
<
s
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xml:space
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">vt ex Analemmate huius propoſ. </
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>
<
s
xml:id
="
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xml:space
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">colligitur. </
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>
<
s
xml:id
="
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xml:space
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">Idem
<
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etiam hinc apparere poteſt, quòd Sol in auſtralibus ſignis exiſtens breuiores vmbras facit in horo-
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<
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gio auſtrali circa meridiem, quàm cum in borealibus ſignis moratur: </
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<
s
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xml:space
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">quia in his maiores meridia
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nas altitudines habet, quàm in illis. </
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>
<
s
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xml:space
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">Vnde cum breuiores vmbræ meridianæ fiant inter centrum
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horologii auſtralis, & </
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>
<
s
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xml:space
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">lineam æquinoctialem, longiores autem vltra eandem lineam æquinoctia-
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lem; </
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>
<
s
xml:id
="
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xml:space
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">perſpicuum eſt, ſigna auſtralia eſſe inter centrum & </
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>
<
s
xml:id
="
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xml:space
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">æquinoctialem lineam, borealia vero
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vltra lineam æquinoctialem, &</
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>
<
s
xml:id
="
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xml:space
="
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">c.</
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>
<
s
xml:id
="
echoid-s14849
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xml:space
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</
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<
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>
<
s
xml:id
="
echoid-s14850
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xml:space
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">QVORVM autem ſignorum arcus ſint hyperbolæ, vel parabolæ, aut Ellipſes, percipiemus
<
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exiis, quæ propoſ. </
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>
<
s
xml:id
="
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xml:space
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">2. </
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>
<
s
xml:id
="
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xml:space
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">huius lib. </
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>
<
s
xml:id
="
echoid-s14853
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xml:space
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">ſcripſimus.</
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>
<
s
xml:id
="
echoid-s14854
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xml:space
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</
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<
note
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="
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xml:space
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">Quomodo ex
<
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uno arcu oppo-
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ſicus arcus de-
<
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ſcribatur, &c.</
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>
<
p
>
<
s
xml:id
="
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xml:space
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">HIC etiam commodius, & </
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>
<
s
xml:id
="
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"
xml:space
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">accuratius deſcribemus hyperbolas ſignorum borealium infra li-
<
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neam æquinoctialem, beneficio hyperbolarum ſignorum auſtralium ſupra lineam æquinoctialem
<
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deſcriptarum; </
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>
<
s
xml:id
="
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xml:space
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">ſi per doctrinam, quam propoſ. </
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>
<
s
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="
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xml:space
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">2. </
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>
<
s
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="
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xml:space
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">huius libri tradidimus, prius inueniantur dia-
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<
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">20</
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metri tranſuerſæ ſectionum oppoſitarum, earumq́; </
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<
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>
<
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<
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<
s
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">POSSVMVS quoque vti duobus illis modis, quos ad finem eiuſdem propoſ. </
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>
<
s
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">2. </
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>
<
s
xml:id
="
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">huius libri
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ſcripſimus. </
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>
<
s
xml:id
="
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xml:space
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">Qua de re conſule ea, quæ ibi tradidimus. </
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<
s
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="
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xml:space
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">Parallelos igitur, ſiue arcus ſignorum Zo-
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diaci in Verticali horologio prædicto deſcripſimus. </
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<
s
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">Quod faciendum erat.</
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<
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</
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</
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<
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style
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<
s
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xml:space
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">HOC modo eaſdem lineas horarias præcedentis figuræ ex H, egredientes deſcribit Andreas Schone
<
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<
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xlink:label
="
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xlink:href
="
note-0237-05a
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xml:space
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">Praxis pulcher-
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rima pro lineis
<
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horariis in figu
<
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ra radioiũ Zo-
<
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diaei ducendis,
<
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ſine interuallis
<
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horariis horo-
<
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logii.</
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>
rus. </
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>
<
s
xml:id
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xml:space
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">Ducta recta H I B, quæ conſtituat angulum A H B, æqualem complemẽto altitudinis poli ſupra Ho
<
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rizontem, vel ipſi altitudini poli ſupra Verticalem circulũ, vt & </
s
>
<
s
xml:id
="
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xml:space
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">nos fecimus, ſumit in ea punctũ quod-
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<
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">30</
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>
cunque φ, per quod ipſi D H, parallelam agit φ V, quæ rectã ductam ex H, ipſi D C, parallelã ſecet in
<
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V, puncto, è quo, vt centro, interuallo {q́ue} V φ, circulum deſcribit. </
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>
<
s
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xml:space
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">Hoc diuiſo in partes 24. </
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>
<
s
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">æquales, eadẽ
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facit, quæ in ſcholio propoſ. </
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>
<
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xml:space
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">2. </
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>
<
s
xml:id
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xml:space
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">huius libri de borizontali horologio docuimus.</
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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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">EX figura autem radiorum conſtructa, vt docet Andreas Schonerus, deſcribi poterit horologiũ Ver
<
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<
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xlink:label
="
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xlink:href
="
note-0237-07a
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xml:space
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">Deſcriptio ho-
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rologii
<
unsure
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Vertica
<
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lis ex figura ra-
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diorũ Andreæ
<
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Schoneri.</
note
>
ticale ad datam ſtyli magnitudinem, vt de horizontali diximus in ſcholio propoſ. </
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>
<
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xml:space
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">2. </
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<
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xml:space
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">huius lib. </
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<
s
xml:id
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xml:space
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">dummodo
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angulus ρ D H, æqualis fiat altitudini poli, non autem eius complemento, vt in horizont ali horologio.</
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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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">STYLVS iuxta poſteriorem modum deſcribendi parallelos ſignorum, qui per figur am radiorum Zo
<
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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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">Qua ratione ex
<
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figura radiorũ
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longitudo ſtyli,
<
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eiusq́; locus in
<
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horologio inue
<
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niatur.</
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>
diaci abſoluitur, habetur, ſi ex D, ad H I, perpendicularis ducatur D ρ, vel certe recta D ρ, faciens angu
<
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lum ρ D I, æqualem angulo complemento altitudinis poli ſupra Horizontem. </
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>
<
s
xml:id
="
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xml:space
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">Longitudo enim ſtyli eſt ip-
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ſa recta D ρ: </
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>
<
s
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xml:space
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">Locus vero eius eſt punctum ρ, diſtans ab H, centro horologij interuallo H ρ, in linea me
<
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<
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>
ridiana, vel ab æquinoctiali linea F K, ſpatio I ρ, in eadem linea meridiana, verſus centrum H.</
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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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">DESCRIPTIS autem lineis horarijs in proxime antecedenti figura ex puncto H, ſi ſecundum
<
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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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">Quomodo per
<
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figuram radio-
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rum Zodiaci
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maius aut mi-
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nus horologiũ
<
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deſcubendum
<
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ſit.</
note
>
poſteriorem hunc modum ex dicta figura radiorum zodiaci deſumptum, maius, aut minus horologium cõ
<
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ſtruendum ſit, deſcribenda erit figura radiorum Zodiaci magis, vel minus diſtans à puncto H, &</
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>
<
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="
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">c. </
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>
<
s
xml:id
="
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">vt de
<
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horologio Horizontali dictum eſt in ſcholio propoſ. </
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>
<
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xml:space
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">2. </
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>
<
s
xml:id
="
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xml:space
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">huius lib.</
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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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">QVOD ſimagnitudo ſiyli data ſit, inueniemus hac ratione diſtantiam figuræ radiorum Zodiaci à
<
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<
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="
right
"
xlink:label
="
note-0237-11
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xlink:href
="
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xml:space
="
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">Quomodo ex
<
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data ſtyli longi
<
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tudine inuenia
<
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tur diſtantia ra
<
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diorum Zodia-
<
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ci à puncto H,
<
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/>
in figura radio-
<
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rum.</
note
>
puncto H, in axe H D. </
s
>
<
s
xml:id
="
echoid-s14894
"
xml:space
="
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">In portione Analemmatis propoſ. </
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>
<
s
xml:id
="
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"
xml:space
="
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">præcedentis abſcindatur ex B D C, protracta
<
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recta D M, æqualis gnomoni dato, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">per M, ipſi A D, diametro Verticalis parallela agatur N O, ſecans
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lb
/>
axem D E, in N, & </
s
>
<
s
xml:id
="
echoid-s14897
"
xml:space
="
preserve
">Aequatoris diametrum F D, in O. </
s
>
<
s
xml:id
="
echoid-s14898
"
xml:space
="
preserve
">Punctum enim D, figurę radiorum huius pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s14899
"
xml:space
="
preserve
">in quo conueniunt omnes radij zodiaci, diſtare debet ab H, interuallo D N, vt de horologio horizõ-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0237-12
"
xlink:href
="
note-0237-12a
"
xml:space
="
preserve
">50</
note
>
tali diximus in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s14900
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s14901
"
xml:space
="
preserve
">huius lib.</
s
>
<
s
xml:id
="
echoid-s14902
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s14903
"
xml:space
="
preserve
">HIC etiam in horologio illo, quod in ſcholio præcedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s14904
"
xml:space
="
preserve
">docuimus conficere, etiam ſi centrũ
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0237-13
"
xlink:href
="
note-0237-13a
"
xml:space
="
preserve
">Qua ratione at
<
lb
/>
cus ſignorũ in
<
lb
/>
horologio Ver-
<
lb
/>
ticali, vbi cen-
<
lb
/>
trum non habe
<
lb
/>
tur, deſcriban-
<
lb
/>
tur.</
note
>
eius non habeatur, deſcribemus arcus ſignorum, vt in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s14905
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s14906
"
xml:space
="
preserve
">huius libri tradidimus.</
s
>
<
s
xml:id
="
echoid-s14907
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s14908
"
xml:space
="
preserve
">QV AMVIS autem rectè demonſtratum ſit hac propoſ. </
s
>
<
s
xml:id
="
echoid-s14909
"
xml:space
="
preserve
">portionem ſuperiorẽ horologij auſtralis,
<
lb
/>
quam horizontalis linea abſcindit, exhibere nobis horologium boreale, ſi omnes eius partes ita permuten-
<
lb
/>
tur, vt ſuperior vertatur in inferiorem, hoc eſt, horizontalis linea occupet ſuperiorem locum, & </
s
>
<
s
xml:id
="
echoid-s14910
"
xml:space
="
preserve
">pars,
<
lb
/>
quæ in eo ſitu nobis ad horologiũ conuerſis dextra eſt, fiat ſiniſtra, & </
s
>
<
s
xml:id
="
echoid-s14911
"
xml:space
="
preserve
">contra: </
s
>
<
s
xml:id
="
echoid-s14912
"
xml:space
="
preserve
">operætamen pretium me fa
<
lb
/>
cturum exiſtimaui, idem vniuerſe hoc loco oſtendere, nimirum non ſolum in Verticali horologia auſtrali,
<
lb
/>
ſed in alijs etiam omnibus (vt in meridiano, polari, in eo quod à Verticali declinat, & </
s
>
<
s
xml:id
="
echoid-s14913
"
xml:space
="
preserve
">in eo quod ab Hori
<
lb
/>
zonte, in inclinato ad Horizontem, & </
s
>
<
s
xml:id
="
echoid-s14914
"
xml:space
="
preserve
">in eo quod à Verticali declinat, ſimulq́, ad Horizontem inclinatũ
<
lb
/>
eſt) lineam horizontalem ad partes ſuperiores portionem auferre, quæ in facie plani horologii </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>