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 TERTIVS.
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horæ 6. </
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<
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xml:space
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">& </
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<
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">æquinoctialis; </
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<
s
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xml:space
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">alias non caderet radius Solis in omnes tres ſectiones, quas planum ho-
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rologij cum illis tribus circulis facit. </
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>
<
s
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"
xml:space
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">quod eſt abſurdum. </
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>
<
s
xml:id
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"
xml:space
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">Quòd autem eadem parallela eſſe de-
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beat lineæ meridianæ, perſpicuè colligitur ex propoſ. </
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>
<
s
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xml:space
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">18. </
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<
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xml:space
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">primi libri. </
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<
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xml:space
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">Quia enim Meridianus, Ho-
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rizon, & </
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>
<
s
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"
xml:space
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">circulus maximus, cui horologium æquidiſtat, communem ſectionem habent axem Ver
<
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ticalis circuli, erunt communes ſectiones, quas Meridianus, & </
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>
<
s
xml:id
="
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"
xml:space
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">Horizon cum plano horologij fa-
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ciunt, parallelæ inter ſeſe, vt in dicta propoſ. </
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<
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">18. </
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<
s
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xml:space
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">demonſtratum eſt.</
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>
<
s
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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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">HANC eandem lineam horizontalem ducemus hac ratione. </
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>
<
s
xml:id
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xml:space
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">Per K, locum ſtyli agatur re-
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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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">Alia deſcriptio
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lineæ horizon-
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talis.</
note
>
cta K A, meridianæ lineæ parallela, ad quam ex quolibet puncto B, excitetur perpendicularis B D,
<
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verſus illam partem horologii, vbi æquinoctialis linea, & </
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>
<
s
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">linea horæ 6. </
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<
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xml:space
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">ſe interſecant. </
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>
<
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xml:space
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">Deinde
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ſumpta recta A B, quæ ſtylo I K, æqualis ſit, conſtituatur in A, angulus B A D, complemento de-
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">10</
note
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clinationis plani ab Horizonte æqualis, ſecetq́ue recta A D, rectam B D, in D. </
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<
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xml:space
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">Nam per punctum
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D, acta ipſi meridianæ lineæ
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parallela dabit horizontalem lineam, vt prius, quæ neceſſario per ho-
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ram 6. </
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<
s
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xml:space
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">in line@ æquinoctiali tranſibit, ſi erratum non eſt. </
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<
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xml:space
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">Atque hoc modo ducendo lineam ho-
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rizontalem facile examinabimus, an hora 6. </
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<
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xml:space
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">ſit rectè deſcripta, necne. </
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>
<
s
xml:id
="
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xml:space
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">Quòd autem linea hori-
<
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zontalis ducenda ſit per punctum D, hac arte inuentum, (Ipſam enim duci per horam 6. </
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>
<
s
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xml:space
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">in linea
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æquinoctiali, & </
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>
<
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="
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xml:space
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">parallelam eſſe lineæ meridianæ, proximè iam demonſtratum eſt) hoc modo ma-
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nifeſtabimus. </
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<
s
xml:id
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"
xml:space
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">Intelligatur triangulum A B D, circa rectam B D, moueri, vſque dum ad horologij
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planum ſit rectam, & </
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<
s
xml:id
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xml:space
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">ſtylus I K, in K, rectus cogitetur eſſe ad horologium. </
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<
s
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xml:space
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">Erunt hac ratione re-
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ctæ I K, A B inter ſe parallelæ, quòd vtraque ad planum horologij recta ſit; </
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<
s
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xml:space
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">ipſa quidem I k, ex
<
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<
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xml:space
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">6. vndec.</
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poſitione, at verò A B, ex defin. </
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">4. </
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<
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">lib 11. </
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<
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">Euclidis. </
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<
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">Cum ergo & </
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<
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xml:space
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">æquales inter ſe ſint, erit & </
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>
<
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xml:space
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<
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">20</
note
>
cta A I, ducta ex A, ad I, (poſita vtraque linea I K, A B, ad planum recta) parallela ipſi B K. </
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>
<
s
xml:id
="
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xml:space
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">Ho-
<
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<
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xlink:label
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xml:space
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">33. primi.</
note
>
rizon ergo tranſiens per I, verticem ſtyli, æquidiſtansq́ue meridianæ lineæ, ac proinde & </
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>
<
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xml:space
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">ipſi
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B K, ducetur per rectam A I, atque adeo per punctum A. </
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<
s
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"
xml:space
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">Et quia angulus B A D, ex conſtructio-
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ne, complemento declinationis plani ab Horizonte ęqualis eſt, erit reliquus A D B, ipſi declinatio-
<
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niæqualis. </
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<
s
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xml:space
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">Quare Horizon per rectam A D, ducetur, cum hac ratione plano horologii occurrat
<
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ſecua
<
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dum angulum declinationis A D B, ita vt A D, communis ſectio ſit Horizontis, & </
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<
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xml:space
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">trianguli
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A B D. </
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<
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xml:space
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">Quocirca Horizon plano horologii occurret in D, puncto, ac propterea per D, ducenda
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erit linea horizontalis.</
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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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">DENIQVE eadem horizontalis linea ducetur hac arte. </
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>
<
s
xml:id
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xml:space
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">Ex figura radiorum, ſi horologium
<
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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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">Horizontalis li
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neæ deſcriptio
<
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alia.</
note
>
Superius ad occaſum ſpecter, ſumantur interualla horæ ſeptimæ à meridie, inter C, & </
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<
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xml:space
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">radium ho
<
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<
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rarum 14. </
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<
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xml:space
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">& </
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<
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">horæ 5. </
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<
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xml:space
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">à meridie inter C, & </
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<
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xml:id
="
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">radium horarum 10. </
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<
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xml:id
="
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xml:space
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">vel ſi ad ortum vergat, horæ 5. </
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<
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xml:id
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xml:space
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">à
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media nocte inter C, & </
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<
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xml:id
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">radium horarum 14. </
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<
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xml:id
="
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xml:space
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">& </
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<
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xml:id
="
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xml:space
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">horæ 7. </
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<
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xml:id
="
echoid-s22914
"
xml:space
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">à media nocte inter C, & </
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>
<
s
xml:id
="
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xml:space
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">radium horarũ
<
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10 & </
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>
<
s
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="
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xml:space
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">transferantur ex C, centro horologii in reſpondentes lineas, imprimendo puncta in ipſis.
<
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</
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>
<
s
xml:id
="
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"
xml:space
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">Per hæc enim puncta erit horizontalis linea ducenda: </
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>
<
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xml:id
="
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"
xml:space
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">quoniam Sol in eo parallelo exiſtens, cuius
<
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arcus diurnus continet horas 14. </
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>
<
s
xml:id
="
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xml:space
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">qui quidem, per ea, quæ demonſtrata ſunt, tranſit in horologio
<
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per inuenta puncta in hora 7. </
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<
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xml:id
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">à meridie, & </
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>
<
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">hora 5. </
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<
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xml:id
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xml:space
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">à media nocte, occidit hora 7. </
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<
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xml:id
="
echoid-s22923
"
xml:space
="
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">à meridie, & </
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>
<
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xml:id
="
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xml:space
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">
<
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oritur hora 5. </
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<
s
xml:id
="
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xml:space
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">à media nocte. </
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>
<
s
xml:id
="
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"
xml:space
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">Exiſtens verò in illo parallelo, cuius arcus diurnus complectitur
<
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horas 10. </
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>
<
s
xml:id
="
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xml:space
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">qui ex demonſtratis quoque tranſit in horologio per puncta inuenta in hora 5. </
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<
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xml:space
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">à meri-
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die
<
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, & </
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<
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">hora 7. </
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<
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xml:id
="
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">à media nocte, occidit hora 5. </
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<
s
xml:id
="
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xml:space
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">à meridie, & </
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>
<
s
xml:id
="
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">oritur hora 7. </
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>
<
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xml:id
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xml:space
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">à media nocte; </
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>
<
s
xml:id
="
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"
xml:space
="
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">ac proin
<
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de per dictas horas in nominatis arcubus diurnis horizontalis linea ducenda erit, quæ vt ante de-
<
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<
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position
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xlink:label
="
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xlink:href
="
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xml:space
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">40</
note
>
monſtrauimu
<
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/>
s, neceſſario per horam 6. </
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>
<
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xml:id
="
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xml:space
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">in linea æquinoctiali tranſibit, & </
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>
<
s
xml:id
="
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xml:space
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">lineæ meridianæ paral-
<
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lela exiſtet. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Adducimus tot modos ducendæ lineæ horizontalis, quia & </
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>
<
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xml:id
="
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xml:space
="
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">iucundum eſt cernere,
<
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tanta varietate ad eundem ſemper ſcopum nos poſſe peruenire, & </
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>
<
s
xml:id
="
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xml:space
="
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">certi eſſe poſſumus, in horarum
<
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deſcriptione nullum errorem fuiſſe commiſſum, ſi omnes modi concordes conſentientesq́ue in-
<
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ter ſe fuerint.</
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>
<
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xml:id
="
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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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">HÆC autem linea horizontalis totum horologium diuidit in duo, quorum maius eſt Supe-
<
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<
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position
="
right
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xlink:label
="
note-0359-09
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xlink:href
="
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xml:space
="
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">Horizontalis Ii
<
unsure
/>
<
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/>
nea dirimit to-
<
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/>
tum horologiũ
<
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/>
in Superius In-
<
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/>
feriusq́ue, & in
<
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/>
diurnum no-
<
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cturnumque.</
note
>
rius, & </
s
>
<
s
xml:id
="
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xml:space
="
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">minus Inferius, vt in præcedentibus oſtenſum eſt; </
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>
<
s
xml:id
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xml:space
="
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">dummodo partes Inferioris immuten-
<
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tur, vt in præcedenti propoſ. </
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>
<
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xml:space
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">diximus.</
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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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">SECATVR horologium quoque totum ab eadem horizontali linea in diurnum, & </
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>
<
s
xml:id
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xml:space
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">noctur
<
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num, veluti in ſuperioribus dictum eſt. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Parallelos igitur, ſiue arcus, &</
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>
<
s
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="
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">c. </
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>
<
s
xml:id
="
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">figurauimus. </
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>
<
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="
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xml:space
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">quod
<
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<
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="
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="
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xml:space
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">50</
note
>
faciendum erat.</
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>
<
s
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="
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"
xml:space
="
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"/>
</
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>
</
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>
<
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="
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"
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="
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"
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="
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"
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="
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">
<
head
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xml:space
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">PROBLEMA 15. PROPOSITIO 15.</
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echoid-s22953
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">PARALLELOS arcuum diurnorum in eodem horologio, quod
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ab Horizonte declinat, deſcribere.</
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">Areuum diu@-
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n
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orum deſcri-
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ptio in eodem
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horologio dec
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li
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nanteab Hori-
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zon
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te.</
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<
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">IN his parallelis deſcribendis nihil difficultatis eſt, cum eodem modo deſcribantur, quo pa-
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ralleli ſignorum Zodiaci in præcedenti propoſ. </
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">delineati ſunt, vt patet, ſi pro ſignorum </
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