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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<
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xml:space
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">CAETERVM quia eodem modo lineę domorum cęleſtium & </
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>
<
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xml:space
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">in orie
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ntali, & </
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<
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xml:space
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">in occidentali horo
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xml:space
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">Lineæ domor@
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cœleſtium eun-
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dem ſ@@um in
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vtroque horolo
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gio Meridiano
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habent. Vnde
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ſatis eſt, vi de-
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ſcribatur he
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ro-
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logium dunta-
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xat orientale@,
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vel occidentale.</
note
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logio deſcribuntur, tam ſecundum Ioan. </
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>
<
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xml:space
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">Regi
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om. </
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>
<
s
xml:id
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xml:space
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">quàm ex ſententia Campani, proptcrea in priori figura
<
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@as delineauimus in horologio orientali. </
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>
<
s
xml:id
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xml:space
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">Nam eædem deſcriptæ in facie occidentali illis correſpondentes
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dabunt domos cęleſtes in horologio occidẽtali, vt numeri indicãt, quorũ illi, qui tropico ♋, appoſiti ſunt,
<
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ad orientale horologium, alii vero tropico ♑, aſcripti ad occidentale pertinent. </
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>
<
s
xml:id
="
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xml:space
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preserve
">In poſteriori autem fi-
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gura duximus lineas domorum in occidentali horologio, propterea quòd eædem in facie orientali ipſis cor
<
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reſpondentes dant domos cęleſtes in horologio orie
<
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ntali. </
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>
<
s
xml:id
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xml:space
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">Numeri enim tropico ♋, aſcripti ad horologium
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occidentale, alii vero tropico ♑, appoſiti ad orientale ſpectant.</
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<
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<
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<
head
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xml:space
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">PROBLEMA 33. PROPOSITIO 33.</
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>
<
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<
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xml:space
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">SIGNA Zodiaci aſcendentia in eodem Meridiano horologio
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deſcribere.</
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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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">ACCIPIANTVR ex prioribus duabus tabellis propoſ. </
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<
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">42. </
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<
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">huius lib. </
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<
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xml:space
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">Sole exiſtente in
<
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<
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xlink:label
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xml:space
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">Deſcriptio ſi-
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gnorum aſcen-
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dentium in eo-
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dem horologio
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Meridiano.</
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principio ♈, & </
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<
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">♎, horæ, quibus 12. </
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<
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">ſigna Zodiaci oriuntur, in horologio quidem orientali, ante
<
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meridiẽ, in occidentali vero poſt meridiem; </
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>
<
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xml:id
="
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xml:space
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">que in circulo ex E, deſcripto numerentur à linea GI,
<
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vel verſus ortũ, vel verſus occaſum, hoc eſt, vel verſus partẽ antemeridianã, aut pomeridianã, prout
<
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<
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">20</
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>
tabellæ indicant. </
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>
<
s
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xml:space
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">In orientali horologio ſemper facienda eſt numeratio verſus dexterã, in occiden-
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tali autem verſus ſiniſtram, hoc eſt, ſemper verſus F, vt patet, ſi circulus ex E, deſcriptus conſidere-
<
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tur in propria poſitione in vtroque horologio. </
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>
<
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xml:space
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">Deinde per fines numerationum, & </
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>
<
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xml:space
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">centrum E, du
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cantur occultæ rectæ ſecantes æquinoctialem lineam ſiue infra horizontalem lineam, ſiue ſupra,
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in punctis, per quæ aſcendentium ſignorum lineæ duci debent. </
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>
<
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xml:space
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">Poſtea notentur ex propoſ. </
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<
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<
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">hu-
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ius lib. </
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>
<
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xml:space
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">in linea horizontali puncta, quibus eam arcus ſignorum ſecant. </
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>
<
s
xml:id
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xml:space
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">In hæc enim proiicientur
<
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vmbrę gnomonis in orientali horologio, cum ſigna oriuntur, at in horologio occidentali, cum oc
<
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cidunt. </
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>
<
s
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xml:space
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">Quæ quidem puncta hac etiam arte inueniemus, etiamſi in horologio arcus omnium ſi-
<
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">Inuentio
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pun-
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ctorum in linea
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<
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horizontali u-
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triuſque horolo
<
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gii Met
<
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idiani,
<
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in quæ vmbra
<
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<
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ſtyli ea dit, cum
<
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ſigna oriuntur,
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aut occidunt.</
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gnorum non ſint deſcripti. </
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<
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xml:space
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">Ex quinta tabella propoſ. </
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<
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">9. </
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<
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">huius lib. </
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<
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xml:space
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">accipiemus arcus ſemidiurnos
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ſignorum, eosq́ue in vtroque horologio à G, verſus F, ſupputabimus, & </
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<
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">à terminis ſupputationũ
<
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<
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per E, centrum ducemus rectas ſecantes æquinoctialem lineam in punctis, per quæ rectæ ęquino-
<
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ctialem lineam ſecantes ad angulos rectos ſecabunt lineam horizontalem in punctis, in quibus ar-
<
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cus ſignorum eandem diuidunt; </
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>
<
s
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xml:space
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">cum, Sole exiſtente in initiis ſignorũ, vmbra ſtyli in ea pũcta pro-
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ijciatur, cum oritur, vel occidit, propterea quòd dictæ lineæ perpendiculares indicent horas or-
<
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tus, & </
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>
<
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xml:space
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">occaſus ſolis in initiis ſignorum exiſtentis, vt ex iis, quæ propoſ. </
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<
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<
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">huius lib. </
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<
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xml:id
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xml:space
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">demonſtraui-
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mus, conſtat. </
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<
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xml:space
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">Cum ergo in ortu, & </
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<
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xml:space
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">occaſu Solis vmbra ſtyli proiiciatur in lineam horizontalẽ, ma-
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nifeſtum eſt, in illis punctis Solem oriri, & </
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<
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xml:id
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">occidere, in quibus lineam horizontalem ſecant dictæ
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lineæ perpendiculares.</
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<
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</
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<
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<
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">EADEM puncta hoc modo reperiemus. </
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<
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xml:space
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">Ex recta E A, figuræ vltimæ propoſ. </
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<
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<
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">huius lib.
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</
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>
<
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xml:id
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xml:space
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<
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xlink:label
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xml:space
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">Qua ratione all
<
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ter inueniantur
<
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puncta in linea
<
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horizõtali, quæ
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prius.</
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>
detrahatur recta æqualis ſtylo horologii Meridiani, & </
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>
<
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="
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xml:space
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">per punctum extremum@huius ducatur ad
<
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<
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xlink:label
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xlink:href
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">40</
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E A, perpendicularis, quæ erit linea horizontalis in orientali horologio. </
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<
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xml:id
="
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xml:space
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">Si igitur à puncto extre-
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mo lineæ, quæ ſtylo ex E A, æqualis abſciſſa eſt, ſumantur interualla omnium punctorum, quibus
<
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dicta perpendicularis à radijs ex M, O, Q, S, V, Y, per centrum E, ductis ſecatur, & </
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>
<
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xml:id
="
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xml:space
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">in lineã ho-
<
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rizontalem horologii orientalis ex A, loco ſtyli transferantur, habebuntur puncta, quæ inquirun-
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tur; </
s
>
<
s
xml:id
="
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xml:space
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">vt perſpicuum eſt, ſi Horizon A B C D, in horologio orientali conc
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/>
ipiatur in propria poſi-
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tione, ita vt punctum extremum rectæ aſſumptæ in E A, ſit in A, loco ſtyli, & </
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<
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xml:id
="
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xml:space
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">perpendicularis per
<
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illud punctum ducta fiat eadem, quæ horizontalis linea in horologio, ac proinde E, in centro mun
<
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di, tanquam vertex gnomonis, ſtatuatur. </
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>
<
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xml:space
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">Ita enim fiet, vt Sole exoriente in pũctis M, O, Q, S, V, Y,
<
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vmbra ſtyli proiiciatur in dicta puncta lineę horizontalis in orientali horologio, vt patet. </
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>
<
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xml:id
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xml:space
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">Eodem
<
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pacto in occidentali horologio eadem puncta deprehendentur, ſi ex E C, eiuſdem figurę propoſ.
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</
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<
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<
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position
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xlink:label
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xml:space
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">50</
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>
21. </
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<
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">huius lib. </
s
>
<
s
xml:id
="
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"
xml:space
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">abſcindatur recta æqualis ſtylo, & </
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>
<
s
xml:id
="
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xml:space
="
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">per extremum punctum ad E C, perpendicula-
<
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ris ducatur pro horizontali linea horologij occidentalis, &</
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>
<
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xml:id
="
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xml:space
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">c.</
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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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">ITAQVE ſi puncta inuẽta in æquinoctiali linea cum punctis reſpondentiũ ſignorũ in orien
<
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tali horolog@o, oppoſitorũ vero in occidẽtali, inuentis in linea horizõtali iungantur rectis lineis,
<
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/>
deſcripta erunt ſigna aſcendentia. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Nam cum in horologio orientali vmbra proiicitur in aliquod
<
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/>
punctum horizontalis lineæ, oritur ſignum illud, in quo Sol exiſtit; </
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>
<
s
xml:id
="
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"
xml:space
="
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">cum autem vmbra in occiden
<
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/>
tali horologio cadit in aliquod punctum lineæ horizontalis, oritur ſignum oppoſitum, cum illud
<
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/>
tunc, in quo Sol eſt, occidat,</
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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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">POSSVMVS quoque in duobus tropicis pũcta reperire ex tertia, & </
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>
<
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xml:space
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">quarta tabella propoſ.
<
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</
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>
<
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xml:id
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xml:space
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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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">Quomodo in
<
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/>
tropicis inueſti-
<
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gentur puncta
<
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aſcendentium
<
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ſignorum.</
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>
9. </
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>
<
s
xml:id
="
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xml:space
="
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">hu@us lib. </
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>
<
s
xml:id
="
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"
xml:space
="
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">per quæ ſigna aſcendentia duci debent; </
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>
<
s
xml:id
="
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xml:space
="
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">deſcribendo videlicet occulte lineam illius
<
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horæ, qua ſignorum quodlibet oritur. </
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>
<
s
xml:id
="
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xml:space
="
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">Vbi enim hæc tropicum ſecuerit, per illud punctum ducen
<
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da eſt linea illius ſigni aſcedentis, vt in horologio horizontali factum eſt. </
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>
<
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xml:space
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">Perutile autẽ eſt, </
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</
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