Clavius, Christoph
,
Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur
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GNOMONICES
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perbolæ illius hyperbolis huius ſint æquales, cum ab æqualibus ſty lis proiiciantur vmbræ eas de-
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ſcribentes in planis Meridiano circulo æquidiſtantibus, congruent quoque hyperbolæ hyperbo-
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lis, nempe hyperbola ♋, congruet hyperbolæ ♑, & </
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<
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<
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xml:space
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">Eademq́ue ratio
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elt de cæteris hyperbolis aliorum ſignorum. </
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<
s
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xml:space
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">Quæ cum ita ſint, liquido conſtat, partem ſuperio-
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rem abſciſſam in vtrolibet horologio exhibere horologium in facie oppoſita plani, ſi inuertatur,
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vt diximus.</
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<
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<
s
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xml:space
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">RVRSVS linea horizontalis A B, vtrumque horologium diuidit in diurnum, & </
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<
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xml:space
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">nocturnũ,
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xlink:label
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xml:space
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">Linea horizon-
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talis diuidit ho
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rologium Me-
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ridianũ in diur
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num, noctur-
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numq́ue.</
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ſicut de Verticali horologio dictum eſt propoſ. </
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<
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xml:space
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<
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talem, hoc verò ſupra eandem exiſtit. </
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<
s
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"
xml:space
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">Nam in partem quidem ſuperiorem orientalis horologii
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proiiceretur vmbra ſtyli poſt mediam noctem vſque ad ortum Soli, niſi denſitas terræ obſtaret: </
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<
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xml:space
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partem verò ſuperiorem horologii occidentalis vmbra ſtyli caderet poſt occaſum Solis vſque ad
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mediam noctem, ſi eam Sol poſſet illuminare.</
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<
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</
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<
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<
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xml:space
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">EOSDEM arcus ſignorum deſcribemus hac ratione. </
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<
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">Ducta recta D C, vtcunque pro radio
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xml:space
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">Alia deſcriptio
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arcuum ſigno-
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rum in horolo-
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gio Meridiano.</
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Æquatoris, & </
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<
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">hinc inde radiis aliorum ſignorum deſcriptis, vt propoſ. </
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<
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horizontali dictum
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eſt, transferantur in
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Aequatoris radium
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D C, ex D, omnia ho
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raria interualla inter
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cepta inter E, centrũ
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<
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circuli F G H I, præ-
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cedentis propoſitio-
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nis, & </
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<
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noctialem A C, ita vt
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recta D C, æqualis
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ſit ſpatio E S, vel EC;
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</
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<
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xml:space
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">& </
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<
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xml:space
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">recta D T, ſpatio
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E N, vel E M, &</
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imprimendo puncta
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in recta D C, per quę
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<
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axi mundi D G, re-
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ctã D C, ad rectos an
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gulos ſecanti paralle
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læ agantur, (quod
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quidem facile fiet, ſi
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omnia puncta rectæ
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D C, traducantur in
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rectã G F, ipſi D C,
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parallelam, &</
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<
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his parallelis numeri horarum ſpatijs horarijs translatis reſpondentes apponantur. </
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<
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xml:space
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">Nam ſi par-
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tes harum parallelarum interceptæ inter radium Æquatoris D C, & </
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<
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transferantur in reſpõdentes horarias lineas horologij à linea æquinoctiali A C, imprimendo pũ
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cta, & </
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<
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xml:space
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">per hęc puncta lineæ curuæ ducantur, vt in ſuperioribus horologiis diximus, deſcripti erũt
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rurſus paralleli Zodiaci. </
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<
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">Æqualiter autem diſtant quilibet paralleli oppoſiti ab æquinoctiali linea.
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</
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<
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xml:space
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">Nam cum anguli, quos Æquatoris radius D T, facit cum radiis oppoſitorum ſignorum, æquales
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<
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ſint, quòd inſiſtant huiuſmodi anguli ad centrum æqualibus arcubus æqualium declinationum;
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</
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<
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<
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<
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xml:space
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inter α, & </
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<
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">radios quorumlibet oppoſitorum ſignorum ęquales. </
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<
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">quod eſt propoſitum. </
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<
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xml:space
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">Idem etiam
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<
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liquido conſtat ex Analemmate huius propoſ. </
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<
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xml:space
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">ſi recte conſiderentur triangula E K N, E K Q;
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</
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<
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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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">Quo pacto ar-
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cus ſignorũ op-
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poſitorum una
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cademq́ue ope-
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ra deſcribantur
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in horologio
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Meridiano.</
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E K O, E K R; </
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<
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<
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<
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">Vnde vna eademq́ue opera quosuis parallelos oppoſitos in horo
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<
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logio deſcribemus, ſi hinc inde à linea æquinoctiali in lineis horariis puncta imprimamus æquali
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ter à linea æquinoctiali diſtantia. </
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<
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xml:space
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">Hanc autem poſteriorem parallelorum Zodiaci deſcriptionem
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hoc modo demonſtrabimus.</
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<
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">INTELLIGATVR in horologio ſtylus A E, ad rectos angulos inſiſtere plano horologii,
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<
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">Demonitratio
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poſterioris de-
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ſcriptionis pa-
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ralleloru
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m So
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lis.</
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& </
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<
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">figura radiorum Zodiaci proxime conftructa circa verticem ſtyli E, circumuerti verſus planum
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horologii, ita vt punctum D, coniungatur cum puncto E, ſeu cum centro mundi, & </
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<
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perpetuo æquidiſtet lineæ horæ 6. </
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<
s
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">hoc eſt, cum axe mundi ſit coniuncta, ac propterea recta D C, à
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plano Aequatoris non recedens illo motu occurrat ſemper lineæ æquinoctiali. </
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<
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">Quo poſito, cadet
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in hac circumuolutione punctum T, v. </
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<
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<
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">in punctum N, propterea quòd in conſtructione recta
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D T, ſumpta fuit æqualis rectæ E N. </
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<
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xml:space
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">Eſt enim recta E N, cadens ex puncto E, in ſublimi poſito,
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nempe à vertice ſtyli, in punctum N, æqualis rectæ E N, in plano horologii; </
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<
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