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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triangulum A B K, concipiatur animo conuerti circa B K, donec rectum ſit ad horologii planũ,
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ac proinde in plano Verticalis circuli inclinationem plani ad Horizontem metientis, & </
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<
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xml:id
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xml:space
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">per B K,
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ducti, erit recta A B, communis ſectio Horizontis, & </
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<
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xml:space
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">dicti Verticalis, & </
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<
s
xml:id
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"
xml:space
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">iuncta recta A F, cõmu-
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nis ſectio Horizontis, ac Meridiani, propterea quod tam Horizon, quàm Meridianus per cen-
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trum Mundi A, & </
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>
<
s
xml:id
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xml:space
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">per pũctum F, ducitur, Quare angulus A F B, quem linea meridiana A F, Ho-
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rizontis cum linea horizontali F B, plani horologij conſtituit, æqualis erit complemento decli-
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nationis horologij à Verticali proprie dicto; </
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>
<
s
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echoid-s26977
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xml:space
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">ac proinde cum angulus A B F, rectus ſit (quoniá
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enim triangulum A B K, rectum eſt, & </
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<
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xml:id
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xml:space
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">ad planum horologij, & </
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<
s
xml:id
="
echoid-s26979
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xml:space
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">ad Horizontem, erunt quoque
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duo hæc plana ad triangulum recta. </
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<
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xml:space
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">Igitur & </
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>
<
s
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xml:space
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">cõmunis eorũ ſectio F B, ad idẽ perpendicularis erit
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<
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xlink:label
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note-0426-01
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xlink:href
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xml:space
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">19. vndec.</
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<
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xml:space
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ac propterea & </
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<
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xml:space
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">ad rectam B A, perpendicularis erit, ex defin. </
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<
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xml:space
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">3. </
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<
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xml:space
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">lib. </
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<
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xml:space
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<
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xml:space
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">Eucl.) </
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<
s
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"
xml:space
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">erit reliquus an-
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gulus B A F, declinationi horologii à Verticali proprie dicto æqualis, hoc eſt, angulo B E G, in
<
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figura latitudinum ortiuarum propoſ. </
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<
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xml:space
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<
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<
s
xml:id
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xml:space
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">Quoniá igitur anguli E, G, trianguli G E H,
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in figura latitudinum ortiuarum æquales ſunt angulis A, B, trianguli B A F, in ſigura huius pro-
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poſ. </
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">latera E G, A B, quibus dicti anguli adiacent, æqualia quoque ex conſtructione, erũt quo-
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que latera E H, H G, lateribus A F, F B, æqualia, & </
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<
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xml:id
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xml:space
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">angulus H, angulo A F B. </
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<
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xml:space
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">Quamcbrem ſi
<
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xml:space
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">26. primi.</
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recta E G, figuræ latitudinum ortiuarum rectę A B, in horologio congruat, congruet quoque re-
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cta E H, rectæ A F, & </
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<
s
xml:id
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xml:space
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">recta H G, rectæ F B, ob æqualitaté angulorum, & </
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<
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xml:space
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">denique tota H G, pro
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ducta in utramque partem toti horizontali lineæ congruet; </
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<
s
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xml:space
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">atque idcirco radii latitudinum orti-
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uarum, occiduarumve lineę horizontali occurrent in punctis tanto ſpatio à pũcto B, vel F, diſtá-
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tibus, quanto ſpatio à puncto G, vel H, abſunt puncta, vbi radii latitudinum rectam G H, ſecát,
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<
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& </
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<
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xml:space
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">c. </
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<
s
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xml:space
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">Signa igitur aſcendentia Zodiaci in eodem horologio declinante ſimul & </
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<
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xml:space
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mus. </
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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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<
s
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">SI eadem aſcendentia ſigna deſcribere velim{us} ſecundum doctrinam Andreæ Schoneri, vtemur
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">Aſcendentis
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figna, quo pa-
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cto ex doctina
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Andreæ Scho-
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neri deſcriban
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tur.</
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>
hac arte. </
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<
s
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xml:space
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">Inpriori figura ſcholij propoſ. </
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<
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<
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">lib. </
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<
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">2. </
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<
s
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xml:space
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">ex recta E D, vel E B, abſcindatur recta E H, æqualis
<
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rectæ L M, quæ in horologio intercipitur inter centrum L, & </
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>
<
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xml:id
="
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xml:space
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">punctum M, vbi æquinoctialis linea, & </
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>
<
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xml:id
="
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xml:space
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<
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meridiana ſe interſecant, & </
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>
<
s
xml:id
="
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xml:space
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">in H, conſtituatur cum recta B D, angul{us} æqualis ei, quem in horologio li-
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nea æquinoctialis cum recta L M, efficit, hac tamen lege, vt poſito centro E, in centro L, & </
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<
s
xml:id
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xml:space
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">recta E D,
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<
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ſupra rectam L M, recta per punctum H, ducta, & </
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<
s
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xml:space
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">dictum angulum conſtituens congruat lineæ æqui-
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noctiali. </
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<
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xml:space
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">Deinde interualla prædictæ rectæ per H, ductæinter H, & </
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<
s
xml:id
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xml:space
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">lineas ſignorum interiecta transfe-
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rantur in lineam æquinoctialem ex puncto M, imprimendo puncta in ipſa æquinoctiali linea. </
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>
<
s
xml:id
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xml:space
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">Si enim ex
<
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puncto, vbi meridiana linea, & </
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<
s
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xml:space
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">horizontalis ſe interſecant, per hæc puncta æquinoctialis lineæ ducantur
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rectæ occultæ, ſecabuntur ambo tropici in punctis, per quæ ſigna aſcendẽtia erunt ducenda, hoc ordine ſer
<
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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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">Ordo ſignorũ
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aſcendentium
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in tropicis.</
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uato. </
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<
s
xml:id
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xml:space
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">Si horologium vergat in ortum, pertinebit punctũ, vbi tropic{us} ♑, lineam horizontalẽ interſecat,
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ad ♑, punctum verò, in quo ſe interſecant tropic{us} ♋, & </
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<
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xml:id
="
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xml:space
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">horizontalis linea, ad ♋. </
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<
s
xml:id
="
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xml:space
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">Proximum deinde
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punctum in tropico infra horizontalem lineam debetur illi ſigno, quod proximè oritur post ♑, vel ♋,
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vt ſigno ♒, vel ♌, & </
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<
s
xml:id
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xml:space
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">ita deinceps ſecundum ſucceſſionem ſignorum. </
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>
<
s
xml:id
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xml:space
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">Si autem in occaſum deflectat ho-
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rologium, tribuendum erit punctum, vbitropicus ♑, & </
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<
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xml:id
="
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xml:space
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">linea horizontalis ſe mutuo ſecant, ſigno ♋;
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</
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<
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xml:space
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">punctum vero, vbi tropicus ♋, eandem horizontalem lineam ſecat, conueniet ſigno ♑. </
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<
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xml:space
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">Deinde proxi-
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<
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mum punctum infra lineam horizontalem illi ſigno reſpondebit, quod ante ♑, vel ♋, oritur, vt ſigno
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♐, vel ♊, & </
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<
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xml:space
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">ſic deinceps contra ſignorum ſucceſſionem. </
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<
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xml:space
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">Exhis facili negotio intelligem{us}, quib{us} ſi-
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gnis reſpondeant puncta tropicorum ſupra horizontalem lineam inuenta. </
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<
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xml:space
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">Nam ſi infra ſeruant ordinẽ
<
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ſecundum ſucceſſionem ſignorum, ſeruabunt ſupra horizontalem lineam ordinem contra ſucceſſionem ſi-
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gnorum, & </
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<
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xml:space
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">contra, vt ex figuris aſcendentium ſignorum, qu{as} hactenus in varijs planis conſtruxim{us},
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perſpicuum eſt. </
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<
s
xml:id
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xml:space
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">Semper autem quælibet recta occulta ex puncto, vbi ſe interſecant meridiana linea, at-
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que horizontalis, ducta per puncta in linea æquinoctiali inuenta, pertinet ad duo ſigna oppoſita, quem-
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admodum & </
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>
<
s
xml:id
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xml:space
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">in priori figura radiorum ſignorum aſcendentium quælibet linea ad duo oppoſita ſigna per-
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tinet: </
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<
s
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xml:space
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<
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xml:space
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">g. </
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<
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xml:space
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">vnum punctum, per quod dicta linea occulta tranſit, pertinet ad ♊, alterum pun-
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ctum, quod eadem recta monſtr at ſiue in oppoſito tropico, ſiue in eodem, pertineat ad ♐, & </
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<
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<
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xml:space
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">vt ex ſu-
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<
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periorib{us} figuris ſignorum aſcendentium, qu{as} in varijs planis depinximus, manifestum eſt.</
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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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">IN propoſito exemplo, vbi meridiana linea, atque æquinoctialis æquidiſtantes ſunt, recta L M,
<
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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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">Quuando æqui
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noctialis linea,
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& meridiana
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parallelæ ſunt,
<
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quid agendum
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in aſcendenti-
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bus ſignis deli-
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meandis.</
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>
ęquinoctialem lineam non ſecat, ſed ei parallela eſt, vnde cum ea angulum conſtituere non poteſt. </
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>
<
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xml:space
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">In
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priori ergo figura ſignorum ducenda erit ipſi E D, linea parallela reſpondens æquinoctiali lineæ in horolo
<
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gio, hac ratione. </
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>
<
s
xml:id
="
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xml:space
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">Ex E C, ſumatur E K, æqualis rectæ, quæ in horologio inter centrum L, & </
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>
<
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xml:id
="
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xml:space
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">punctum,
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vbi linea horizontalis æquinoctialem diuidit, intercipitur, & </
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<
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xml:space
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">per K, excitetur ad E K, perpendicularis
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ſecans lineas ſignorum in punctis, quæ accepta ex puncto K, & </
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>
<
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xml:id
="
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xml:space
="
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">translata in lineam æquinoctialem ex di-
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cto puncto, vbi ſe ſecant linea æquinoctialis, & </
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>
<
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xml:id
="
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xml:space
="
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">horizontalis, dabunt in æquinoctiali linea pun-
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cta, vt pri{us}.</
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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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">QVOD ſi in horologio primæ figuræ propoſ. </
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<
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<
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