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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parallela agatur F K, communis videlicet ſectio Verticalis circuli, & </
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<
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triangulorum per axẽ in G, H, I, K, &</
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<
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<
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xml:space
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">Si igitur puncta G, H, I, K, in lineam Verticalem A D, horologij transferantur ex A, infra hori-
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zontalem lineam, & </
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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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ctiones conicæ tranſeuntes per puncta G, H, I, K, (quæ quidem conicæ ſectiones hyperbolæ ſunt,
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ex propoſ. </
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<
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<
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">cum Meridianus, cui planum horologij æquidiſtat, per polos paral-
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lelorum Horizontis deſcriptus ipſos omnes ſecet.) </
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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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tes, quo longius productæ fuerint ex vtraque parte Verticalis lineæ A D, deſcripti erunt paralleli
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Horizontis. </
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<
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</
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<
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">ALITER Deſcripto quadrante A B C, cuiuſcunque magnitudinis, diuiſoq́ue in 90. </
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xml:space
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pa@allelorũ Ho
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rizontis i
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n eo-
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dem horologi
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o
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Meridi
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ano.</
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vel in pauciores partes pro numero parallelorum deſcribendorum, emittantur ex centro A, per
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puncta diuiſionum rectæ lineæ, quæ reſpon-
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debunt radiis parallelorũ Horizontis in qua
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drante E C D, præcedentis figuræ contentis;
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</
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<
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mus rectæ A B, ſit paralleli Horizontis grad. </
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15. </
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<
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<
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<
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xml:space
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cant. </
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<
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xml:space
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ſitionis ſumantur interualla inter centrum
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F, & </
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<
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talem lineam interſecant, eaque ex A, hu-
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ius figuræ in rectam A B, tranferantur, aſcri-
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ptis numeris Verticalium linearum prope
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puncta, quæ translata interualla in recta A B,
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terminant, atq; </
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<
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xml:space
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A C, parallelæ.</
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Quod facile fiet, ſi ipſi A B, pa
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rallela ducatur G H, & </
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<
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A B, transferantur, &</
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<
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<
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xml:space
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gura pręcedentis propoſ. </
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<
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transferatur in rectam A B, huius figuræ
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<
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vſquead punctũ D, apponendo numerũ 60.
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</
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<
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">& </
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<
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">per D, ipſi A C, parallella agatur D E, &</
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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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">HAC antem figura ita conſtructa, deſcri
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bentur paralleli Horizontis hoc modo. </
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<
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xml:space
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ſa inter rectam A B, radium v. </
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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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nea horizontalis in figura præcedẽtis propoſ. </
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<
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xml:space
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">ſecatur à lineis Verticalibus, in lineas Verticales cor
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reſpondentes numeris in recta A B, notatis, ſignando puncta in Verticalibus lineis: </
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<
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">vt v. </
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<
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<
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D E, accipiatur æqualis L M, in Verticali linea grad. </
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<
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<
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">ſic de cæteris. </
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<
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xml:space
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poſite iungantur linea quadã inflexa, deſcriptus erit parallelus Horizontis gr. </
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<
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<
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xml:space
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">Eodem modo
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reliqui paralleli Horizontis deſcribentur, ſi rectæ inter lineam A B, & </
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<
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xml:space
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<
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tis interiectæ transferantur in lineas Verticales correſpondentes, ex linea horizontali, &</
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<
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<
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hac ratione demonſtrabimus.</
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</
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<
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<
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<
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">Demonſtratio
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poſterioris de-
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ſcriptionis pa-
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rallelorum Ho
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rizontis.</
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angulos inſiſtere plano horologij in puncto A, & </
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<
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">figura proxime cõſtructa circa punctũ F, quod
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eſt in centro mundi, circumduci verſus horologiũ, ita vt punctum A, coniungatur cũ centro mũ-
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di, ſeu puncto E, & </
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<
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">recta A C, perpetuo lineæ Verticali A D, æquidiſter, hoc eſt, coniuncta ſit cũ
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axe Horizontis, eiuſque parallelorum, & </
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<
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">idcirco recta A B, à plano Horizontis non recedens oc-
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currat ſemper illo motu horizontali lineæ. </
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<
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xml:space
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">Nam in hac circumductione cadet punctum D, v. </
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<
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<
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punctum L, horizontalis lineæ, propterea quòd rectæ F L, in præcedenti propoſ. </
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<
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<
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æqualis, A D. </
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<
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">Eſt enim recta F L, cadens ex puncto F, in ſublimi, nempe à Vertice ſtyli, rectæ
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F L, in plano horologii æqualis; </
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<
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">vt conſtat, ſi triangulum F A L, in ſublimi conferatur cum trian-
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gulo F A L, in plano horologij, quemadmodũ propoſ. </
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<
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dictum eſt. </
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<
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xml:space
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">Cum igitur tam recta L M, quàm D E, axi Horizontis æquidiſtet, erunt etiam L M,
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<
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D E, inter ſe parallelæ, & </
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<
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cum in illa circumductione in L, conueniant; </
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<
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xml:space
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">ac proinde cum L M, ſumpta ſit æqualis rectæ D E,
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cadet punctum E, in punctum M, atque adeo radius paralleli Horizontis grad. </
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<
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<
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horologii in puncto M. </
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<
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xml:space
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">Per punctum ergo M, tranſibit arcus paralleli Horizontis grad. </
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<
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<
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in illud radius dicti paralleli in illa circumuolutione incidat, vt demonſtratum eſt. </
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<
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demus punctum F, eiuſdem radii cadere in punctum N, & </
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<
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<
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xml:space
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zontis in eodem horologio Meridiano deſcripſimus. </
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<
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