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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linquunt arcus ſemidiurnos quadrantis Eclipticæ borealis inter principium ♈, & </
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poſiti; </
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<
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principium ♋, interiecti.</
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<
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xml:space
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<
s
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tc
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Eclipticę ſiue auſtralis, ſiue borealis, omnes amplitudines ortiuę occiduęve, habebuntur etiam latitu-
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dines ortiuæ, ſiue occiduę pro omnibus punctis Eclipticę, vt ex demonſtr atione patet: </
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<
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clinationes punctorum vnius quadrantis Eclipticæ, ex quibus latitudines ortiuę & </
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<
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æquales ſunt declinationibus reliquorum punctorum Eclipticæ, vt alibi ostenſum eſt à nobis.</
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<
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<
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ad datam poli altitudinem inuenire.</
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<
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<
s
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xml:space
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">QVAMVIS problema hoc per triangula ſphærica poſſit abſolui, vt in ſcholio ſequenti de-
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monſtrabimus, multo tamen breuius, & </
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<
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</
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<
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">Sit enim Meridianus Analemmatis A B C D, cuius centrum E; </
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<
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<
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ticalis B D; </
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<
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<
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<
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xml:space
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">diameter paralleli Solis K L, ſiue borealis,
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ſiue auſtralis, circa quam ſemicirculus paralleli deſcribatur K P L, cuius centrum erit punctum
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M, vbi axis, & </
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<
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<
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K L, ipſam K L, bifariam diuidit. </
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<
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xml:space
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">Ex puncto autem S, vbi diameter paralleli diametrum Hori-
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<
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zontis ſecat, erigatur ad K L, perpendicularis S Q, quæ communis ſectio erit Horizontis, & </
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<
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leli. </
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<
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munis ſectio ad eundem perpendicularis; </
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<
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<
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<
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paralleli K L. </
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<
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">Cum ergo communis illa ſectio per punctum S, vbi ſe mutuo ſecant Horizon, & </
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parallelus in Meridiano, tranſeat, erit S Q, perpendicularis exiſtens ad k L, communis ſectio Ho-
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rizontis, & </
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<
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<
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">Igitur K Q, arcus erit ſemidiurnus paralleli, cum intercipiatur inter Hori-
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zontem, qui per punctum Q, tranſit, & </
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<
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diameter paralleli Horizontis X Y, infra Horizontem, in quo exiſtit Sol, cum crepuſculum matu-
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<
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tinum incipit, vel veſpertinum deſinit, ita vt tam arcus A X, quàm C Y, comprehendat grad. </
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<
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</
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<
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">Tot enim gradibus ab Horizonte abeſt Sol in initio matutini crepuſculi, vel in fine veſpertini,
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vt communis eſt opinio, licet aliqui auctores minorem faciant hanc diſtantiam, & </
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<
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vt refert Petrus Nonius in parte ſecunda libri de crepuſculis propoſ. </
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<
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<
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paralleli Solis diametrum K L, in T, puncto, à quo ad K L, educatur perpendicularis T R, quæ
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communis ſectio erit paralleli Solis, & </
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<
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ſculi. </
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<
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eſt, erit & </
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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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">ad rectam K L, in Meridiani plano exiſtentem perpendicularis, qualis eſt recta T R. </
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<
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longitudo crepuſculi arcus Q R, quandoquidem Sol in puncto R, exiſtit, quando occupat Hori-
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<
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zontis parallelum X Y, in quo principium eſt crepuſculi matutini, vel finis veſpertini; </
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<
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<
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cto Q, oritur, vel occidit. </
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<
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xml:space
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">Cum enim T R, ſit communis ſectio paralleli Solis, & </
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<
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ralleli X Y, ſecabunt ſeſe mutuo hi paralleli in R, atque adeò Sol in puncto R, exiſtens vtrumque
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parallelum poſſidebit. </
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<
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xml:space
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ante diximus, S Q, ſit communis ſectio Horizontis, & </
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<
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<
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ad A C, perpendicularis K N, ſecans X Y, in O, eritq́; </
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<
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rallelo K L, exiſtentis, hoc eſt, ſinus arcus K A; </
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<
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xml:space
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<
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xml:space
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">recta K O, compoſita ex K N, ſinu altitudinis
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meridianæ, & </
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<
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xml:space
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">N O, ſinu diſtantię Solis ſub Horizonte in principio crepuſculi matutini, uel fine
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veſpertini. </
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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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ex arcu ſemidiurno k Q, & </
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<
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">arcu crepuſculi Q R, quem videlicer Sol in ſuo parallelo percurrit,
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<
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gnitudo, quo
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modo inueſtige
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tur, Sole exi-
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ſtente in quo-
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cunque paralle
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10.</
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dum crepuſculum durat, compoſitus.</
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<
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">ITAQVE quoniam in triangulo K O T, recta S N, baſi O T, parallela eſt, erit vt k N, ſinus
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altitudinis Meridianæ ad K O, rectam compoſitam ex ſinu altitudinis meridianæ, & </
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<
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diſtantiæ Solis ſub Horizonte in principio crepuſculi matutini, vel fine veſpertini, ita K S, ſinus
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verſus ſemidiurni arcus ad K T, ſinum verſum arcus compoſiti ex arcu ſemidiurno, & </
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<
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<
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ſculi. </
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<
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">Quamobrem ſi fiat, vt ſinus altitudinis meridianæ (quo pacto autem meridiana altitudo in-
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ueniatur ex cognita declinatione Solis, in ſequenti ſcholio exponemus) ad rectam compoſitam
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ex ſinu altitudinis meridianę, & </
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<
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<
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<
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">(tot enim gradibus ſecundum communem ſenten-
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tiam Sol infra Horizontem deprimitur in Verticali per centrum Solis tunc tranſeuntis) ita ſinus
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verſus arcus ſemidiurni ad aliud, habebitur ſinus verſus arcus compoſiti ex arcu ſemidiurno, & </
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<
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arcu crepuſculi. </
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<
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xml:space
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">Ex hoc ergo ſinu verſo ita inueniemus quantitatem crepuſculi. </
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<
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