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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rca ducta recta Q F, ſinus rectus erit eiuſdem arcus B F, (Sinus enim verſus cuiuſuis arcus terminatur
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in ſinu recto eiuſdem arcus, vt conſtat ex tractatione ſinuum) & </
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<
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cularis. </
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<
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ſcholio propoſ. </
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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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xml:space
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">parallela eſt ipſi S T, ob æquales arcus F T, M S. </
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<
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xml:space
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">Igitur recta F L M, per
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punctum Q, tranſit. </
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<
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">planum horologij, & </
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">planum parallelogrammi per O P, E Q,
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ductirectum eſt ad Meridianum, erit quoque communis eorum ſectio ad eundem recta in Q, ac propte-
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<
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xml:space
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">19. vndec.</
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rea, per defin. </
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<
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<
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<
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<
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">Eucl. </
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<
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xml:space
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">ad rectam B Q, in Meridiano exiſtentem perpendicularis in puncto Q. </
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<
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">Re-
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cta igitur F Q, perpendicularis ad B Q, communis ſectio erit horologij & </
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<
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xml:space
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">parallelogrammi per O P,
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E Q, ducti: </
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<
s
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">ac proinde latus eiuſdem parallelogrammi ex P, ductum in rectam Q F, cadet; </
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<
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dem recta F Q, & </
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<
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">latus dictum in plano illius parallelogrammi exiſtunt. </
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<
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xml:space
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">Et quoniam E P, E Q,
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rectis A Z, A H, parallelæ ſunt oſtenſę, erit angulus P E Q, angulo Z A H, ęqualis: </
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<
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xml:space
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">Eſt autem angu-
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<
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xml:space
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">10. vndec.</
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lus Z A H, rectus: </
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<
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">oſtendimus enim ſupra Z Y, perpendicularẽ eſſe ad axem. </
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<
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xml:space
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">Igitur & </
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<
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">angulus P E Q,
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rectus eſt. </
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<
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xml:space
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">At recta F Q, perpendicularis oſtenſa ad Meridianum, perpendicularis quoque eſt, per defin.
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</
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<
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<
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">lib. </
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<
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<
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">Eucl. </
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<
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">ad rectam E Q, in Meridiano exiſtentem. </
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<
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xml:space
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">Igitur rectę Q F, E P, in eodem plano paral-
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lelogrammi per O P, E Q, ducti exiſtentes, cum ad rectam E Q, ſint perpendiculares, parallelę inter
<
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<
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ſe erunt. </
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<
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">Parallelogrammum ergo erit quadrilaterum, cuius latera ſunt E Q, E P, latus cylindri du-
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<
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ctum ex P, & </
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<
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">portio rectę Q F, inter Q, & </
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<
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">dictũ latus ex P, ductum. </
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<
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">Eſt enim & </
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<
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">latus ex P, ductum
<
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rectę E Q, parallelum, quòd illud latus, & </
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<
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">recta E Q, ſi producantur, coniungant rectasęquales in ba-
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<
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xml:space
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ſibus cylindri ęqualibus, nempe rectam E P, & </
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<
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">aliam rectam d b, in oppoſita baſi ei reſpondentem, quę
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videlicet ſinus rectus eſt arcus b e, quatuor horarum, quemadmodum & </
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<
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">E P, ſinus rectus eſt arcus B P,
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quatuor horarum; </
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<
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">quę quidem rectæ ęquidiſtantes ſunt, cum ſint ſectiones baſium ęquidictantium factę
<
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<
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à parallelogrammo per O P, E Q, ducto. </
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<
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<
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parallelogrammi, hoc eſt, ſegmento rectę Q F, inter Q, & </
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<
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<
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">Eſt autem E P,
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ſinus rectus arcus B P, quatuor horarum ęqualis ſinui recto K μ, (qui ex K, ducitur perpendicularis ad
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B H) arcus C K, quatuor quoque horarum, quòd circuli θ Y B Z, C R X, æquales ſint, ex conſtructione.
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</
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<
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<
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">portio rectæ Q F, intercepta inter Q, & </
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<
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">latus cylindri ex P, ductum ęqualis erit ſinui recto
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K μ. </
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<
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">Cum ergo Q L, ipſi K μ, ſit ęqualis, ob parallelogrammum L μ, tranſibit omnino latus cylindri ex
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<
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