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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M R, ſinum complementi diſtantię Solis à meridie K, ita K λ, medietas ſinus altitudinis meridianæ ad
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λT, differentiam inter T N, ſinum altitudinis Solis, & </
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<
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xml:space
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">rectam λ N, medietatem ſinus altitudinis me-
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ridianæ: </
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<
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xml:space
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">Sifiat vt ſinus totus adſinum complementi diſtantię Solis à meridie, ita medietas ſinus altitu-
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dinis meridianæ ad aliud, inuenietur
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recta, quæ addita medietati prędi-
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ctę, ſi diſtantia à meridie minor eſt
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quadrante, vel ab eadem medietate
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ablata, ſi maior eſt diſtantia à meri
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die quadrante, dabit ſinum altitudi-
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nis Solis tempore obſeruationis. </
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autem distantia Solis à meridie qua-
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dranti fuerit ęqualis, erit ipſamet
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medietas λ N, ſinus altitudinis So
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lis tempore obſeruationis. </
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quoniam in ſecunda figura, vbi pa-
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rallelus totus ſupra Horizontem ex-
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tat, & </
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<
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">illum non tangit, eſt vt K M,
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ſinus totus ad M R, ſinum complemẽ
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ti diſtantiæ Solis à meridie K, ita K λ, medietas differentiæ K θ, inter ſinum maioris altitudinis meridia
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næ, & </
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<
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">ſinum minoris altitudinis meridianæ ad λ T, differentiam inter T N, ſinum altitudinis Solis, & </
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rectam λ N, compoſitam ex dictamedietate λ θ, ac ſinu θ N, minoris altitudinis meridianæ: </
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<
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xml:space
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">Si fiat,
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vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita medietas differentiæ inter ſinum maio-
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ris altitudinis meridianę, & </
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<
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">ſinum minoris altitudinis meridianæ ad aliud, reperietur recta, quæ ablata
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ex recta compoſita ex dicta medietate, ac ſinu minoris altitudinis meridianæ, ſi diſtantia Solis à meridie
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fuerit quadrante maior, vel eidem rectæ compoſitæ addita, ſi diſtantia quadrante fuerit minor, dabit ſinũ
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altitudinis Solis tempore obſeruationis, Si autem diſtantia quadranti æ qualis extiterit, erit ipſamet re-
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cta compoſita ex dicta medietate, & </
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<
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">ſinu altitudinis meridianæ minoris, ſinus altitudinis Solis tempore
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obſeruationis. </
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<
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xml:space
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">Quę omnia ex hiſce duabus appoſitis figuris facile colligi poſſunt.</
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<
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">VICISSIM, ſi fiat, vt K λ, medietas ſinus altitudinis meridianæ in priori figura, vel medietas
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rectæ K θ, in poſteriori, quæ differentia eſt inter ſinum maioris altitudinis meridianæ, & </
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<
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">ſinum minoris al-
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titudinis meridianæ, ad λ T, differentiam inter ſinum altitudinis Solis, & </
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<
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">medietatem ſinus altitudinis
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meridianæ in priori figura, vel inter ſinum altitudinis Solis, & </
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<
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">rectam λ N, quę componitur ex medieta-
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te differentiæ inter ſinum maioris altitudinis meridianæ, & </
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<
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">ſinum minoris altitudinis meridianæ, atque
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ſinu minoris altitudinis meridianæ, vt in poſteriori figura apparet, ita ſinus totus ad aliud, reperietur ſi-
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nus complementi diſtantiæ Solis à meridie K. </
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<
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">Quod complementum additum quadranti, quando ſinus al-
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titudinis Solis minor eſt, quàm recta λ N, hoc eſt, quàm medietas ſinus altitudinis meridianæ in priori
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figura, vel quàm recta compoſita ex ſinus minoris altitudinis meridianæ, & </
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<
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">medietate differentiæ inter ſi-
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num maioris altitudinis meridianæ, & </
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<
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">ſinum minoris altitudinis meridianæ in figur a poſteriori, dabit di-
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stantiam Solis à meridie, vt in poſteriori figura apparet. </
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">Idem vero complementum à quadrante ſublatũ,
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quando ſinus altitudinis Solis maior eſt, quàm dicta recta λ N, relinquet diſtantiam Solis à meridie.
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</
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<
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">SED facilius hęc res conficietur illo modo, quem vltimo loco tractauimus, antequàm problema hoc
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propoſitum per triangula ſphærica explicaremus. </
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<
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">Nam ſi fiat, vt K M, ſinus totus ad K R, ſinum verſum
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diſtantiæ Solis à meridie K, ita K λ, medietas ſinus altitudinis meridianæ in priori figura, vel in poſterio-
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ri ita medietas differentiæ inter ſinum maioris altitudinis meridianę, & </
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<
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">ſinum minoris altitudinis meri-
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dianę, ad aliud, nota euadet K T, differentia inter ſinum maioris altitudinis meridianæ, vel certe in prio-
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ri figura ipſius altitudinis meridianę, & </
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<
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">ſinum altitudinis Solis quæſitę.</
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<
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">ITEM ſi fiat, vt medietas præ dicta ad differentiam inter ſinum maioris altitudinis meridianæ, vel
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certe in priori figura ipſius altitudinis meridianę, & </
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<
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">ſinum altitudinis Solis, ita ſinus totus ad aliud, pro-
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ueniet ſinus verſus distantiæ Solis à meridie K. </
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<
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">Vt ex ijſdem figuris manifeſtum eſt.</
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<
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">QVOD ſi polus mundi in vertice, ſeu polo Horizontis extiterit, erit in quolibet die Solis alti-
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tudo perpetuo æqualis declinationi paralleli, quem tunc Sol deſcribit motu primi mo-
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bilis: </
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<
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">Quia tunc Aequator idem est, qui Horizon, & </
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zontis à parallelis Solis, vel Aequatoris non diffc-
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runt, vt perſpicuum eſt.</
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