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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172152GNOMONICES rca ducta recta Q F, ſinus rectus erit eiuſdem arcus B F, (Sinus enim verſus cuiuſuis arcus terminatur
in ſinu recto eiuſdem arcus, vt conſtat ex tractatione ſinuum) & ad meridianam lineam B H, perpendi-
cularis. Eſt autem recta F L M, ad eandem meridianam lineam perpendicularis; propterea quòd, ex
1129. primi.

126[Figure 126]221033204430 ſcholio propoſ. 27. lib. 3. Eucl. parallela eſt ipſi S T, ob æquales arcus F T, M S. Igitur recta F L M, per
punctum Q, tranſit. Quoniam vero & planum horologĳ, & planum parallelogrammi per O P, E Q,
ductirectum eſt ad Meridianum, erit quoque communis eorum ſectio ad eundem recta in Q, ac propte-
5519. vndec.6640 rea, per defin. 3. lib. 11. Eucl. ad rectam B Q, in Meridiano exiſtentem perpendicularis in puncto Q. Re-
cta igitur F Q, perpendicularis ad B Q, communis ſectio erit horologĳ & parallelogrammi per O P,
E Q, ducti: ac proinde latus eiuſdem parallelogrammi ex P, ductum in rectam Q F, cadet; quandoqui-
dem recta F Q, & latus dictum in plano illius parallelogrammi exiſtunt. Et quoniam E P, E Q,
rectis A Z, A H, parallelæ ſunt oſtenſę, erit angulus P E Q, angulo Z A H, ęqualis: Eſt autem angu-
7710. vndec. lus Z A H, rectus: oſtendimus enim ſupra Z Y, perpendicularẽ eſſe ad axem. Igitur & angulus P E Q,
rectus eſt. At recta F Q, perpendicularis oſtenſa ad Meridianum, perpendicularis quoque eſt, per defin.
3. lib. 11. Eucl. ad rectam E Q, in Meridiano exiſtentem. Igitur rectę Q F, E P, in eodem plano paral-
lelogrammi per O P, E Q, ducti exiſtentes, cum ad rectam E Q, ſint perpendiculares, parallelę inter
8828. primi. ſe erunt. Parallelogrammum ergo erit quadrilaterum, cuius latera ſunt E Q, E P, latus cylindri du-
9950 ctum ex P, & portio rectę Q F, inter Q, & dictũ latus ex P, ductum. Eſt enim & latus ex P, ductum
rectę E Q, parallelum, quòd illud latus, & recta E Q, ſi producantur, coniungant rectasęquales in ba-
101033. primi. ſibus cylindri ęqualibus, nempe rectam E P, & aliam rectam d b, in oppoſita baſi ei reſpondentem, quę
videlicet ſinus rectus eſt arcus b e, quatuor horarum, quemadmodum & E P, ſinus rectus eſt arcus B P,
quatuor horarum; quę quidem rectæ ęquidiſtantes ſunt, cum ſint ſectiones baſium ęquidictantium factę
111116. vndec. à parallelogrammo per O P, E Q, ducto. Quapropter recta E P, ęqualis erit oppoſito lateri prædicti
121234. primi. parallelogrammi, hoc eſt, ſegmento rectę Q F, inter Q, & latus cylindri ex P, ductum. Eſt autem E P,
ſinus rectus arcus B P, quatuor horarum ęqualis ſinui recto K μ, (qui ex K, ducitur perpendicularis ad
B H) arcus C K, quatuor quoque horarum, quòd circuli θ Y B Z, C R X, æquales ſint, ex conſtructione.
Igitur & portio rectæ Q F, intercepta inter Q, & latus cylindri ex P, ductum ęqualis erit ſinui recto
K μ. Cum ergo Q L, ipſi K μ, ſit ęqualis, ob parallelogrammum L μ, tranſibit omnino latus cylindri ex
131334. primi.

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