Theodosius <Bithynius>; Clavius, Christoph - Theodosii Tripolitae Sphaericorum libri tres

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9886

HOC _etiam Theorema demonſtrabitur ex propoſ. 8. buius lib. quemadmodum_
_propoſitio 9. ex propoſ. 6. fuit oſtenſa, dummodo maximi circuli propoſ. 9. ex A,_
_prodeuntes tangant eundem circulum minoremillo, quem_ D C, _tangere debet, & c._

THEOREMA 10. PROPOS. 10.

1111.

SI polus parallelorum ſit in circunferentia ma
ximi circuli, quem duo alij maximi circuli ad angu
los rectos ſecent, quorum alter ſit vnus parallelo-
rum, alter verò ſit obliquus ad parallelos; in hoc
autein obliquo circulo ſumãtur duo quælibet pun
cta ad eaſdem partes maximi illius paralleli, perq́;
polum parallelorum, & per vtium que illorum pun
ctorum deſcribantur maximi circuli: Erit, vt cir-
cunferentia maximi parallelorum intercepta inter
maximum circulum primò poſitum, & proximum
maximum circulum per polum, & per vnum pun-
ctorum deſcriptum, ad circunferentiam obliqui
circuli inter eoſdem circulos interceptam, ita cir-
cunferentia maximi parallelorum intercepta inter
duos magnos circulos per polum, perque vtrum-
que punctorum deſcriptos, ad circunferentiam
aliquam, quæ ſit minor, quam circunferentia obli-
qui circuli inter vtrum que punctum intercepta.

SIT polus A, parallelorum in circunferentia maximi circuli A B, quem
duo alij maximi circuli B D, C D, ſecent ad angulos rectos, & ſit B D, paral-
lelorum maximus, & C D, ad parallelos obliquus; in quo ſumptis duobus
punctis vtcunque E, F, deſcribantur per A, polum, & per E, F, circuli ma-
2220. 1. huius ximi A E G, A F H. Dico, vt eſt arcus B H, ad arcum C F, ita eſſe arcum H G,
ad arcum minorem arcu F E. Aut enim arcus C F, F E, commenſurabiles
ſunt, aut incommenſurabiles. Sint primum commenſurabiles, vt in prima fi-
gura; & inuenta eorum maxima menſura P, diuidantur arcus C F, F E, in ar-
333. decimi. cus maximæ menſuræ æquales, perque puncta diuiſionum, & polum A, circu-
4420. 1. huius li maximi ducantur I M, K N, L O. Quoniam igitur arcus continui C L, L

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