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

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8573 erit & arcus G Q, omnium ex G, cadentium minimus, hoc eſt, minor, quàm
11Schol. 21. 2
huius. G H: quod arcus G Q, G H, minores ſint ſemicirculo, cum ſe non inter-
ſecent, antequàm parallelo N O, occurrant. Vterque igitur arcus F G,
G H, vtroque G P, G Q, maior eſt. Et quoniam recta per G, & centrum
ſphæræ ducta, id eſt, communis ſectio circulorum maximorum A P, E C, ſe-
cant paralleli I K, planum intra ſphæram; (non enim recta illa ad centrum
ſphæræ perueniet, hoc eſt, ad centrum maximi circuli B D, niſi prius planum
circuli I K, ſecet; quòd parallelus I K, poſitus ſit inter maximum parallelo-
rum, & punctum G.) ſecabit eadem recta planum paralleli N O, extra ſphæ-
ram, ſirecta illa, & planum circuli ad partes G, producantur: propterea
quòd punctum G, poſitum eſt inter maximum parallelorum, & parallelum
N O. Quoniam igitur duo circuli maximi A P, E C, ſe mutuo ſecant in G,
puncto, & à circulo E C, vtrinque à puncto G, duo arcus æquales ſumpti
ſunt G F, G H, & per F, H, plana parallela circulorum I K, N O, ducta,
quorum N O, occurrit commnni ſectioni circulorum maximorum A P,
E C, extra ſphæram, vt oſtenſum eſt, eſtq́ue vterque arcuum G F, G H, ma-
ior vtroque arcuum G P, G Q, erit arcus G P, maior arcu G Q. Eſt au-
224. huius. tem arcus G P, arcui I L, & arcus G Q, arcui L N, æqualis. Igitur & arcus
3310. 2. huius. I L, arcu L N, maior erit. Quare ſi in circunferentia maximi circuli ſit po-
lus, & c. Quod demonſtrandum erat.

THEOREMA 6. PROPOS. 6.

SI in circunferentia maximi circuli ſit polus
parallelorum, huncq́; maximum circulum ad an-
gulos rectos ſecentduo alij circuli maximi, quo-
rum alter ſit vnus parallelorũ, alter verò obliquus
ſit ad parallelos; ſumantur autem ab obliquo circu
lo æquales circunferentiæ deinceps ad eaſdem par
tes maximi illius paralleli, & per puncta terminan-
tia æquales circũferentias, perq́; polum, deſcriban-
tur maximi circuli: Hi circunferentias inæquales
intercipient de maximo parallelorum, quarum
propior maximo circulo primo poſito ſemper erit
remotiore maior.

IN circunferentia maximi circuli A B C D, ſit A, polus parallelorum,
eumq́ue ſecent duo maximi circuli B D, E C, adangulos rectos, quorum B D,
ſit parallelorum maximus, at E C, ad parallelos obliquus, ex quo

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