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

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THEODOSII

SPHAE RICORVM
LIBER SECVNDVS.

44[Figure 44]

DEFINITIO.

IN ſphæra circuli ſe mutuo tangere di-
cuntur, cum communis ſectio plano-
rum vtrumque circulum tetigerit.

THEOREMA 1. PROPOS. 1.

111

IN ſphæra paralleli circuli circa eoſdem po-
los ſunt.

IN ſphæra A B C D E F, paralleli circuli

45[Figure 45] ſint B F, C E. Dico eos circa eoſdem polos
eſſe. Sint enim A, D, poli circuli B, F, & cõ-
2221. 1. huius. nectatur recta A D, quæ ad circulum B F, re-
cta erit, tranſibitq́; per centrum ſphæræ.
3310. 1. huius. Quoniam igitur recta A D, ad circulũ B F,
perpendicularis eſt, erit quoque ad circulũ
parallelum C E, perpendicularis. Quare cũ
44Schol. 14.
vndec. tranſeat per centrum ſphæræ, vt oſtenſum
eſt, cadet in polos circuli C E. Sunt ergo
558. 1. huius. A, D, poli circuli C E: ſunt autem & poli
circuli B F. In ſphæra igitur paralleli circu-
li B F, C E, circa eoſdem polos A, D, ſunt. Quod erat demonſtrandum.

THEOREMA 2. PROPOS. 2.

662

IN ſphæra circuli, qui ſunt circa eoſdem po-
los, ſunt paralleli.

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