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

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8068 cunferentia A F B, in F, in partes inæquales, & ſit F B, minor. Ex F, demitta-
tur in planum circuli A C B D, perpendicularis F L, quæ ad partes ſegmenti
A D B, cadet, propterea quod ſegmentum A F B, ad ſegmentum A D C, eſt
inclinatum, ita vt punctum L, ſit vel intra ſegmentum A D B, vel extra, vel
certe in ipſa circunferentia A D B. Per centrum autem E, & punctum L, dia-
meter agatur C D, & ex F, in circunferentiam A C B, plurimæ rectæ cadant
F B, F G, & c. Dico omnium minimam eſſe F B; & F G, minorem quàm F H:
omnium autem maximam eſſe F C: Item F A, eſſe omnium minimam, quæ ex
F, in circunferentiam A C, cadunt; & F I, minorem quàm F K. Ducantur ex
L, rectæ lineæ L B, L G, L H, L A, L I, L K, eruntque omnes anguli ad L,
quos facit perpendicularis F L, recti, ex defin. 3. lib. 11. Eucl.

88[Figure 88]

Quoniam igitur recta L D, eſt omnium minima, (hæc autem linea nihil eſt om
117. vel 8. vel
15. tertil. nino in ea figura, vbi punctum L, cadit in D.) & L B, minor, quàm L G, L H,
L C, L K, L I, L A, & omnium maxima L C, & c. demonſtrabimus, vt in præ-
227. vel 8. vel
15. tertij. &
47. primi. cedenti, rectam F B, eſſe omnium minimam, & F G, minorem quàm F H: Item
F C, omnium maximam, & F A, minimam omnium ex F, in circunferentiam
A C, cadentium; & F I, minorem quàm F K. Si igitur recta linea ſecans circu-
lum, & c. Quod erat oſtendendum.

THEOREMA 3. PROPOS. 3.

SI in ſphæra duo circuli maximi ſe mutuo ſe-
cent, ab eorum verò vtroque æquales circunfe-
rentiæ ſumantur vtrinque à puncto, in quo ſe ſe-
cant: Rectæ lineæ, quæ extrema puncta circunfe-
rentiarum connectunt ad eaſdem partes, æquales
inter ſe ſunt.

IN ſphæra duo circuli maximi A B C, D B E, ſe mutuo ſecent in B, & in
vno quoque vtrinque à B, ſumantur duo arcus æquales B A, B C, & B D, B

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