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

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7866 tiore minor eſt. Si verò recta linea ſubiectum circu
lum ſecans ſit eius diameter, & reliqua omnia ea-
dem ſint, vt ſupra; recta linea ſubtendens mino-
rem partem circunferentiæ ſegmenti inſiſtentis,
minima eſt rectarum ductarum ab illo eodem
puncto ad primi, & ſubiecti circuli circunferen-
tiam; ea verò, quæ maiorem partem circunferen-
tiæ ſegmenti inſiſtentis ſubtendit, maxima eſt.

RECTA linea A B, ſecet circulum A C B D, cuius centrum E, in partes

87[Figure 87] inæquales, quarum maior ſit A C B: Inſiſtat
autem ipſi A B, rectum circuli ſegmentum
A F B, ſemicirculonó maius, quod in partes in-
æquales diuidatur in F; ſitque minor pars B F:
Ex F, demittatur in circulum A C B D, per-
1111. vndec. pendicularis F L, quæ in A B, communem ſe-
2238. vndec. ctionem cadet: Per E, autem, & L, diameter
agatur C D; & ex F, in circunferentiam A C B,
maioris ſegmenti circuli A C B D, plurimę
rectæ cadãt F B, F G, F H, F C, F A, F I, F K.
Dico omnium minimam eſſe F B, & F G, mino-
rem, quàm F H; Omnium autem maximam eſ
ſe F C. Item F A, eſſe omnium minimam, quæ
ex F, in portioncm A C, cadent; & F I, minorem, quàm F K. Ducantur ex L,
lineæ rectę L G, L H, L I, L K; eruntq́ue ex defin. 3. lib. 11. Eucl. omnes an-
guli ad L, quos recta F L, facit, recti. Quoniam igitur recta L D, eſt omnium
rectarum ex L, cadentium minima, & L B, minor, quàm L G, L H, L C, L K,
337. tertij. L I, L A; erunt quadrata ex F L, L B, minora quadratis ex F L, L G: Eſt au-
tem tam quadratum ex F B, quadratis ex F L, L B, quàm quadratum ex F G,
4447. primi. quadratis ex F L, L G,æquale. Igitur erit quoq; quadratum ex F B, minus qua-
drato ex F G; atq; adeo & recta F B, minor erit quàm F G. Nõ aliter oſtẽdemus,
rectá F B, minoré eſſe, quàm F H, F C, F K, F I, F A. Quare F B, omniũ minima eſt.

RVRSVS quia L G, minor eſt, quàm L H, erunt quadrata ex F L, L G,
557. tertij. minora quadratis ex F L, L H: Eſt autem tam quadratum ex F G, quadratis
ex F L, L G, quàm quadratum ex F H, quadratis ex F L, L H, æquale. Igitur
6647. primi.& quadratum ex F G, quadrato ex F H, minus erit; atq; adeo & recta F G, mi-
nor erit, quàm recta F H.

AMPLIVS quia L C, omnium ex L, cadentium maxima eſt; erunt qua-
777. tertij. drata ex F L, L C, maiora quadratis ex F L, L K: Eſt autem tam quadratum
ex F C, quadratis ex F L, L C, quàm quadratum ex Fk, quadratis ex F L, Lk,
8847. primi. æquale. Igitur & qua dratum ex F C, maius erit quadrato ex F K; ac proinde &
recta F C, maior erit, quàm recta F K. Non aliter demonſtrabimus, rectam F C,
maiorem eſſe, quàm F I, & F A. Eſt ergo recta F C, omnium maxima.

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