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

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6553

IN ſphæra parallelos A B, C D, E F, ſecet in H, O; I, N; K, M, non ta-
men per polos, circulus maximus GHIKLMNO, ſitque ſupra hemiſphæ-

75[Figure 75] rium G B L, polus conſpicuus P, occultus
autem Q Dico arcum O B H, maiorem eſſe,
quàm vt ſimilis ſit arcui N D I, & N D I, ma
iorem, quàm vt ſimilis ſit arcui M F K. Per
polum enim parallelorum P, & puncta I, N,
1120. 1. huius. deſcribãtur duo circuli maximi P I, P N, ſe-
cantes parallelum A B, ſupra circulũ G I L N,
in R, S: eritque arcus R B S, arcui I D N, ſi-
2210. huius. milis. Cum ergo arcus O B H, maior ſit ar-
cu R B S, maior quoque erit, quam vt ſimilis
ſit arcui N D I. Eodem modo oſtendemus
arcum N D I, maiorem eſſe, quàm vt ſimilis
ſit arcui M F K, ſi nimirum per polum P, &
puncta K, M, duo alij circuli maximi deſcri-
bantur. Igitur ſi in ſphæra maximus circulus parallelos aliquot, & c. Quod
demonſtrandum erat.

COROLLARIVM.

HINC fit, ſimpliciter arcum O B H, maiorem eſſe partem ſui paralleli A B, quàm ar-
cum N D I, ſui paralleli, & c. quandoquidem arcus R B S, tanta pars eſt ſui paralleli, quanta
eſt arcus I D N, ſui paralleli, cum hi arcus demonſtrati ſint eſſe ſimiles, & c.

THEOREMA 19. PROPOS. 21.

3325.

SI in ſphæris æqualibus maximi circuli ad ma-
ximos circulos inclinentur, ille cuius polus ſubli-
mior ſupra planum ſubiectum eſt, inclinatior erit:
illi vero circuli, quorum poli æqualiter diſtant à ſu
biectis planis, æqualiter inclinantur.

IN ſphæris æqua-
libus A B C D, E F G H,

76[Figure 76] quarum centra I, K,
ad circulos maximos
A B C D, E F G H, quo
rum poli L, M, incli-
nẽtur duo circuli ma-
ximi B N D, F O H, quo-
rum poli, P, Q; ſitque
primum polus P, ſubli-
mior ſupra planum cir
culi A B C D, quàm po
lus Q, ſupra planũ cir-
culi E F G H. Dico

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