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

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10593

THEOREMA 12. PROPOS 12.

1114.

Slin ſphæra maximi circuli tangant vnum, eun
demq́; parallelorum, intercipiantq́; ſimiles paralle-
lorum circunferentias inter vtrũque maximorum
circulorum interiectas; alius autem maximus cir-
culus ad parallelos obliquus circulos tangat ma-
iores illis, quos tangunt maximi circuli primò po-
ſiti, ſecetq́; obliquus idem circulus eoſdem maxi-
mos circulos primò poſitos in punctis poſitis in-
ter maximum parallelorum, & circulum, quem tan
gunt circuli maximi primo poſiti: Diameter ſphæ
ræ ad diametrum circuli, quem tangit obliquus
circulus, maiorem rationem habet, quàm circun-
ferentia maximi paralleli intercepta inter circulos
primo poſitos, eundemq́; circulum tangentes ad
circunferentiam obliqui circuli inter eoſdem cir-
culos interceptam.

IN ſphæra duo maximi circuli AB, CD, tangant eundem parallelum
AC, intercipiantq́; ſimiles paralle-

109[Figure 109] lorum circunferentias inter ipſos in-
teriectas; alius autem circulus maxi-
mus EF, tangat parallelum EG, ma-
iorem parallelo AC, in E, ſitque o-
bliquus ad parallelos, & ſecet duos
priores AB, CD, inter maximum pa
rallelorum HF, & parallelum AC,
in punctis I, K. Dico maiorem eſſe
rationem diametri ſphæræ ad diame-
trum paralleli EG, quàm circunfe-
rentiæ BD, ad circunferentiam IK.
Per L, enim polum parallelorum, &
puncta E, I, K, maximi circuli deſcri-
2220.1.huius. bantur LH, LM, LN; ac per K, pa-
rallelus KO, ſecanscirculum AB, in P. Quoniam igitur maior eſt ratio dia-
metri ſphæræ ad diametrum circuli EG, quàm arcus HM, ad arcum EI; ra-
3311.huius.

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