Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ad ſectorem GEB; </
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<
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to igitur maior erit proportio trianguli GAE, ad triangulum GEI,
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quàm ſectoris GCE, ad ſectorem GEB: </
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maior erit proportio trianguli GAI, ad triangulum GEI, quàm ſe-
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ctoris GCB, ad ſectorem GEB: </
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<
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triangulum GEI, itarecta AI, ad rectam IE; </
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ad ſectorem GEB, ita angulus BGC, ad angulum BGE. </
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ſexti.</
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erit quoque proportio AI, ad IE, quàm anguli BGA, hoc eſt, quàm an-
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guli ſibi æqualis IKE, ad angulum IGE: </
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<
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GI, ad IK. </
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ti.</
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quàm anguli IKE, ad angulum IGE. </
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">IISDEM poſitis, Diameter ſphæræ ad diametrum paralleli per
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punctum obliqui circuli, per quod maximus circulus è polo tranſit,
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deſcripti, minorem rationem habet quàm circunferentia maximi pa
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rallelorum intercepta inter maximum circulum primo poſitum, & </
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maxmum circulum per polos parallelorum tranſeuntem, ad circun-
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ferentiam obliqui circuli inter eoſdem circulos interceptam.</
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diametri ſphæræ ad diametrum paralleli _GE,_ quàm circunferentiæ _BC,_ ad circun-
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ferentiam _DE._ </
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_
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,_ quæ diametri illorum
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erunt, cum _AB,_ per eorum po-
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los ductus ipſos ſecet bifariã,
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& </
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go _BI,_ diameter etiã ſphæræ.
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nitur rectus ad _AB,_ tranſi-
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bit _DE,_ per polos ipſius _AB._ </
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Eodem modo _
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C,_ per polos
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eiuſdem _AB,_ tanſibit, cum re-
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ctus ad ipſum ponatur. </
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re M, punctum, vbi ſe mutuo
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ſecant, polus erit circuli _AB;_
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quod rectum eſt ad circulum
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_AB,_ inæqualiter diuidetur in
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E, puncto, vbi circuli _DE, GE,_
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ſe interſecant, minorq́ pars
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erit _ED:_ </
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cus _MD, ML,_ æquales ſunt, quod rectæ illis ſubtenſæ, ex defin. </
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