Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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minor eſt. </
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ferentiam circuli cadunt, à maxima æqualiter diſtantes.</
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<
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">_SVPER_ diametro _A D,_ circuli _A B C D E,_ conſtituatur rectum circuli ſegmen-
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tum _A F D,_ quod ſecetur non bifariam in _F,_ ſitque minor pars _A F,_ & </
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<
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</
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<
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xml:space
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">Cadant autem ex _F,_ plurimæ rectæ lineæ _F A, F I, F H, F B, F C, F D, F E._ </
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omnium minimam eſſe _FA;_ </
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<
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_F I,_ minorem, quàm _F H._ </
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">&</
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<
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">c. </
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<
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xml:space
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">Denique duas _F E, F C,_ æquales eſſe, ſi æqualiter diſtent
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à maxima _F D,_ hoc eſt, ſiarcus _D E, D C,_ æquales ſint. </
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<
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num circuli _A B C D E,_ perpendicularis _F G,_ quæ in _A D,_ communem ſectionem ca-
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det: </
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<
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xml:space
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">eritque punctum _G,_ vel inter puncta _A D,_ vt in prima figura; </
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<
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">(Id quod ſemper
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continget, quando ſegmentum _A F D,_ ſemicirculo maius non eſt, quamuis idem accide-
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re poſsit in ſegmento maiore.) </
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<
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">vel extra circulum in diametro _D
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,_
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protracta, vt poſteriores duæ figuræ indicant. </
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">Id quod ſolumin ſegmento, quod ſemi-
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circulo maius ſit, contingere poteſt. </
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">In prima autem figura non erit _G,_ centrum cir-
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culi _A B C D E,_ quod _G F,_ non diuidat bifariam ſegmentum _A F D:_ </
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in poſterioribus duabus figuris erit _G,_ centrum circuli _
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CDE._ </
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<
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_G I, G H,
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, G C, G E;_ </
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<
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<
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80
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/070-01
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Quoniam vero rectarum ex _G,_ in circulum _
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CDE,_ cadentium in prima figura,
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tij.</
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& </
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D;_ </
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C,_ ma-
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ior, quàm _
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_; </
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I,_ minor, quàm _
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H;_ </
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<
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C:_ </
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<
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E,_ æquales: </
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propterea in prima, & </
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<
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,
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F,_ minora duo-
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<
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bus quadratis recfarum _
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,
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F:_ </
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<
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">quibus cum æqualia ſint quadrata rectarum _
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,_
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_FI;_ </
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<
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<
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_F A,_ minor erit quàm _F I._ </
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<
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xml:space
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">Eodem modo oſtendemus _F A,_ in eadem figura prima, & </
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tertia minorem eſſe, quàm F H, &</
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<
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<
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quam _F I,_ vel _F H,_ &</
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<
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<
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">propterea quòd in triangulis _A I F, A H F,_ (in quibus an-
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<
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gulus _A,_ rectus eſt, ex defin. </
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<
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<
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<
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tendit angulum acutum _I,_ vel _H,_ at recta _F I,_ vel _F H,_ &</
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<
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<
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</
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<
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<
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ex _G D, G F,_ maiora duobus quadratis ex _G C, G F:_ </
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<
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<
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dxata ex _F D, F C;_ </
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<
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<
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inde & </
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<
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">recta _F D,_ maior erit, quam recta _F C._ </
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<
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