Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
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<
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tur per centrum illius, erit hęc ad planum circuli perpendicularis,
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& </
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<
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">_IN_ eadem adbuc figura ex _A,_ polo circuli _B G D H,_ per centrum eius _F,_ demit
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tatur linea recta _A F,_ occurrens ſuperficiei ſphæræ in _C._ </
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dicularem eſſe ad planum circuli _B G D H,_ & </
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culi. </
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teribus _A F, F D,_ & </
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quoque duos angulos _A F B, A F D,_ æquales, atque adeo rectos. </
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ctæ _B D,_ inſiſtit ad angulos rectos. </
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inſiſtere rectæ _G H._ </
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recta _A F,_ ad rectos inſiſtet angulos. </
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ad rectos eſt angulos plano circuli _B G D H,_ ducta erit _F A,_ ex centro circuli _F,_ ad pla
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num circuli perpendicularis. </
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vtramque partem protracta in vtrumque polum circuli cadet, ac proinde _C,_ reli-
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quus polus erit circuli _B G D H,_ quod eſt ſecundo loco propoſitum.</
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<
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eius in ipſum ducatur perpẽdicularis recta linea,
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cadet hæc in circuli centrum, & </
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det in reliquum polum ipſius circuli.</
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<
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">IN Sphæra A B C D, ſit circulus B F D G, à cuius polo A, ad eius pla-
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num perpendicularis ducatur A E, occurrens ſuperficiei ſphæræ in C. </
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E, centrum eſſe circuli B F D G, & </
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polum. </
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que B D, F G, connectantur earum extrema
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cum polo A, rectis A B, A D, A F, A G, quæ
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omnes inter ſe æquales erũt, ex definitione po
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li. </
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E, recti, ex defin. </
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quadratũ ex A B, quadratis ex A E, E B, quàm
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quadratum ex A G, quadratis ex A E, E G, æ-
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quale; </
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<
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">adeò cum quadrata rectarum A B,
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A G, æqualium æqualia ſint, erunt quadrata
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ex A E, E B, ſimul quadratis ex A E, G E, ſi-
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mul æqualia. </
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<
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rectarum E B, E G, æqualia erunt, ac proinde & </
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<
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eſt circuli BFDG; </
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