Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ſunt autem & </
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<
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<
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">15. primi.</
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æqualia, cum ſint ſemidiametri circuli A D C E. </
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<
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æqualia erunt:</
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<
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<
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">ſemidiametri K D, K E, æquales. </
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<
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rectæ D M, E N, æquales erunt. </
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<
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">Rurſus quoniam recta B K, ex B, polo circuli
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A D C E, ad eiuſdem centrum K, ducta, recta eſt ad planum circuli, erit an-
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huius.</
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gulus M K L, in triangulo K L M, rectus, ex defin. </
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tur K M L, acutus erit. </
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<
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">Cum ergo duo anguli F M N, H N M, duobus ſint
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rectis æquales; </
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ti oſtendemus, arcus E H, minor erit, arcu D F; </
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ſint arcus B D, B E, quòd rectæ ſubtenſæ B D, B E, ex defin. </
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<
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les, maior erit arcus B H, arcu B F. </
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mutuo ſecent, &</
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">_QVOD_ autem arcus _E H,_ arcw _D F,_ minor ſit, facile demonſtrabimus, hoc propoſi-
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to theoremate prius demonſtrato.</
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<
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">SI arcui circuli recta ſubtendatur, ad quam ex arcu duæ perpen-
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diculares demittantur auferentes verſus terminos arcus duos arcus
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æquales; </
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<
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duæ perpendiculares ad rectam ſubtenſam ducantur auferẽtes duas
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rectas æquales; </
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arcu demittantur duæ perpendiculares B E, C F, auferentes duos arcus
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A B, D C, æquales. </
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æquales rectas A E, D F. </
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tertij.</
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recta B C, erunt A D, B C, parallelæ,
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ob æqualitatem arcuum A B, D C: </
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autem & </
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grammum igitur eſt B E F C, atque adeò
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& </
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<
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<
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<
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ctæ ſubtenſæ A B, D C, æquales ſunt; </
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<
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lia. </
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dratis ex D F, C F; </
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<
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æqualia erunt quadrata rectarum A E, D F; </
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<
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D F, æquales erunt. </
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<
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<
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D F. </
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<
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æquales, ſit, ſi fieri potest, maior arcus A B, à quo æqualis abſcindatur
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A G, & </
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<
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proxime demonſtr atum eſt, recta A H, rectæ D F, æqualis, atque adeò
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& </
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<
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maior arcu D C: </
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">eademque ratione neque minor erit. </
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