Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
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">ITEM quia L A, minor eſt, quàm L I, Lk, L C; </
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">erunt quadrata ex F L,
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L A, minora quadratis ex F L, L I: </
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dratis ex F L, L A, quam quadratum ex F I, quadratis ex F L, L I, æqua-
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le. </
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<
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">quadratum ex F A, minus erit quadrato ex F I; </
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<
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cta quoque F A, minor erit quàm recta F I. </
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<
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">Eodem modo oſtendemus, rectam
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F A, maiorem eſſe, quàm F K, F C. </
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<
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">Eſt ergo F A, omnium rectarum ex F, in
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arcum A C, cadentium minima.</
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<
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<
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">erunt quadrata ex F L, L I,
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minora quadratis ex F L, L K: </
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tis ex F L, L I, quàm quadratum ex F K, quadratis ex F L, L K, æquale. </
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tur & </
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<
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">quadratum ex F I, minus erit quadrato ex F K, ideoque & </
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<
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nor erit, quàm recta F K.</
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<
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diameter, demonſtratum à nobis iam eſt theoremate tertio ſcholij propoſ.</
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<
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neceſſe, idem hoc loco demonſtrare. </
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hic proponuntur. </
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Quod oſtendendum erat.</
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huius.</
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<
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">SI recta linea ſecans circulum ſegmentum au-
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ferat, quod ſemicirculo minus non ſit, ſuper ipſa
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autem recta linea ſtatuatur aliud circuli ſegmen-
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tum, quod & </
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natum ſit ad alterum ſegmentum, quod ſemicircu
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lo maius non eſt; </
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menti circunferentia in partes inæquales: </
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linea ſubtendens minorem circunferentiæ partem
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minima eſtrectarum omnium ductarum ab illo
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puncto, à quo ipſa ducitur, ad ſubiecti circuli cir-
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cunferentiam illam, quæ ſemicirculo minor non
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eſt: </
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<
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<
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mentum A C B, ſemicirculo non minus, ſed vel ſemicirculo æquale, vt in pri-
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ma figura, vel maius, vt in alijs figuris; </
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tum aliud circuli A F B, ſemicirculo non maius, ſed vel ſemicirculo æquale,
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vt in poſtrema trium figurarum, vel minus, vt in primis duabus figuris, & </
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clinatum ad ſegmentum alterum A D B, quod ſemicirculo maius non eſt, cum
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A C B, vel ſemicirculo æquale, vel maius ponatur. </
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