Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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uallis autem AC, BC, circuli non maximi delineentur KCN, OCP, qui il-
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lis maximis paralleli erunt: </
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<
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xml:space
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">tam hi, quam illi ad circulum ABDGH, re-
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cti erunt, cum ille per horũ polos trãſiens ad ipſos ſit rectus. </
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fuſio vitetur, in circulo ABDGH, ſeorſum deſcripto ſint communes ſectio-
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nes ipſius, & </
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">circulorum ex polis A, B, deſcriptorum, nempe DF, GH, com-
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munes ſectiones ipſius, & </
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">maximorum circulorum DLEF, GMEH, quæ
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ipſorum diametri erunt ſeſe in centro ſphæræ X, interſecantes: </
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communes ſectiones eiuſdem, & </
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in S; </
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">quæ ipſis DF, GH, parallelæ erunt; </
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<
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xml:space
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">diametri circulorum KCN,
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OCP; </
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">quòd maximus circulus ABDGH, per eorum polos tranſiens eos
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bifariam ſecet, nimirum per eorum diametros. </
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tri AX, ſecans KN, in Y; </
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diametri AX, BX, perpendiculares ad circulos per DF, KN, GH, OP,
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ductos; </
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B, ducantur per X, ſphæræcen-
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trum: </
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R, recti erunt, ex defin. </
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OP, perpendiculares AV, KQ,
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KT. </
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">Erit igitur, per ea, quæ in
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tractatione ſinuum ſcripſimus,
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AV, ſinus rectus arcus AB; </
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KY, ſinus rectus arcus AK, hoc
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eſt, arcus AC, cum arcus AK,
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AC, ex defin. </
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<
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verſus arcus BO, id eſt, arcus BC, cum arcus BO, BC, æquales ſint, ex defin. </
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poli. </
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AB, AC, propterea quod, ex defin. </
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rans, æqualis eſt arcui AC: </
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ſinum verſum tertij arcus BC, & </
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qualium AB, AC, hoc eſt, ſinum verſum arcus BK. </
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verſus arcus KC, in circulo non maximo KCN, cum recta ex C, in commu-
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nes ſectiones circulorum KCN, OCP, cum circulo ABDGH, hoc eſt, in
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punctum S, cadens, (quæ quidem ad circulũ ABDGH, recta eſt, vtpote com-
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munis ſectio circulorum KCN, OCP, ad eundem circulum ABDGH, re-
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ctorum) ſinus rectus ſit eiuſdem arcus KC. </
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ſus arcus DL, hoc eſt, anguli A, qui quidem arcus arcui KC, ſimilis eſt. </
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monſtrandum igitur eſt, ita eſſe quadratum ſinus totius, hoc eſt, rectangulum
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ſub DX, XA, contentum, ad rectangulum ſub ſinubus rectis AV, KY, ar-
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cuum AB, AC, contentum, vt eſt ſinus verſus DZ, anguli A, ad KT, diſ-
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fer entiam inter BR, ſinum verſum arcus BC, & </
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differentiæ arcuum inæqualium AB, AC. </
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<
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ctus Y, angulo recto R; </
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angulo ISR, trianguli ISR, æqualis, hoc eſt, angulo ad verticem KST.
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angulus XAV, trianguli XAV, reliquo angulo SKT, trianguli SKT,
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æqualis Quam ob rem erit, vt XA, ad AV, ita SK, ad KT. </
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