Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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æquales; </
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<
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xml:space
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">atque adeò cum H Q, ſit quadrans, omnes illi arcus quadrantes
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erunt. </
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<
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xml:space
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">Quare cum demonſtratum ſit eos tranſire per polos tangentium, erunt
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puncta Q, S, T, V, R, poli circulorum tangentium, quæ quidem omnia
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1. huius.</
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ſunt in parallelo Q T R, quod vltimo loco proponebatur demonſtrandum.
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<
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">Iam vero quia arcus circulorum maximorũ ex E, polo circuli maximi A B C D,
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ad Q, S, T, V, R, polos tangentium ducti metiuntur diſtantias poli E, à
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polis tangentium; </
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<
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">eſtq́ue omnium maximus E Q; </
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<
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huius.</
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les verò E S, E T; </
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<
s
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xml:space
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">denique E T, maior, quàm E V, quòd omnes hi arcùs
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ſint ſemicirculo minores; </
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<
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xml:space
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">(eſt enim E Q, quadrante E A, minor; </
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<
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reliqui eum non ſecabunt citra punctum Q, ideoque ſemicirculo minores
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erunt.) </
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<
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">erit circulus H K, minimè inclinatus ad circulum maximum A B C D;
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huius.</
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& </
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">at M P, N K, æqualiter, ſeu ſimiliter; </
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N K, quod primo loco demonſtrandum proponebatur. </
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ra maximus circulus. </
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tangentium à contactibus ad nodos ſint æqua-
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les;</
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<
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">RVRSVS in ſphæra maximus circulus A B C D, cuius polus E, tangat
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circulum A F, ſecet autem alium huic parallelum G B H D, poſitum inter
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ſphæræ centrum, & </
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<
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que E, polus maximi circuli A B C D, inter vtrumque circulum A F, G B H D:
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Tangãt deinde in punctis
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M, N, circuli maximi
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M O, N P, circulũ G B H D,
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ſecantes A B C D, in O,
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P, nodis, ſintq́ue arcus
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M O, N P, æquales. </
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co circulos M O, N P,
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ſimiliter inclinari ad ma-
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ximum circulum A B C D.
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lum circuli A B C D, & </
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polum parallelorum cir-
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culus maximus G A C: </
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per I, polum parallelorũ,
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& </
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<
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culi maximi I M, I N, qui
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per polos quoque circu-
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lorum tangentium tran-
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ſibũt;</
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angulos rectos ſecabunt.
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<
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Quoniam igitur ſegmenta circulorum æqualia, nempe ſemicirculi, qui ten-
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dunt ex M, & </
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<
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inſiſtunt diametris circulorum M O, N P, (eſt enim communis ſectio </
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