Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ſcribatur G I H K, qui circulum A C E F D B, ſecabit duobus in punctis, vt in
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I, K, ad angulos rectos. </
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<
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xml:space
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los maximorum circulorum A C E F D B, C D, tranſit, ex conftructione, trã-
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ſibunt hi viciſsim per illius polos. </
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<
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">Puncta igitur C, D, vbi ſe duo hi circuli
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huius.</
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interſecant, poli erunt circuli GIHK; </
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<
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xml:space
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">(alias non vterque circulus A C E F D,
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C D, per polos circuli G I H K, tranſiret) ac proinde ductæ rectę C I, C K, ex
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defin. </
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<
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">poli, æquales erunt, ac propterea & </
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cus C I, C K, inter ſe erunt æquales. </
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autem & </
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">arcus A C, C E, per hypotheſim,
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æquales Reliqui igitur arcus A I, E K, æqua
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les quoque erunt. </
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<
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">Rurſus quia ſemicirculus
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I G K; </
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">ſemicirculo G K H, æqualis eſt; </
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dunt enim ſe mutuo circuli A C E F D B, & </
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G I H K, bifariam; </
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culus eft; </
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">Arcus autem G K H, ſemicireulus
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eſt propter G, H, polos parallelorum.) </
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<
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pto communi arcu G K, erunt reliqui arcus
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G I, H K, æquales. </
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<
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">Quoniam igitur in dia-
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metro circuli I C K D, ſegmenta circulorũ
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æqualia I G K, K H I, quæ ſemicirculi ſunt,
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<
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vt oſtendimus, inſiſtunt ad angulos rectos, ſuntque arcus I G, K H, æquales,
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& </
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<
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">non ſunt ſegmentorum ſemiſſes, ſiue quadrantes, cum G, H, non ſint poli
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circuli I C K D: </
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<
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">Item æquales ſunt arcus I A, K E, vt demonſtratum eſt;
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</
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<
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">erunt rectæ demiſſæ G A, H E, æquales. </
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<
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">Quarc circuli A B, E F, æquales in-
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ter ſe erunt.</
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huius.</
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<
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norom eſſe circulo E F. </
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">Sumpto enim arcu C L, quiæqualis ſit arcui C E, erit,
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vt proxime demonſtratum eſt, parallelus per L, deſcriptus æqualis parallelo
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E F: </
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<
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">ſed parallclus A B, minor eſt, quàm parallelus per L, deſcriptus, cum ille
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longius à maximo parallelorum, atque adeo à centro ſphæræ, abſit. </
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tur quoque eſt parallelus A B, quam E F. </
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ergo paralleli circuli, inter quos & </
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<
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lorum interceptæ inter maximum parallelorum,
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& </
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<
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<
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æquales: </
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<
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">Illæ vero, quæ intercipiuntur inter maio-
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rem parallelum, & </
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<
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<
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">IN ſphæra ſint duo paralleli æquales A B, C D, & </
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<
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fit E F: </
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<
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">Hos autem omnes parallelos ſecet maximus alius circulus A C D B.
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</
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<
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