Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
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">_HINC_ fit, ſi circulorum maximorũ ad alios inclinatorum poli equaliter diſtent
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à polis maximorum, ad quos inclinantur, inclinationes eſſe equales: </
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<
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">cuius vero polus
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vicinior ſit pola eius, ad queminclinantur, inclinationem eſſe maiorem. </
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<
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xml:space
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1. huius.</
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_L P, MQ_, ſint æquales, erunt & </
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_GM;_ </
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<
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">atque adeo poli _P, Q,_ circulorum inclinatorum æqualiter diſtabunt à ſubie-
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ctis planis circulorum _A B C D, E F G H._ </
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<
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<
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">æqualeserunt inclinationes circulorum _B N D, F O H,_ ad circulos _A B C D, E F G H._ </
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Si vero arcus _L P,_ minor ſit arcu _M Q,_ erit reliquus arcus _C P,_ ex quadrante
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maior arcu _G Q,_ reliquo ex quadrante. </
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<
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erit inclinatio circuli _B N D,_ ad circulum _A B C D,_ quam circuli _F O H,_ ad cir-
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culum _E F G H._</
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bunc modum.</
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<
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<
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">SI in ſphæris æqualibus maximi circuli ad maximos circulos
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æqualiter inclinentur, erunt diſtantiæ polorum ipſorum à ſubiectis
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planis æquales: </
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">Illius verò, qui magis inclinatur, ſublimior erit po-
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lus. </
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nantur, à polis circulorum, ad quos inclinantur, æquales erunt: </
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ſtantia vero poli illius circuli, qui magis inclinatur, à polo circuli,
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ad quem inclinatur, minor erit.</
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<
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">_SI_ namque circuli _B N D, F O H,_ al circulos _A B C D, E F G H,_ æqualiter in-
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clinentur, erunt anguli _A I N, E K O,_ æquales, ex defin 7 lib. </
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& </
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">Additis igitur quadrantibus _N P, O Q,_ æqudo
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les erunt arcus _A P, E Q;_ </
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æquales erunt.</
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">_SI_ verò circulus _B N D,_ ad circulum _A B C D,_ magis inclinetur, quam circulus
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_F O H,_ ad circulum _E F G H,_ erit minor angulus _A I N,_ angulo _E K O,_ vt in defi-
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nitionem 7. </
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tcrtij.</
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Additis igitur quadrantibus _N P, O Q,_ minor erit arcus _A P,_ arcu _EQ;_ </
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de reliquus _C P,_ ex ſemicirculo _A N C,_ reliquo _G Q,_ ex ſemicirculo _F O G,_ maior erit.</
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">_RVRSVS,_ ſi circuli æqualiter inclinentur, erunt arcus _C P, G Q,_ vt pro-
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xime oſtendimus, æquales. </
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1. huius.</
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_L P, M Q,_ æquales.</
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<
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">_SI_ denique circulus _B N D,_ magis inclinetur, erit exproxime demoſtratis, ar@
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cus _C P,_ maior arcu _G Q._ </
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lique _M Q,_ ex quadrante _G M,_ &</
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licet.</
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<
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inclinantur ad maximum parallelorum: </
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lum tangit, inclinatior eſt ad maximum parallelorum. </
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