Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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tio autem arcus HM, ad arcum EI, maior eſt, quàm arcus MN, ad arcum
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huius.</
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IK; </
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<
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">erit quoq; </
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<
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">maior ratio diametri ſphæræ ad diametrum circuli EG, quàm
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arcus MN, ad arcum IK. </
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<
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">Et quia arcus PK, ſimilis eſt arcui BD, ex hy-
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potheſi, & </
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<
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<
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<
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">erit
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quoque arcus BD, minor arcu MN; </
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<
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">ac proinde minor erit ratio arcus BD,
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ad arcum IK, quàm arcus MN, ad eundẽ arcum IK. </
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<
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">Cum ergo oſtenſum ſit, ra
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tionem diametri ſphæræ ad diametrum circuli EG, maiorem eſſe, quàm arcus
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MN, ad arcum IK; </
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<
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">Multo maior erit ratio diametri ſphæræ ad diametrum
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cireuli EG, quàm arcus BD, ad arcum IK. </
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<
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culi tangant vnum, &</
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<
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">_IN_ exemplari græco habetur, maiorem eſſe rationem duplæ diametri ſphæræ ad
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diametrum circuli _
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,_ quàm arcus _
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D,_ ad arcum _IK_ Quod quidem ex noſtra de-
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monſtratione liquidò conſtat. </
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ad diametrum circuli _EG,_ quàm arcus _BD,_ ad arcum _IK;_ </
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<
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habebit dupla diametri ſphæræ ad diametrum circuli _
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,_ quàm arcus _
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D,_ ad ar-
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cum _IK;_ </
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,_ maiorem
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rationem habet, quàm diameter ſphæræ ad eandem diametrum circuli EG.</
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cunferentias maximi alicuius circuli vtrinq; </
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les ab illo puncto, in quo ipſe maximus circulus
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ſecat maximum parallelorum; </
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terminantia æquales circunferentias, & </
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lelorum polos deſcribantur maximi circuli, aut ſi
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deſcribantur maximi circuli, qui vnum eundem-
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que parallelorum tangant: </
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cunferentias de maximo parallelorum.</
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<
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">IN ſphæra AB, paralleli circuli CD, EF, auferant de maximo circulo
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AF, duas circunferentias
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æquales GC, GF, vtrin-
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que à puncto G, in quo
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circulus AF, ſecat maxi-
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mum parallelorum BG;
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</
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cãtur maximi circuli ſi-
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ue per polos parallelo-
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rum, vt in priori figura,
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ſiue tangẽtes vnum eun-
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demque parallelũ, vt in figura poſteriori, ſecantes maximum parallelorum </
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