Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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Recta igitur ducta _ED,_ minor erit, quàm recta _EG;_ </
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<
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">ac proinde cum circulus _GE,_
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huius.</
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minor ſit circulo _DE,_ mator erit circunferentia _
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,_ quàm circunferentia _DE._
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<
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">Sienim recta rectæ _ED,_ æqualis aufert ex circulo _GE,_ maiorem arcum, quàm
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huius.</
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recta _DE,_ ex circulo _DE;_ </
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<
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,_ quæ maior eſt, quàm recta
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_ED,_ vt oſtendimus, maiorem arcum auferet, &</
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tio arcus _
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C,_ ad arcum _GE,_ quàm ad arcum _DE._ </
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ad totam circunferentiam cir-
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culi _BC,_ ita arcus _
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E,_ ad to-
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tam circũferentiã circuli _GE,_
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propter ſimilitudinem arcuum
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_BC, GE;_ </
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">(In hoc enim conſiſtit
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ſimilitudo arcuum, vt ad ſuo-
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rum circulorum circunferen-
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tias integras eandem habeant
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proportionem, vt in ſcholio pro
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poſ 33. </
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atque adeo permutando, vt ar-
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cus _BC,_ ad arcũ _
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E,_ itateta
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circunferentia circuli _BC,_ ad
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totam circunferentiam circuli
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_
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E;_ </
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<
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tio circunferentiæ circuli _BC,_
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ad circunferentiã circuli _
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E,_
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quàm arcus _
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C,_ ad arcum
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_DE:_ </
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circuli _
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C,_ ad circunferentiam circuli _GE,_ ita eſt diameter _BI,_ (quæ ſphæræ etiam
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diameter eſt.) </
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">ad diametrum _GH,_ vt Pappus demonſtrauit, & </
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medis de dimenſione circuli oſtendimus. </
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tri ſphæræ _
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I,_ ad _
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H,_ diametrum paralleli _
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E,_ quàm arcus _
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C,_ ad circunferen-
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tiam _DE._ </
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rum interceptæ inter maximum circulum AB, primo poſitum, & </
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per polos parallelorum tranſeuntem, ad circunferentiam DE, obliqui circuli inter coſdem
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circulos interceptam, quàm ſinus totius ad ſinum circunferentiæ AE, maximi circuli per
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polos parallelorum tranſeuntis; </
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AD, maximi circuli primò poſiti inter polos parall elorum, & </
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ceptæ. </
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<
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">Quoniam enim hoc Theoremate oſtenſum eſt, maiorem eſſe rationem arcus BC, ad
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arcum DE, quàm diametri ſphæræ ad diametrum paralleli GE: </
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ſphæræ ad GH, diametrum circuli GE, ita eſt BK, ſemidiameter, hoc eſt, ſinus rotus, ad
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GN, ſemidiametrum, hoc eſt, ad ſinum arcus AE. </
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">(Cum enim arcus AG, AE, æquales ſint,
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ſitque GN, ſinus arcus AG; </
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tatio arcus BC, ad arcum DE, quàm ſinus totius BK, ad GN, ſinum arcus AE.</
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diametri ſphæræ ad diametrum paralleli DF: </
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trum paralleli DF, ita eſt BK, ſinus totus ad DO, ſinum artus AD. </
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<
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eſt proportio arcus BC, ad arcum DE, q̃ ſinus totius ad ſinũ arcus AD. </
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<
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