Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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maiorem eſſe, quàm _F B,_ &</
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<
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<
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<
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xml:space
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nibus figuris erunt duo quadrata ex _G C,_ _
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F,_ maiora duobus quadratis ex _
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,_
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_
<
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F:_ </
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<
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xml:space
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">quibus cum æqualia ſint quadrata ex _F C,
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;_ </
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<
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">erit quoque quadratum ex _F C,_
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maius quadrato ex _FB;_ </
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<
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<
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">recta _F C,_ maior erit, quàm _F B._ </
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<
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ter oſtendemus, rectam _F C,_ quæ propinquior eſt maximæ _F D,_ maiorem eſſe quacun-
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quealia remotiore, &</
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<
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F,_
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minora duobus quadratis ex _
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H,
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F:_ </
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<
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xml:space
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">quibus cum æqualia ſint quadrata ex _F I,_
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note
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_FH;_ </
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<
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">erit quoque quadratum ex _F I,_ minus quadrato ex _FH;_ </
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<
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">proptereaq́ & </
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_F I,_ minor, quàm _F H,_ erit. </
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<
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<
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">modo demonſtrabimus, rectam _F I,_ quæ pro-
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pinquior eſt minimæ _F A,_ minorem eſſe quacunque alia remotiore, &</
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<
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<
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erunt duo quadrata ex _
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C,
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F,_ æqualia duobus quadratis ex _
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E,
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F:_ </
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<
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cum æqualia ſint quadrata ex _F C, F E,_ æqualia quoque erunt quadrata ex _F C,_
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xml:space
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_FE;_ </
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<
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">rectæ _F C, F E,_ æquales erunt. </
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<
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xml:space
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</
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<
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">Cæterum vt ex demonſtratione patet, eam rectam dicimus propinquiorem maximæ
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_F D,_ quæ cadit in puctum vicinius pucto _D:_ </
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quæ cadit in puctum propinquius puncto _A._</
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">SI in ſphæræ ſuperficie intra circuli cuiuſque peripheriam pun-
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ctum ſignetur præter eius polum, ab eo autem ad circuli circunfe-
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rétiam plurimi arcus circulorum maximorum ducantur ſemicircu
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lo minores; </
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">maximus eſt, qui per circuli polum ducitur; </
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autem, qui ei adiacet: </
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<
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">Reliquorum verò propinquior maximo, re-
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motiore ſemper maior eſt: </
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minimo æqualiter remoti inter ſe æquales ſunt.</
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<
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">_SIT_ in ſphæra circulus _A B C D E,_ cuius polus F, ſigneturq́; </
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<
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">in ſphæræ ſuperfi-
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tie intra peripheriam circuli præter polum _F,_ punctum quodlibet _G,_ à quo plurimi
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<
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arcus maximorum circulorum ad circunferen-
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tiam circuli _A B C D E,_ ducantur, quorum _G A,_
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in vtramque partem eductus tranſeat per polum
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F; </
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<
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xml:space
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">arcus verò _G B,_ propinquior ſit ipſi _G A,_ quàm
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_GC;_ </
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<
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">duo denique _G B, G E,_ æqualiter diſtent ab
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eodem _G A,_ vel à _GD;_ </
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<
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micirculo minores: </
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<
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ſe mutuo non interſecabunt in alio puncto, quàm
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in _G._ </
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<
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xml:space
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">Cum enim circuli maximi ſe mutuo diui-
<
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<
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dant bifariam, erunt arcus _G A, G E,_ ſemicircu-
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lo minores, cum nondum ſe interſecent. </
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<
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</
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<
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ſemicirculo, ſi ſe mutuo non interſecent. </
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<
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eſſet ſemicirculus, tranſirent omnes alij per punctum A, eſſentq́; </
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<
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Si vero _G A,_ eſſet ſemicirculo maior, ſecarent eum omnes alij, antequam ad circun-
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ferentiam peruenirent, eſſentq́; </
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<
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<
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poſſet. </
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<
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">Dico arcum _G A,_ omnium eſſe maximum, & </
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<
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iorem eſſe arcu _
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C;_ </
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<
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B, G E,_ eſſe æquales. </
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<
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ſecat circulum _
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C,_ bifariam, & </
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">erit recta ſubtenſa _A D,_ dia-
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<
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