Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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cus K O, arcui N A, & </
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arcus K P, arcui N B, æ-
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qualis, vt ſint quoque ſe
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micirculi A M O, O F A;
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<
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<
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tur ſemicirculi A M O,
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B H P, non coeuntes, cũ
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ſe mutuo non ſecent. </
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<
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dem modo nõ coeuntes
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erunt ſemicirculi B G P,
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A F O. </
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<
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lelorum A B, L E, M H,
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interceptos inter ſemi-
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circulos A M O, B H P,
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non coeuntes ſimiles eſ-
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ſe, necnon & </
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<
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">arcus A B,
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C D, F G, interceptos in
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ter ſemicirculos B G P,
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A F O, non concurren-
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tes ſimiles eſſe: </
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<
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">Arcus vero maximorum circulorum A C, A L, B D, B E, æ-
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quales eſſe; </
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<
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<
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<
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">quorum illi inter paralle-
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los A B, C D E, hi vero inter parallelos C D E, F G H, interijciuntur: </
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demq́; </
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<
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">pacto æquales eſſe arcus A F, A M, B G, B H, inter parallelos A B,
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F G H, interiectos. </
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">puncta contactuum A, B, circuli
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maximi deſcribantur Q A I R, S B I T, ſecantes parallelos in Q, S, V, X.
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<
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">Tranſibunt hi circuli maximi per polos quoque circulorum A F K, B H K; </
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ac proinde bifariam ſecabunt ſegmenta C A L, D B E, C V L, D X E: </
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ſegmenta F A M, G B H, F Q M, G S H. </
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rectos ſecabunt parallelos A B, C D E, F G H, & </
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<
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">maximos circulos A F K,
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B H K. </
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ſtunt ad angulos rectos ſegmenta circulorum æqualia, nempe ſemicirculi in-
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choati à punctis A, B, & </
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<
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">per I, tranſeũtes, donec iterũ ſecent circulos A F K,
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B H K; </
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les ſint; </
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enim dimidij ſint arcuum A I R, B I T, quòd, ex defin. </
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puncta A, B, R, T, atque adeo arcus quoque ſint æquales: </
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A I R, B I T, ſemicirculo minores, quòd ſemicirculi tendant ex A, & </
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I, vſque ad circulos A F K, B H K; </
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">erunt arcus A I, B I, minores dimidijs par
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tibus illorum ſemicirculorum.) </
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li defin. </
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<
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B D, æqualis, propterea quòd arcus C A L, D B E, bifariam ſecantur, vt de-
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monſtratum eſt. </
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dem modo oſtendemus, æquales eſſe quatuor arcus A F, A M, B H, B G; </
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propterea & </
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parallelos intercipiuntur. </
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<
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<
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dia æqualia ſint, vt demonſtratum eſt; </
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quales, quæ quidem arcubus quoque C V L, D X E, ſubtenduntur; </
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