Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
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">IN diametris A C, D F, circulorum æqualium A B C, D E F, inſiſtant
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ipſis circulis ad angulos rectos ſegmenta circulorũ æqualia A G C, D H F:
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">ſumanturq́ æquales arcus A G, D H, ita vt puncta G, H, ſecent ſegmenta
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A G C, D H F, non bifariam. </
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<
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">Ex G, H, denique in circunferentias circulo-
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rum A B C, D E F, cadant rectæ æquales G B, H E. </
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<
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A B, D E, eſſe æquales. </
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<
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culorum A B C, D E F, perpendiculares, quæ in communes ſectiones A C,
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D F, cadent in puncta I, K. </
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">Sumptis quoque L, M, centris circulorũ A B C,
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D E F, ducantur rectæ L B, B I, A G; </
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<
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<
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cta I, K, in ſemidiametros A L, D M. </
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<
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æquales ſunt, nec non & </
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<
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<
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">æquales quoque erunt arcus, C G,
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F H; </
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<
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">ac propterea anguli G A C, H D F, illis inſiſtentes æquales. </
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& </
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<
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que duo triangula A I G, D K H, habent duos angulos G A I, A I G, duo-
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bus angulis H D K,
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D K H, æquales. </
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bent autem & </
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A G, lateri D H, ęqua
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le, (ob æqualitatẽ ar
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cuum A G, D H.)
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bus I, K, ſubtenditur. </
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Igitur & </
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teri D K, & </
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lateri H K, æquale e-
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rit. </
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guli G I B, H K E, re
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cti ſunt ex defin. </
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">erunt quadrata ex G B, H E, quæ inter ſe æ-
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qualia ſunt, ob æqualitatem rectarum G B, H E, quadratis ex G I, I B, & </
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H K, K E, æqualia, ac {pro}pterea quadrata ex G I, I B, quadratis ex H K, K E,
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æqualia erunt. </
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<
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">Ablatis ergo quadratis æqualibus rectarum æqualiũ G I, H K,
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remanebunt quadrata rectarũ I B, K E, æqualia; </
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æquales. </
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<
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">Et quia A L, D M, ſemidiametri circulorum æqualiũ æquales ſunt;
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<
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quales. </
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<
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tem & </
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les erunt; </
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<
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<
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ctas ad A, & </
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<
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">quod quidem contingere poteſt, quando ſegmenta A G C,
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D H F, ſemicirculo ſunt maiora; </
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<
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demus, vt prius, angulos G A C, H D F, eſſe æquales; </
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<
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<
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G A C, G A I, quàm H D F, H D K, duobus ſint rectis æquales, erũt & </
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<
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H D K, æquales. </
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<
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<
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<
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ra G A, H D, æqualia, ob æquales arcus A G, D H, erunt, vt prius, rectæ
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<
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G I, I A, rectis H K, K D, æquales; </
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<
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<
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æquales erunt. </
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<
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lum L, angulo M, æqualem eſſe: </
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<
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<
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<
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<
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