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Euclid: Elementa

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Euclid: Elementa
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gre ΙΙI,32
λέγω, ὅτι ἃς ποιεῖ γωνίας ἡ ΒΔ μετὰ τῆς ΕΖ ἐφαπτομένης, ἴσαι ἔσονται ταῖς ἐν τοῖς ἐναλλὰξ τμήμασι τοῦ κύκλου γωνίαις, τουτέστιν, ὅτι ἡ μὲν ὑπὸ ΖΒΔ γωνία ἴση ἐστὶ τῇ ἐν τῷ ΒΑΔ τμήματι συνισταμένῃ γωνίᾳ, ἡ δὲ ὑπὸ ΕΒΔ γωνία ἴση ἐστὶ τῇ ἐν τῷ ΔΓΒ τμήματι συνισταμένῃ γωνίᾳ.
Pic2544
Pic2545
eng
I say that the angles which BD makes with the tangent EF will be equal to the angles in the alternate segments of the circle, that is, that the angle FBD is equal to the angle constructed in the segment BAD, and the angle EBD is equal to the angle constructed in the segment DCB.
lat Sic
Dico quoniam anguli quos facit recta DB cum EZ contingenti equales erunt eis qui in permutatis circuli portionibus angulis, hoc est, quoniam angulus quidem ZBD equalis est in DAB sectione constituto angulo.
lat Gerard
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lat Adelard
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lat Hermann
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ara Uppsala
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ara Tuṣi
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ara Nairizi
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per Shirazi
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san
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lat Clavius
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kin 幾何原本
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