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Euclid: Elementa

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Euclid: Elementa
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Euc
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gre ΙΙI,36
Ἐὰν κύκλου ληφθῇ τι σημεῖον ἐκτός, καὶ ἀπ᾽ αὐτοῦ πρὸς τὸν κύκλον προσπίπτωσι δύο εὐθεῖαι, καὶ ἡ μὲν αὐτῶν τέμνῃ τὸν κύκλον, ἡ δὲ ἐφάπτηται, ἔσται τὸ ὑπὸ ὅλης τῆς τεμνούσης καὶ τῆς ἐκτὸς ἀπολαμβανομένης μεταξὺ τοῦ τε σημείου καὶ τῆς κυρτῆς περιφερείας ἴσον τῷ ἀπὸ τῆς ἐφαπτομένης τετραγώνῳ.
Pic2550
Pic2551
eng
If a point be taken outside a circle and from it there fall on the circle two straight lines, and if one of them cut the circle and the other touch it, the rectangle contained by the whole of the straight line which cuts the circle and the straight line intercepted on it outside between the point and the convex circumference will be equal to the square on the tangent.
lat Sic
Si quis extra circulum punctus sumatur et ab ipso ad circulum accidant due recte et hec quidem ipsarum secet circulum, illa vero contingat, erit quod sub tota secante et ea que extra inter punctum et convexam periferiam deprehenditur equale ei quod a contingente tetragono.
lat Gerard
No Latin
lat Adelard
No Latin
lat Hermann
No Latin
ara Uppsala
No Arabic
ara Tuṣi
No Arabic
ara Nairizi
No Arabic
per Shirazi
.
san
No Sanskrit
lat Clavius p. 309
SI extra circulum sumatur punctum aliquod, ab eoque in circulum cadant duæ rectæ lineæ, quarum altera quidem circulum secet, altera vero tangat: Quod sub tota secante, & exterius inter punctum & conuexam peripheriam assumpta comprehenditur rectangulum, æquale erit ei, quod a tangente describitur, quadrato.
kin 幾何原本 p. 180
圜外、任取一點。從點、出兩直線。一切圜。一割圜。其割圜之全線、偕規外線、矩內直角形。與切圜線上直角方形等。
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