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Euclid Book 4 Definitions
Statement
A rectilinear figure is said to be inscribed in a rectilinear figure when the respective angles of the inscribed figure lie on the respective sides of that in which it is inscribed.
Original statement
σχῆμα ϵὐθύγραμμον ϵἰς σχῆμα ϵὐθύγραμμον ἐγγράϕϵσθαι λέγϵται, ὅταν ἑκάστη τῶν τοῦ ἐγγραϕομένου σχήματος γωνιῶν ἑκάστης πλϵυρᾶς τοῦ, ϵἰς ὃ ἐγγράϕϵται, ἅπτηται.
Statement
Similarly a figure is said to be circumscribed about a figure when the respective sides of the circumscribed figure pass through the respective angles of that about which it is circumscribed.
Original statement
σχῆμα δὲ ὁμοίως πϵρὶ σχῆμα πϵριγράϕϵσθαι λέγϵται, ὅταν ἑκάστη πλϵυρὰ τοῦ πϵριγραϕομένου ἑκάστης γωνίας τοῦ, πϵρὶ ὃ πϵριγράϕϵται, ἅπτηται.
Statement
A rectilinear figure is said to be inscribed in a circle when each angle of the inscribed figure lies on the circumference of the circle.
Original statement
σχῆμα ϵὐθύγραμμον ϵἰς κύκλον ἐγγράϕϵσθαι λέγϵται, ὅταν ἑκάστη γωνία τοῦ ἐγγραϕομένου ἅπτηται τῆς τοῦ κύκλου πϵριϕϵρϵίας.
Statement
A rectilinear figure is said to be circumscribed about a circle, when each side of the circumscribed figure touches the circumference of the circle.
Original statement
σχῆμα δὲ ϵὐθύγραμμον πϵρὶ κύκλον πϵριγράϕϵσθαι λέγϵται, ὅταν ἑκάστη πλϵυρὰ τοῦ πϵριγραϕομένου ἐϕάπτηται τῆς τοῦ κύκλου πϵριϕϵρϵίας.
Statement
Similarly a circle is said to be inscribed in a figure when the circumference of the circle touches each side of the figure in which it is inscribed.
Original statement
κύκλος δὲ ϵἰς σχῆμα ὁμοίως ἐγγράϕϵσθαι λέγϵται, ὅταν ἡ τοῦ κύκλου πϵριϕέρϵια ἑκάστης πλϵυρᾶς τοῦ, ϵἰς ὃ ἐγγράϕϵται, ἅπτηται.
Statement
A circle is said to be circumscribed about a figure when the circumference of the circle passes through each angle of the figure about which it is circumscribed.
Original statement
κύκλος δὲ πϵρὶ σχῆμα πϵριγράϕϵσθαι λέγϵται, ὅταν ἡ τοῦ κύκλου πϵριϕέρϵια ἑκάστης γωνίας τοῦ, πϵρὶ ὃ πϵριγράϕϵται, ἅπτηται.
Statement
A straight line is said to be fitted into a circle when its extremities are on the circumference of the circle.
Original statement
ϵὐθϵῖα ϵἰς κύκλον ἐναρμόζϵσθαι λέγϵται, ὅταν τὰ πέρατα αὐτῆς ἐπὶ τῆς πϵριϕϵρϵίας ᾖ τοῦ κύκλου.