Education in Ancient Egypt: Fragment 925

This papyrus preserves definitions 1-10 of Euclid's Elements, a treatise on the nature of geometric features. Here, we reproduce the first seven definitions.

Written in a small, rather personal hand on a narrow piece of papyrus, it probably represents notes written for himself by a schoolmaster, or perhaps a cheat sheet prepared by a student. This sort of geometry would have been very important to engineers who were responsible for constructing the canals that fed water to agricultural zones, as well as to architects designing public buildings and palaces.

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(1) σημεῖόν ἐστιν οὗ μόρ<ι>ον
οὐθέν· (2) γραμμὴ δὲ μῆκος̣
ἀπλατές. (3) γραμμῆς δὲ πέρα-
τα σημεῖα. (4) εὐθεῖα γραμμὴ
ἐστι{ς} ἥτις ἐξ ἴσου τοῖς ἐ-
φ’ ἑαυτῆς σημείοις κε<ῖ>ται. (5)
ἐπιφάνειά ἐστι̣ ὁ̣ μ̣ῆ̣κ̣[ο]ς̣ κα[ὶ]
πλάτος μόνον ἔχει. (6) ἐπι-
φανείας δὲ πέρατα γραμ<μ>αί. (7)
ἐπίπεδος ἐπιφαν<ε>ιά ἐστιν
ἥτις ἐξ ἴσου τα̣ῖ̣ς ἐφ’ ἑαυ-
τῆς εὐθεί̣αις κεῖται.

(1) A point is that which has no part.
(2) A line is a line without breadth,
(3) and the limits of a line are points.
(4) A straight line is one which lies evenly with points upon it.
(5) A surface is that which has length and breadth only;
(6) and the limits of a surface are lines.
(7) A plane surface is one which lies evenly with the straight lines upon it.

Click the teacher to hear the passage recited by Dr. H.D. Cameron in Ancient Greek pronunciation.

Click the student to hear the passage recited by Dr. N. Litinas in Modern Greek pronunciation.