I.

Definitions.

1. A point is that which has no part. original: "Σημεῖόν" (Sēmeion). Euclid defines the point as the most basic unit of geometry, possessing location but no size or dimension.

2. A line is breadthless length. original: "Γραμμὴ" (Grammē). A line is understood here as having only one dimension.

3. The extremities of a line are points.

4. A straight line is a line which lies evenly with the points on itself. original: "Εὐθεῖα γραμμή" (Eutheia grammē). This definition suggests that the points on the line do not deviate in any direction.

5. A surface is that which has length and width only.

6. The extremities of a surface are lines.

7. A plane surface is a surface which lies evenly with the straight lines on itself. original: "Ἐπίπεδος ἐπιφάνειά" (Epipedos epiphaneia). Similar to the definition of a straight line, this describes a flat surface where any straight line connecting two points stays entirely within that surface.

8. A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line. original: "Ἐπίπεδος δὲ γωνία" (Epipedos de gōnia).

9. And when the lines containing the angle are straight, the angle is called rectilineal. original: "εὐθύγραμμος" (euthygrammos). This distinguishes angles formed by straight lines from those formed by curves.

10. And when a straight line set up on a straight line makes the adjacent—

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1. Hero, Definitions, 1. 2. Ammonius, On the Categories, page 43, 66. Psellus, page 34. See also Philoponus, On the Physics, folio 6 recto. Martianus Capella, Book 6, 708. Boethius, page 374, lines 1 and 2. Sextus Empiricus, page 466, line 27; page 470, line 24; page 704, line 28. Hero, Definitions, 2. 3. Philoponus, On the Physics, folio 6 recto. Ammonius, On the Categories, page 66. Martianus Capella, Book 6, 708. Boethius, page 374, lines 2 and 3. Boethius, page 374, lines 3 and 4. Hero, Definitions, 4. 5. Sextus Empiricus, page 716, line 28; page 717, line 10. Philoponus, On the Prior Analytics, Book 2, folio 4 verso, folio 15. Psellus, page 34. Boethius, page 374, line 5. 5. Hero, Definitions, 9. Boethius, page 374, line 6. 6. Boethius, page 374, line 7. 7. Hero, Definitions, 11. Psellus, page 35. Boethius, page 374, line 7. 8. Hero, Definitions, 16. Psellus, page 35. See also Sextus Empiricus, page 718, line 12. Boethius, page 374, line 10. Martianus Capella, Book 6, 710.