Definition:Euclid's Definitions - Book I

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Euclid's Definitions: Book $\text{I}$

These definitions appear at the start of Book $\text{I}$ of Euclid's The Elements.

  1. A point is that which has no part.
  2. A line is breadthless length.
  3. The extremities of a line are points.
  6. The extremities of a surface are lines.
  7. A plane surface is a surface which lies evenly with the straight lines on itself.
  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.
  9. And when the lines containing the angle are straight, the angle is called rectilineal.
  11. An obtuse angle is an angle greater than a right angle.
  12. An acute angle is an angle less than a right angle.
  15. A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another;
  16. And the point is called the center of the circle.
  21. Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute-angled triangle that which has its three angles acute.
  23. Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in either direction, do not meet one another in either direction.