Euclid’s Definitions, Axioms or Postulates
- A point is that which has no part.
- A line is a breadthless length.
- The ends of a line are points.
- A straight line is a line which lies evenly with the points on itself.
- A surface is that which has length and breadth only.
- The edges of a surface are lines.
- A plane surface is a surface which lies evenly with the straight lines on itself.
Undefined Terms: There are some terms like point etc which have no definitions, these terms are called undefined terms.
In geometry, a point, a line and a plane (in Euclid’s words, a plane surface) are undefined terms.
Euclid’s Axioms
- Things which are equal to the same thing are equal to one another.
- If equals are added to equals, the wholes are equal.
- If equals are subtracted from equals, the remainders are equal.
- Things which coincide with one another are equal to one another.
- The whole is greater than the part.
- Things which are double of the same things are equal to one another.
- Things which are halves of the same things are equal to one another.
