Introduction to Euclid’s Geometry
Euclid’s Definitions
Definition 1: A point is that which has no part.
Definition 2: A line is breathless length.
Definition 3: The ends of a line are points.
Definition 4: A straight line is a line which lies evenly with the points on itself.
Definition 5: A surface is that which has length and breadth only.
Definition 6: The edges of a surface are lines.
Definition 7: A plane surface is a surface which lies evenly with the straight line on itself.
Euclid’s Postulates:
Postulate 1: A line can be drawn from any point to any point.
Postulate 2: A terminated line can be produced indefinitely.
Postulate 3: It is possible to describe a circle with any centre and any distance.
Postulate 4: All right angles are equal to one another.
Postulate 5: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together les then two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
Euclid’s Axioms
Axiom 1: Things which are equal to the same thing are also equal to one another.
Axiom 2: If equals are added to equals, then the wholes are equal.
Axiom 3: If equals are subtracted from equals, then the remainders are equal.
Axiom 4: Things which coincide with one another are equal to one another.
Axiom 5: The whole is greater than the part.
Axiom 6: Things which are double of the same things are equal to one another.
Axiom 7: things which are halves of the same things are equal to one another.