Euclid 325-265 BC

1
Euclid 325-265 BC

• Author of The Elements
• 13 books in all.
• Standard textbook for Geometry for about
• 2000 years.
• Taught in Alexandria, Egypt.

2
Euclids Elements The first 4 axioms

• A modern form of the axioms.
• For every point P and every point Q not equal to
  P there exists a unique line that passes through
  P and Q.
• For every segment AB and for every segment CD
  there exists a unique point E such that B is
  between A and E and the segment CD is congruent
  to segment BE.
• For every point O and every point A not equal to
  O there exists a circle with center O and radius
  OA.
• All right angles are congruent to each other.

3
Euclids ElementsThe Parallel Postulate

• That, if a straight line falling on two straight
  lines make the interior angle on the same side
  less than two right angles, the two straight
  lines, if produced indefinitely, meet on that
  side on which are the angles less than two right
  angles.