Euclidean Geometry

• Euclid was a Greek mathematician who is considered to be the Father of Geometry and lived and worked in Alexandria around 300 BCE.
• His main work was ‘Elements’, which holds all the theories of Euclidean Geometry including a description of Prime Numbers.

Works

• Euclid's Elements
  • Euclid wrote this Work in 13 Books divided into 3 sections:

1. Plane Geometry: Books 1-4
   • Book 1: Euclid’s 10 Axioms. Parallel Postulate. Pythagoras' Theorem, Bridge of asses Theorem.
   • Book 2: Book of Geometric Algebra. Square Roots.
   • Book 3: Circles and their properties. Thales Theorem.
   • Book 4: incircle and circumcircle of a triangle. Regular Polygons.
2. Ratios and Proportions: Books 5-10
   • Book 5: Proportions of Magnitudes.
   • Book 6: Proportions in Geometry. Similar Figures.
   • Book 7: Elementary number theory: Divisibility, Prime Numbers, Euclid’s Algorithm.
   • Book 8: Proportions in number theory and geometric sequences.
   • Book 9: Conclusions of Books 7-8. The infinitude of Prime Numbers. The sum of Geometric Series. The construction of Even Perfect Numbers.
   • Book 10: Classification of irrational magnitudes.
3. Spatial Geometry: Books 11-13
   • Book 11: Review of Books 1-6 in relation to space.
   • Book 12: Volumes of cones, pyramids and cylinders.
   • Book 13: Platonic solids

List of Theorums

• Thales Theorem
• Pythagoras' Theorem
• Bridge of asses Theorem
• Sum of the angles of a triangle