Euclid’s Elements

• Euclid’s Elements is a Work on Geometry written in 13 Books.
• It was written in c. 300 BCE by the Greek Mathematician Euclid based in Alexandria in Egypt.

Books 1-4: Plane Geometry

• • 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.

Books 5-10: Ratios and Proportions

• • 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.

Books 11-13: Spatial Geometry

• • Book 11: Review of Books 1-6 in relation to space.
  • Book 12: Volumes of cones, pyramids and cylinders.
  • Book 13: Platonic solids.

Other Theorums

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