What subjects besides geometry are included in Euclid’s Elements?

While it is a common misconception that Euclid’s Elements is exclusively a work of geometry, the text covers several other mathematical disciplines. In addition to plane and solid geometry, the Elements includes:1

• Number Theory: Books VII–IX focus on what the Greeks called arithmetic, which is the study of positive integers. This section covers properties such as prime numbers, greatest common divisors, and geometric sequences.12
• Geometric Algebra: Book II is often described as geometric algebra because it expresses algebraic identities through theorems about equivalent geometric figures.1
• Theory of Ratios and Proportions: Book V presents a general theory of proportions that applies to both commensurable and incommensurable magnitudes (irrational numbers), providing a foundation for the geometric theory of numbers.12
• Stereometry: Books XI–XIII are dedicated to the geometry of three-dimensional figures, including the study of intersections of planes and the construction of the five regular Platonic solids.12

By integrating these fields, Euclid created a comprehensive foundation for mathematics that remained authoritative for centuries.12