page_title: Measurement of a Circle
section_title: Proposition one
hierarchical_section_title: Measurement of a Circle / Propositions / Proposition one
context_page_description: Measurement of a Circle or Dimension of the Circle is a treatise that consists of three propositions by Archimedes, ca. 250 BCE. The treatise is only a fraction of what was a longer work.
context_section_description: Proposition one states:
  The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle.
  Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r. This proposition is proved by the method of exhaustion.
caption: The circle and the triangle are equal in area.