Measurement of a Circle Measurement of a Circle Measurement of a Circle or Dimension of the Circle (Greek: , "Kuklou metrēsis") 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. 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
Distance from a point to a line a side, and "h" is the perpendicular height from the opposite vertex. This proof is only valid if the line is neither vertical nor horizontal, that is, we assume that neither "a" nor "b" in the equation of the line is zero. The line with equation "ax" + "by" + "c" = 0 has slope -"a"/"b", so any line perpendicular to it will have slope "b"/"a" (the negative reciprocal). Let ("m", "n") be the point of intersection of the line "ax" + "by" + "c" = 0 and the line perpendicular to it which passes through the point ("x", "y").