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 The line through these two points is perpendicular to the original line, so Thus, formula_7 and by squaring this equation we obtain: Now consider, using the above squared equation. But we also have, since ("m", "n") is on "ax" + "by" + "c" = 0. Thus, and we obtain the length of the line segment determined by these two points, This proof is valid only if the line is not horizontal or vertical. Drop a perpendicular from the point "P" with coordinates ("x", "y") to the line with equation "Ax" + "By" + "C" = 0. Label the foot of