Area of a circle Measurement of a Circle" (c. 260 BCE), compare the area enclosed by a circle to a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius. If the area of the circle is not equal to that of the triangle, then it must be either greater or less. We eliminate each of these by contradiction, leaving equality as the only possibility. We use regular polygons in the same way. Suppose that the area "C" enclosed by the circle is greater than the area "T" = ⁄"cr" of the triangle. Let "E" denote
Distance from a point to a line formula_19, and formula_20in terms of the coordinates of P and the coefficients of the equation of the line to get the indicated formula. Let "P" be the point with coordinates ("x", "y") and let the given line have equation "ax" + "by" + "c" = 0. Also, let "Q" = ("x", "y") be any point on this line and n the vector ("a", "b") starting at point "Q". The vector n is perpendicular to the line, and the distance "d" from point "P" to the line is equal to the length of the orthogonal projection of formula_21 on n. The