Area of a circle of Cnidus in the fifth century B.C. had found that the area of a disk is proportional to its radius squared. Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book "Measurement of a Circle". The circumference is 2"r", and the area of a triangle is half the base times the height, yielding the area "r" for the disk. Prior to Archimedes, Hippocrates of Chios was the first
Distance from a point to a line the same point and the line is |"ax" + "c"| / |"a"|, as measured along a horizontal line segment. If the line passes through two points "P"=("x","y") and "P"=("x","y") then the distance of (x,y) from the line is: The denominator of this expression is the distance between "P" and "P". The numerator is twice the area of the triangle with its vertices at the three points, (x,y), "P" and "P". See: . The expression is equivalent to formula_4, which can be obtained by rearranging the standard formula for the area of a triangle: formula_5, where "b" is the length of