Area of a circle Archimedes is not rigorous by modern standards, because it assumes that we can compare the length of arc of a circle to the length of a secant and a tangent line, and similar statements about the area, as geometrically evident. The area of a regular polygon is half its perimeter times the apothem. As the number of sides of the regular polygon increases, the polygon tends to a circle, and the apothem tends to the radius. This suggests that the area of a disk is half the circumference of its bounding circle times the radius. Following Archimedes' argument in "The
Distance from a point to a line has coordinates: Horizontal and vertical lines In the general equation of a line, "ax" + "by" + "c" = 0, "a" and "b" cannot both be zero unless "c" is also zero, in which case the equation does not define a line. If "a" = 0 and "b" 0, the line is horizontal and has equation "y" = -"c"/"b". The distance from ("x", "y") to this line is measured along a vertical line segment of length |"y" - (-"c"/"b")| = |"by" + "c"| / |"b"| in accordance with the formula. Similarly, for vertical lines ("b" = 0) the distance between