Archimedean Spiral

In polar coordinates, the equation of Archimedean spiral $OPR$ is $r=a \theta$ . At point $P$ let the tangent to the spiral be drawn and let this tangent intersect in point $Q$ the line through $O$ that is perpendicular to $OP$ . Archimedes showed that the straight-line segment $OQ$ is equal in length to the circular arc $PS$ of the circle with center $O$ and radius $OP$ that is intercepted between the initial line and line $OP$ .