The last three circular functions complete the picture. The cotangent is read on the horizontal axis that touches the cycle at $B$; the secant and cosecant appear when we draw the tangent line to the cycle in $P$ and see where it cuts the axes. The story The names “secant” and “tangent” come from the geometry of the circle: the tangent line touches the circumference (tangere, touch) and the secant line cut (secare, cut). In the definition figure, the segment $\overline{OS}$ lies on a straight line that, when extended, is secant to the cycle, and the segment $\overline{AT}$ lies on the tangent line at $A$. These segments were already tabulated by Arab astronomers: Abu al-Wafa, in the 10th century, organized the six functions and showed how each one derives from the others.