Quotes from Lancelot Hogben

Fig. 148. Cartesian Equation of the Cone Mid-point of base as Origin. The distance (d) between two points (P1 and P2) in 3-dimensional space (Fig. 147) is given by: d2 = (x2 ? x1)2 + (y2 ? y1)2 + (z2 ? z1)2 It is sometimes easier to obtain the Cartesian equation of a figure by first defining it in cylindrical co-ordinates and substituting: y = r sin A; x = r cos A Figs. 148 and 149 disclose the genesis of Cartesian equations which describe the cone and the sphere: