Page:Indian mathematics, Kaye (1915).djvu/23

 before the 12th century and that no Indian writer quotes Āryabhata as recording this value. Other noteworthy points are the rules relating to volumes of solids which contain some remarkable inaccuracies, e.g., the volume of a pyramid is given as half the product of the height and the base; the volume of a sphere is stated to be the product of the area of a circle (of the same radius as the sphere) and the root of this area, or $\scriptstyle{\pi\frac{3}{2}\gamma^3}$. Similar errors were not uncommon in later Indian works. The rule known as the epanthem occurs in Āryabhata's work and there is a type of definition that occurs in no other Indian work, e.g., "The product of three equal numbers is a cube and it also has twelve edges."