[Pramāṇa](https://indike.org/pramana/) › [Studies](https://indike.org/pramana/ins) › [Science, technology and education](https://indike.org/pramana/ins.science) › [The Science of the Shulba: A Study in Early Hindu Geometry](https://indike.org/pramana/ins.science.datta-1932) › c11.10 # The Science of the Shulba: A Study in Early Hindu Geometry c11.10 The Science of the Śulba: A Study in Early Hindu Geometry c11.10 - **Language:** English ### [c11.10](https://indike.org/pramana/ins.science.datta-1932.c11.10) If n is not a square number, simplification can be made by expressing it, when possible, as the sum of two square numbers. Thus if $n=p²+q²$ where p, q are rational quantities, then if x denote a side of the required square and c a side of the given square, we shall have $x²=(pc)²+(qc)²=(p²+q²)c²=nc².$ So that with one construction only, we shall get a square n times the given square. Kātyāyana has given some instances of this kind. He says: - [Previous: c11.9](https://indike.org/pramana/ins.science.datta-1932.c11.9) - [Next: c11.11](https://indike.org/pramana/ins.science.datta-1932.c11.11) - [Up: c11](https://indike.org/pramana/ins.science.datta-1932.c11) --- Source: [https://indike.org/pramana/ins.science.datta-1932.c11.10](https://indike.org/pramana/ins.science.datta-1932.c11.10) · Pramāṇa