[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) › c12.8 # The Science of the Shulba: A Study in Early Hindu Geometry c12.8 The Science of the Śulba: A Study in Early Hindu Geometry c12.8 - **Language:** English ### [c12.8](https://indike.org/pramana/ins.science.datta-1932.c12.8) From the longer side \*AC\* cut off a portion \*CE\* equal to the breadth \*CD\* of the rectangle. Complete the square \*CDFE\*. Divide the remaining part \*ABFE\* of the given rectangle into two halves by the line \*GH\*. Take the remoter half \*ABHG\* and place it after inversion on the other side of the square \*CDFE\* in the position \*DG'H'F\*. Complete the square \*CGPG'\*, by adding the portion \*HPH'F\*. The given rectangle is easily found to be equal to the difference of the two squares \*G'PG'C\* and \*HPH'F\*. This difference can be found by the method taught before. That is, draw a circle with centre \*G'\* and radius \*G'P\* cutting \*DH\* at \*M\*. Draw \*MN\* perpendicular to \*G'P\*. Then $G'N² = G'M² - MN² = G'P² - HP²$ so that \*G'N\* is the side of the square which is equivalent to the given rectangle \*ABDC\*. - [Previous: c12.7](https://indike.org/pramana/ins.science.datta-1932.c12.7) - [Next: c12.9](https://indike.org/pramana/ins.science.datta-1932.c12.9) - [Up: c12](https://indike.org/pramana/ins.science.datta-1932.c12) --- Source: [https://indike.org/pramana/ins.science.datta-1932.c12.8](https://indike.org/pramana/ins.science.datta-1932.c12.8) · Pramāṇa