Hindu Achievements in Exact Science: A Study in the History of Scientific Development c9.4

c9.4

1. The so-called Pythagorean theorem: The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
2. Construction of squares equal to the sum or difference of two squares;
3. Conversion of oblongs into squares, and *vice versa*;
4. Drawing of a perpendicular to a given straight line at a given point of it;
5. Construction of lengths equal to quadratic surds: The approximate value of √()
6. Circling of squares;
7. Squaring of circles,—"that rock upon which so many reputations have been destroyed," both in the East and West. The earliest Hindus got π = 3.0044;
8. Construction of successive larger squares from smaller ones by addition;
9. Determination of the area of a trapezium, of an isosceles trapezium, at any rate, when the lengths of its parallel sides and the distance between them are known.