Principles of Hindu Reckoning

Principles of Hindu Reckoning (Kitab fi usul hisab al-hind) is a mathematics book written by the 10th- and 11th-century Persian mathematician Kushyar ibn Labban.

It is the second-oldest book extant in Arabic about Hindu arithmetic using Hindu-Arabic numerals ( ० ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹), preceded by Kitab al-Fusul fi al-Hisub al-Hindi by Abul al-Hassan Ahmad ibn Ibrahim al-Uglidis, written in 952.

Although Al-Khwarizmi also wrote a book about Hindu arithmetic in 825, his Arabic original was lost, and only a 12th-century translation is extant.

Very much like the Chinese counting rod numerals, a blank on a sand board grid stood for zero, and zero sign was not necessary.

[1] Principles of Hindu Reckoning consists of two parts dealing with arithmetics in two numerals system in India at his time.

Divide by 2 or "halving" in Hindu reckoning was treated with a hybrid of decimal and sexagesimal numerals: It was calculated not from left to right as decimal arithmetics, but from right to left: After halving the first digit 5 to get 21⁄2, replace the 5 with 2, and write 30 under it: Final result: Kushyar ibn Labban described the algorithm for extraction of square root with example of

Kushyar ibn Labban's example of 25 degree 42 minutes multiplied by 18 degrees 36 minutes was written vertically as with a blank space in between[1]: 80 Kushyar ibn Labban's Principles of Hindu Reckoning exerted strong influence on later Arabic algorists.