In the following pages we give an account of their...
In the following pages we give an account of their contribution in the domain of mathematics and astronomy. It may be pointed out that this is only a brief chapter in the general history of Muslim philosophy. The account will, therefore, be of a descriptive nature, shorn of all technicalities and confined to some of the fundamental ideas put forward by the Muslim peoples in the fields of arithmetic, algebra, geometry, trigonometry, and astronomy.
It is neither possible nor desirable to give here an exhaustive account of the work done by each and every Muslim scholar. We have restricted ourselves to important contributions of the prominent Muslim mathematicians and astronomers. B - Arithmetic The Arabs started work on arithmetic in the second/eighth century. Their first task in this field was to systematize the use of the Hindu numerals which are now permanently associated with their names.
Obviously, this was an immense advance on the method of depicting numbers by the letters of the alphabet which was universal up to that time and which prevailed in Europe even during the Middle Ages. The rapid development in mathematics in the subsequent ages could not have taken place without the use of numerals, particularly zero without which all but the simplest calculations become too cumbersome and unmanageable.
The zero was mentioned for the first time in the arithmetical work of al-Khwarizmi written early in the third/ninth century. The Arabs did not confine their arithmetic to integers only, but also contributed a great deal to the rational numbers consisting of fractions. This was the first extension of the domain of numbers, which, in its logical development, led to the real, complex, and hyper-complex numbers constituting a great part of modern analysis and algebra.
They also developed the principle of error which is employed in solving algebraic problems arithmetically. AlBiruni (363-432/973-1040), ibn Sina (370-428/980-1037), ibn al-Sam$ (d. 427/1035), Muhammad ibn Husain al-Karkhi (d. 410/1019 or 420/1029), abu Said al-Sijzi (c. 340-c. 415/c. 951-c.