Al-Khwarizmi 2

For example, start with:		x² - 3x + 12 = 5x² +2,
using al-gabr, we get:		x² + 12 = 8x² +2
and now using al-muqabala, we obtain:		x² + 10 = 8x²

Al-Khwarizmi discusses five different forms of quadratic equations:

ax² = bx,
ax² = c,

ax² + bx = c,
ax² + c = bx,
ax² = bx + c,

with positive coefficients a,b,c.

These are all the possibilies of quadratic equations which can have positive solutions.)

But note that Al-Khwarizmi uses only words to describe the expressions and the calculations, - no symbols (not even figures) are used!

Only in the 15^th century, arabic mathematicians start to use symbolic expressions, e.g.:

		stands for the equation x² + 10x = 56
the numbers are the coefficient (from right to left), above 10 is the first letter of say (= "thing", in German "Coss" - the variable x) above 1 is the first letter of mal (= the square of the variable)