Algebra in Islam

Abstract

Many ancient mathematical works contain problems requiring the discovery of an unknown quantity. Sometimes this is a geometrical magnitude which is related by the conditions of the problem to known magnitudes, one example being the problem solved in Euclid’s Elements II,11 of dividing a given line segment AB into segments AG and GB so that the rectangle whose sides are AB and GB is equal to the square whose side is AG (Fig. 4.1). Here there is one known magnitude, AB, one unknown segment, AG, for GB = AB - AG. and the one condition that AB⋅GB = AG². The reader will recall that this is the division of a line segment into “the section” we spoke of in Chapter 3 in our discussion of Problem 5 of Abu l-Wafā’’s treatise in which a pentagon was inscribed in a circle.