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Two Ancient Solutions to Quadratic Equations

The Greeks, Hindus and Arabs had quite an influence on early algebra. The Greeks took a geometric approach to solving problems. The Hindu style was more verbal, or rhetorical, with some symbolism. The Arabs conquered Egypt, acquiring many Greek works from the Alexandrian library. They also conquered part of India. Here they came in contact with the Hindus and their mathematics. The Arabs translated the Greek and Hindu works, and Hindu numerals entered Arabia. Hence, Arabic algebra was a mix of Greek and Hindu algebra. They used a geometric approach like the Greeks and a more numerical approach like the Hindus.

Solutions to certain quadratic equations were found by the Greeks and Hindus. As you might expect, the Greek solution was more geometric than the Hindu solution. Each is described in the links below using modern notation.

Greek Solution
Hindu Solution