A number of Indian mathematicians gave rules equivalent to the quadratic formula. It is possible that certain altar constructions dating from ca. 500 BC represent solutions of the equation, but even should this be the case, there is no record of the method of solution (Smith 1953, p. 444). The Hindu mathematician Āryabhata (475 or 476-550) gave a rule for the sum of a geometric series that shows knowledge of the quadratic equations with both solutions (Smith 1951, p. 159; Smith 1953, p. 444), while Brahmagupta (ca. 628) appears to have considered only one of them (Smith 1951, p. 159; Smith 1953, pp. 444-445). Similarly, Mahāvīra (ca. 850) had substantially the modern rule for the positive root of a quadratic. Srīdhara (ca. 1025) gave the positive root of the quadratic formula, as stated by Bhāskara (ca. 1150; Smith 1953, pp. 445-446). The Persian mathematicians al-Khwārizmī (ca. 825) and Omar Khayyám (ca. 1100) also gave rules for finding the positive root.