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Babylonians found out that they can write on clay tablets which led to them using it for mathematics and soon became algebra.
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Euclid's Elements gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots.The construction is due to the Pythagorean School of geometry.
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He is usually called the “Father Of Algebra” because he was one of the first mathematicians to introduce symbolism into algebra.
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He Invented the method of solving indeterminate equations of the second degree and is the first to use algebra to solve astronomical problems. He also develops methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the sun and the moon
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He founded the word Algebra. He also found algebra as an independent discipline and for introducing the methods of "reduction" and "balancing"
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He had the idea of reducing geometrical problems such as duplicating the cube to problems in algebra
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He developed algebra by extending Al-Khwarizmi's methodology to incorporate integral powers and integral roots of unknown quantities
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He founded that you can find numerical solutions of polynomial equations of arbitrary degree
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He gave a complete classification of cubic equations with positive roots and gives general geometric solutions to these equations found by means of intersecting conic sections.
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He made the definition of algebra: “[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known
