Viete introduced a new level of abstraction in algebra by using letters to stand for known quantities in an equation. Before Viete’s time, each equation had to be solved on its own. For instance, the quadratic equations had to be solved separately by completing the square. Viete’s idea was to consider all quadratic equations at once by writing where a, b, and c are known quantities. Thus, he made it possible to write a formula involving a, b, and c that can be used to solve all such equations in one fell swoop.

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