De reductione aequationum

work by Hudde

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June 17, 2026

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Johan van Waveren Hudde's work, De reductione aequationum (1713), contributed to the theory of equations by being the first to treat literal coefficients in algebra as either positive or negative. This was a significant step in the development of elementary algebra, which uses symbols to represent numerical quantities and operations.12

Hudde's earlier discoveries, known as Hudde's rules, from 1657-1658, foreshadowed calculus algorithms. He also anticipated power-series expansions and the use of space coordinates. Algebraic equations are statements of equality between expressions, formed using algebraic operations, and finding their solutions (roots) is fundamental to mathematics.13

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Johan van Waveren Hudde
In his De reductione aequationum (1713; “Concerning Reduction of Equations”), he was the first to take literal coefficients in algebra as indifferently positive or negative. Two of his discoveries, dating from 1657 to 1658, are known as Hudde’s rules and point clearly toward algorithms (a special process…
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In his De reductione aequationum (1713; “Concerning Reduction of Equations”), he was the first to take literal coefficients in algebra as indifferently positive or negative. Two of his discoveries, dating from 1657 to 1658, are known as Hudde’s rules and point clearly toward algorithms (a special process…
Read More