Abstract
Abstract Descartes’s analytic geometry allowed him to use algebra to solve geometric construction problems. That turned out to be an important key to the proof of the impossibility of solving the classical problems by ruler and compass. Descartes himself believed that he could prove this impossibility. But his rather strange proof was not rigorous. Still, after the proof had been modified during the eighteenth century, it appeared convincing to many leading mathematicians of the Enlightenment. The French Academy therefore declared that they would no longer evaluate circle quadratures, cube duplications, and angle trisections. The original question of constructions by ruler and compass was almost lost sight of.
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