Although analytic techniques provided solutions to long-standing problems, including problems of quadrature and the finding of tangents, the proofs of these solutions were not known to be reducible to the synthetic rules of Euclidean geometry.
尽管分析技术为长期存在的问题提供解决方案，包括求积的问题和切线的发现，但这些解决方案的证明并不被认为可以简化为欧几里德几何学的合成规则。