The Theorems of Pappus and Desargues (for the projective plane over a field) are generalized here by two identities involving determinants and cross products. These identities are proved to hold in the three-dimensional vector space over a field. They are closely related to the Arguesian identity in lattice theory and to Cayley-Grassmann identities in invariant theory.

中文翻译：

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推广 Pappus 和 Desargues 定理的恒等式

Pappus 和 Desargues 的定理（对于场上的射影平面）在这里通过涉及行列式和叉积的两个恒等式进行了概括。这些恒等式被证明在一个场的三维向量空间中成立。它们与格理论中的 Arguesian 恒等式和不变论中的 Cayley-Grassmann 恒等式密切相关。