A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations.

中文翻译：

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证明和表面

本文介绍了处理Menelaus配置的正式后续系统。该系统的无公害现象源于2个周期的Δ复合物。定义了结果的欧几里得和投影解释，并证明了结果的正确性。该系统是可判定的，其可证明的结果可提供发生结果。生成器和关系表示与该系统相关的循环操作结构。