Affine Localizations of Desargues Axiom 1

together with its indirect forms are introduced. Logical relationships between these formulas and between them and the classical Desargues Axiom are demonstrated. MML Identifier: AFF 3. The articles [1], [3], and [2] provide the notation and terminology for this paper. We follow a convention: AP denotes an affine plane, a, a ′ , b, b ′ , c, c ′ , o, p, q denote elements of the points of AP, and A, C, P denote subsets of the points of AP. Let us consider AP. We say that AP satisfies DES1 if and only if