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Given 2 triangles in a plane over a field \( F \) which are in perspective from a vertex \( V \), the resulting Desargues line or axis \( l \) may or may not be on \( V \). To avoid degenerate cases, we assume that the union of the vertices of the 2 triangles is a set of six points with no three collinear. Our work then provides a detailed analysis of situations when \( V \) is on \( l \) for any \( F \), finite or infinite.