A theorem, which states a seemingly simple geometric fact that every quadrangle is a perspective image of a square, may be considered as known for a long time. Namely, even some renaissance painters have discovered it, albeit on an intuitive level. However, a correct formulation together with various proofs that cover this statement in full generality are not so common and can be found only in recent literature. In the first part, this thesis approaches the theorem by analysing classic examples of a perspectivity or, more specifically, central projections. This method was systematically treated by famous mathematician Brook Taylor in his book New Principles of Linear Perspective from 1719. Next, a stereometric proof of A. Emch is provided and square conics are observed, as sections of a double square cone with planes. Furthermore, the theorem on perspective images of a square is associated with the fundamental theorem of projective geometry, which gives interesting results on decomposition of projective collineations. These types of decompositions are of great importance in modern applications such as computer vision, animation and video analysis. In the final part, an analysis of real relative dimensions of objects on a photograph is shown by applying perspectivity laws. This analysis is brought into relation with the theorem on mapping of a square and Taylor’s interpretation.