The Algebra of Points

Projective mapping is simphfied when expressed algebraically in terms of coordinates, as was done for affine transformation before. 

Since AXA Y is a quadrangle, any single point of the quadrangular set Q PooPxPo, PooPyPxy) IS Uniquely determined by the others. 

The perspectivities [P, ] a [X] a [Pxy] and [Py] a [1 ] a [Pxy] which define multiplication, imply the projectivities PoqPqPiPx a PooPoPyPxy and PooPoPlPy A PooPoPxPxy 

The combination of projectivities ( ), (m) and (Hi) yields a more general projective transformation that will be shown to have the form (3.5) 

According to the fundamental theorem a projectivity is completely determined once three pairs of homologies are assigned. Suppose that in a given 

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