I'm writing a project on Cayley's algebra. I have some topics which I have to follow and I've managed to solve most of them,except 2. I have written about their rule of multiplication,together with the Fano plane,the Cayley-Dickson construction(pair of quaternions) and other properties such as conjugate,norm ecc.
However,there are 2 topics where I've got stuck. I have to write about the affine space associated with them(I know what an affine space is,but don't have idea how to prove it here) and about why the Desargues theorem doesn't stand in this case.