Firstly we need to determine if by 'increase' you mean by a multiplicative constant or a additive constant. Additive would be weird and as Stuart points out yes, multiplicative is the 'correct' way to think about it. (or is it... read on...)
Although, looking through some very wide lenses I do wonder if the distribution of 'wideness' (correct terms someone?) does actually hold constant - some lenses seem to be push a lot of information into the centre of the image and then go crazy stretchy at the extremes - i.e. a non-constant distribution. Therefore, your long (usually) horizontal aspect sees a wider-wider image (as opposed to just wider).
Did I just ask your same question in a different way?
Obviously all I have to add here is confusion