That is why when you use a lens designed for a APS-C camera on a full-frame camera, the actual focal length of the lens is 1.5 times of the printed focal length.
How is the vertical difference calculated? The deltas of the width and the height look different, but in the diagram we only seem to see the effect of the focal length on the width of the image.
I think it works pretty much the same way, if you just imagine turning the image 90 degrees clockwise. I'm pretty sure this implies that the ratio of deltaWidth/width is just exactly the same as the ratio of deltaHeight/height, meaning that the deltas are not exactly the same, but are in the same proportion to their respective measurements.