A Newtonian telescope's diagonal must be offset in order to be optically aligned and to center the cone of illumination at the center of the field of view. Let's see why.
First, we'll pick a 12 inch [30cm] F4 telescope and select a 2.6 inch [6.6cm] minor axis diagonal with a diagonal to focal plane distance of 10 inches.
...and in detail...
Oops, centering the diagonal on the primary mirror's axis results in the diagonal not being centered under the focal point. Projection causes the near edge of the diagonal to appear bigger because it is closer and the far edge of the diagonal to appear smaller because it is further away. The diagonal does not evenly intercept the light rays converging from the primary mirror.
Re-aligning the primary mirror slightly upward so that the converging light cone is aimed squarely at the diagonal does not work because the reflected converging beam will not be centered under the focuser, because the re-aimed mirror's axis is no longer coincident with the mechanical axis resulting in pointing errors and because the tilted incoming beam of light is vignetted by the upper end.
Our only recourse is to slide the diagonal towards the primary mirror and away from the focuser like this.
Now the diagonal intercepts the entire light cone converging to the focal point. But what about the field of view, particularly the edges of the field? Here's the layout for a 1.5 inch [3.8cm] wide field.
Let's add in the light cones from the left side and right side of the field. Note that just like the light cone converging to the focal point, the light cones have an angle of 14.4 degrees.
Now let's place the diagonal, offset to illuminate the focal point properly as above.
First, we see that both light cones are vignetted by the diagonal size, leaving us with illumination falloff at the edges of the field of roughly 0.4 magnitude. My diagonal calculator is designed to help you make the optimal tradeoff. Secondly, we see that the right edge of the field receives a bit more light than the left edge of the field. In this case, the difference is about +-0.03 magnitudes of light from the mean. Not meaningful for visual observers, knowing this could be important for careful digital imagers who reuse precise flat fields. The diagonal can be repositioned by removing some of the offset to balance the illumination reaching the left and right edges of the field, but then the focal point will no longer receive the primary mirror's entire converging cone of light.