This is a matter of physics and geometry, not theory. The trajectory still has to follow the law of gravity, and the slope (up-hill or down-hill) is still as much a geometrical angle as ever, no matter whether you're shooting a .220 Howell or a .22 Short.
Gravity pulls the bullet downward vertically from the extension of the bore axis at the moment of its exit from the muzzle, no matter what that line's angle from the horizontal. This downward pull is always vertical, always the same, no matter what the velocity, the ballistic coefficient. etc. But the amount of this drop looks different through the scope when the angle is high or low.
Many years ago, before I knew the math and science explanation for this, I figured it out for myself intuitively � which may be the best way to "explain" it for accurate but unscientific understanding and visualization �
Imagine shooting with the line of sight
(a) horizontal,
(b) vertical, muzzle-up, and
(c) vertical, muzzle-down (from a great height, as out the open bomb-bay doors of a bomber at a very high altitude).
Remember, the line of sight is at a slight angle to the bore axis.
� In situation (a), the bullet arcs slightly upward, above the line of sight a small but increasing distance, then curves over and down to cross the line of sight at the "zero" range, then drops increasingly below the line of sight.
� In situation (b), the bullet arcs away from the line of sight and curves backward overhead, farther and farther from the line of sight, never crossing the line of sight again as it reaches the peak of its upward travel and falls to earth.
� In situation (c), the bullet goes straight down along the extension of the bore axis, but the line of sight angles increasingly farther away from the extension of the bore axis, so the bullet never crosses it again.
Once you "see" these three situations clearly, you'll see that at slighter, less extreme upward and downward angles, the effect is the same, but to a lesser extent, whether the angle of the line of sight is above or below the horizontal. And the greater the angle above or below the horizontal, the farther "above" the line of sight the bullet travels on the line of flight that gravity gives it.
With a variety of muzzle velocities and ballistic coefficients, different bullets travel with slightly different divergences but always following exactly the same principles as in the extreme situations that I've just described. Trajectories of specific bullets with specific muzzle velocities and ballistic coefficients, at specific angles above or below horizontal, have to be calculated independently to get specific figures for the differences in drop below the line of sight. But the proven physical and mathematical principles that govern the outcome do not vary � ever.
