Good thread...
I, too, used to think that bullets flew in an arc from a horizontal barrel...
The term "flat-shooting" gets thrown around alot, especially in the LR target game.
But after doing a little reading about external ballistics, it appears not to be the case. The "rise" of the bullet is due to the sighting plane as mentioned above- depends on where your rifle sights, or scope, is zeroed. As kraigwy simply stated, the barrel is pointed up. The parabolic flight of the bullet is due to the angle of the bore.
Due to the near parabolic shape of the projectile path, the line of sight or horizontal sighting plane will cross the projectiles trajectory at two points called the near zero and far zero in case the projectile starts its trajectory (slightly) inclined upward in relation to the sighting device horizontal plane, causing part of the bullet path to appear to rise above the horizontal sighting plane. The distance at which the firearm is zeroed, and the vertical distance between the sighting device axis and barrel bore axis, determine the apparent severity of the "rise" in both the X and Y axes (how far above the horizontal sighting plane the rise goes, and over what distance it lasts).
Many firearms ballistics tables and graphs show a rise in trajectory at distances shorter than the one (far zero) used for sight-in. This apparent "rise" of the projectile in the first part of its trajectory is relative only to the sighting plane, and is not actually a rise. The laws of physics dictate that the projectile will begin to be pulled down by gravity as soon as it leaves the support of the barrel bore at the muzzle, and can never rise above the axis of the bore. The apparent "rise" is caused by the separation of the plane of the sighting device axis and that of the bore axis and the fact that the projectile rarely leaves the bore perfectly horizontally. If a firearm is zeroed at 100 meters, then the far horizontal sighting plane and the projectile path must "cross" at that distance; the sighting line must be adjusted to intersect with the projectile path at 100 meters. In the case of a bore axis that is maintained in a perfectly horizontal position, the sighting device must be inclined downward to achieve this intersection. The axial separation distance between the line of sight and the bore axis and trajectory of the projectile dictate the amount of angular declination required to achieve the required intersection.