I'm reading a popular science encyclopedia now, particularly chapters about the history of physics. The chapter goes on to evaluate the development of the concept of kinetic energy, starting with Aristotle's (grossly incorrect) explanation of a flying arrow saying that it's kept in motion by the air behind it, and then continuing to medieval impetus theory. Added: The picture below illustrates the trajectory of a flying cannonball as described by Albert of Saxony.

What struck me immediately was how drastically different from observations its predictions were. The earliest impetus theory predicted that a cannonball's trajectory was an angle: first a slanted straight line until the impetus runs out, then a vertical line of freefall. A later development added an intermediate stage, as seen on the picture to the left. At first the impetus was at full force, and would launch the cannonball in a straight line; then it would gradually give way to freefall and curve until the ball would be falling in a straight line.

While this model is closer to reality than the original prediction, I still cannot help but think... How could they deviate from observations so strongly?

Yes, yes, hindsight bias.

But if you launch a stream of water out of a slanted tube or sleeve, even if you know nothing about paraboles, you can observe that the curve it follows in the air is symmetrical. Balls such as those used for games would visibly not produce curves like depicted.

Perhaps the idea of verifying theories with experiments was only beginning to coalesce at that time, but what kind of possible thought process could lead one to publish theories so grossly out of touch with everyday observations, even those that you see without making any explicit experiments? Did the authors think something along the lines of "Well, reality should behave this way, and if it doesn't, it's its own fault"?