Volume five of Samuel Sturmy’s Mariners Magazine, Mathematical and Practical Arts, published in 1669, contained an illustration of the trajectory a cannonball would follow assuming various amounts of gunpowder in the cannon.
The illustration was substantially the same as the first known representation, 130 years earlier, of the trajectory of a ballistic projectile from Tartaglia’s 1537 book Nova Scientia.
The cannonball leaves the cannon, which is angled at around 45 degrees, then travels in a straight line to the apex of its flight, at which point it follows the path of a partial circle—not a parabola—and then the cannonball is drawn falling straight down, in this case, to point “F.”
When guns were developed in Europe in the 1300s, and still 350 years later when the Mariners drawing was made, the physics of projectiles was not the physics we have today coming from Galileo and Newton; it was a theory from two millennia earlier. It was Aristotle’s theory of motion. By the time just before Galileo’s insights changed our understanding of projectiles and much else, Aristotle’s theory had been augmented but the physics implied in these drawings remained fundamentally Aristotelian.
Sturmy’s mariners were being instructed with a theory, the essential part of which was nearly 2000-years old and which was—let’s not mince words—wrong. Astonishingly wrong.
A straight line up at 45-degree angle? Wouldn’t it have been obvious from throwing a ball or a rock or from peeing standing up that trajectories take the form of parabola?
One recent commentator, James Hannam, writes:
“Historians have long been puzzled how anyone could believe that a projectile could travel in a straight line and then drop out of the sky. After all, experience should have taught otherwise. But experience can be misleading.”
Why didn’t any of the cannoneers from 1300 to 1700 just open their eyes and look? Well, they did. And they drew what they saw. Such is the power of a theory. They saw through the tinted lens of their paradigm. Straight out, then a little arc in the shape of a semi-circle, and then straight down.
The proper description of ballistics was achieved by Galileo who saw his way to why projectiles—when assuming air resistance is zero—travel through the air making a line in the shape of a parabola.
To be fair to the Medieval theories, air resistance makes the actual trajectories somewhat like their drawings. But the wrongness of augmented Aristotelian theory definitely infects their drawings and thus the way they saw the world.
As eminent a mind as Edmund Halley, appointed Astronomer Royal in 1705, said in 1695 something similarly blinkered by Aristotelian physics. Halley was writing about how it would be better and create more damage if we could just get the cannonballs to hit the ground at an oblique angle instead of straight down. He said that when…
“bombs are discharged with great elevations of the mortar, they fall […] perpendicular, and bury themselves too deep in the ground, to do all that damage they might, if they came more oblique, and broke upon or near the surface of the earth; which is a thing acknowledged by the besieged in all towns, who unpaved their streets, to let bombs bury themselves, and thereby stifle the force of their splinters.”
So it turns out the townsfolk believed the Aristotelian theory of motion too.
A preliminary understanding of Aristotle’s physics of motion can be obtained by looking at three quotations. But don’t expect them to make sense. They are alien to us—like interdimensional travelers, they come from another paradigm.
First:
“Everything that is in motion must be moved by something.”
This is the first sentence of his Physics Book 7. The original Greek could also be translated as, “Everything that is changed is changed by something.”
Second is the question guiding his inquiry:
“If everything that is in motion is moved by something, how comes it that certain things, missiles for example, that are not self-moving nevertheless continue their motion… when no longer in contact with the agent that gave them motion?” (from Physics Book 8).
The third thought begins to formulate an answer to that question. He says, invoking his teleological theory,
“Nature is a cause of movement in the thing itself.”
He goes on,
“Force [is] a cause [of motion] in something else.”
And:
“All movement is either natural or forced. Force will accelerate natural motion and is the sole cause of unnatural motion.”
What these quotations say is that the natural, essential, teleological quality inherent in a thing will cause it to move towards its telos. Applying force to a thing can add to natural (teleological) motion or can move the thing otherwise than in the direction that is natural to it, i.e., “unnatural motion.” But this does not yet answer the question in the second quotation. What is moving it after it’s flying out on its own, no longer being acted on by the initial force?
A laymen today would say its momentum, or something like that, explains it. But momentum was not a part of Aristotle’s theory. According to Aristotle, what moves the thing when it is no longer in physical contact with whatever gave it the initial force to move is as follows: “The air is employed as a kind of instrument of the action,” meaning—as best as I can tell, following Lang (1998)—that the air in the path of the projectile swirls around the thing and to the back like a vortex and pushes the projectile forward from the back.
This ludicrous seeming theory was augmented by what’s called “impetus theory” before Tartaglia drew the first representation we have of ballistic trajectories. Impetus theory says that when you throw something you impart a kinetic power to it, which moves the object rather than the air around it. The “motive power” is temporary and self-expending, so eventually the object’s natural motion takes over.
To return to the diagrams... Tartaglia in 1537 and still Samuel Sturmy in 1669 understood the straight line at the beginning of the trajectory as being the “unnatural motion” (also called “violent motion”) caused by the force of the gunpowder. The natural motive power within was apparently held in abeyance during this time. (They did not mix to come up with a trajectory between the two forces, the two force-vectors. Galileo would get a parabola by understanding that the two forces gravity and gunpowder—while being independent—combined vector-wise to make a parabolic arc.)
When the unnatural motion begins to wear out or approaches its complete expenditure, we get a change which “the men described in the only curved shape they knew any math about—the circle.” This was called “mixed motion,” or “crooked motion.” (Why these men allowed the motions to mix at the apex but not also during the so-called “violent motion,” I do not know.) Eventually natural motion is the only motion the cannonball is undergoing and it falls straight down, with no more forward motion.
With Galileo, we get a physics resembling today’s physics. Galileo understood motion not on the impetus theory but on what’s come to be called an inertia theory. A body at rest or constant speed will stay at rest or constant speed unless acted on by a force. As Descartes would eventually say, men had been asking the wrong question about motion before Galileo. Instead of asking what keeps a body moving, they should have been asking what causes it ever to stop.