• If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • Finally, you can manage your Google Docs, uploads, and email attachments (plus Dropbox and Slack files) in one convenient place. Claim a free account, and in less than 2 minutes, Dokkio (from the makers of PBworks) can automatically organize your content for you.


Mechanics and Motion in the Middle Ages

Page history last edited by Nicole Hagstrom 12 years, 6 months ago

 Motion in the Middle Ages


     Medieval physics was founded primarily on Aristotle's philosophy of motion requiring a mover and a medium. There were two predominant theories of motion: forma fluens and fluxus formae. Forma fluens held that motion described the moving body and the succession of places it occupies, while fluxus formae stated that motion was a quality or property of a body in motion. The English philosopher William of Ockham argued for forma fluens by use of what is known Ockham's Razor, a principle that the simplest explanation is prefered. He compared the following two sentences:


"Every motion is produced by a mover." (fluxus formae)

"Every thing that is moved is moved by a mover." (forma fluens)


Since forma fluens postulates the existence of fewer things, it is more economical and hence should be the preferred theory.  Jean Buridan, however, was an advocate of fluxus formae. If motion were a property, he argued, it could be possible without the discussion of a change in place. This in turn allowed God to impart a motion to the universe if He so desired, without the problem of there being a place for it to go.


      The dynamics of motion in the Middle Ages followed Aristotle's theory that all motion must have a mover.  In order to account for the mover in the case of natural motion, however, various ideas of an internal motive force were proposed. One of these was Jean Buridan's impetus theory.  When an object is subject to projectile motion, an impetus is given to the object which then keeps that body in motion.  The reason that an object in violent motion stops is because impetus dissipates over time.  This allows an explanation of the cause of the motion of the stars. God could have imparted an impetus to the celestial bodies, which continue to move due to the lack of resistance from the aether.  In the case of natural motion of falling objects, as soon as it is let go, the falling body's speed increases as the impetus increases.


     Members of Merton College at Oxford also thought about motion in Buridan's terms. They gave definitions for velocity, uniform and nonuniform motion, and various types of accelerated motions. They also made an attempt at defining instantaneous velocity. They developed their ideas on velocity through the theory of intensification and remission of properties. Nicole Oresme developed a geometrical representation of this, which allowed the proof of the mean speed theorem for example. He represented intervals of time through horizontal line segments, and intensities of velocity through vertical line segments perpendicular to the first. These would form figures the are of which became associated with distance - the quantity of motion. All this was just an intellectual endeavor though, and was not meant to be applied to the real world. In fact, it is difficult to find motions such as uniform acceleration in nature.


     Nicole Oresme's geometric proof:



     Many medieval scholars believed it possible to quantify the dynamic relations between force, resistance and velocity. According to Aristotle's claims, velocity is proportional to the force and inversely proportional to the resistance. In modern terms, this is expressed as:


                                                          v = F/R


While useful, this equation is also misleading. Aristotle, after all, had no clear conception of velocity as a technical and quantifiable term. Hence, the relationship also does not hold for all values of F and R. From this premise came Bradwardine's Law. It holds that, for example, when the velocity is doubled, the ratio F/R is squared: 2V= (F/R)², 3V= (F/R)³, and so on.


      According to Aristotle, if the swiftness of a falling body is a function of the resistance it encounters, then in a vacuum with no resistance at all there would be nothing slowing the object, and it would therefore move at infinite speed. At infinite speed, an object would take no time to reach from point A to point B, meaning it would be at both point A and B at the same time. From this, Aristotle concluded that void space was an impossibility. John Philoponus criticized this conclusion. He pointed out that we cannot test Aristotle's claim experimentally because there is no means of determining the relative densities of the media. We must think about the cause of motion rather than the resistance of motion. We can consider two objects falling in a void. Assuming one is twice the weight of the other, the heavier object will descend a given distance in half the time required by the lighter object. The efficient cause of the descent of a falling body is weight. In a void where there is no resistance, the sole determinant of motion will be the weight of the body. Heavier bodies will traverse a given distance more rapidly than lighter bodies, but never at infinite speed. In a medium, the resistance of the medium slows the motion by a certain amount, and the net effect of this slowing is to close the gap in swiftness between heavier and lighter bodies.


 Optics in the Middle Ages


    Optics, the study of light and vision, was another topic studied on a broad scale during the Middle Ages.  Chiefly concerned with the refraction and reflection of light, a range of schors attemtped to explain the phenomenon of sight.  Influenced by Aristotle's intromissionist theory and Euclid's extramissionist theory, the Islamic astronomer, Alhazen, merged the two theories using the visual cone from extramissionists and the physical explanations from the intromissionists.  Two scholars, Bacon and Grosseteste, used the information presented by Alhazen and Aristotle to further study the field of optics.  Bacon went on to use optics and the notion that a universal force was the instrument of causation, to develop his natural philosophy.

     Theodoric of Freiburg used this theory of optics to give an explanation of rainbows.  He determined that rainbows were formed from the refraction and reflection of light in a raindrop.  Colors are determined by the angle at which light enters the raindrop, from the viewer's perspective.  The smallest angle produces purple, and the largest angle produces the color red.  Theodoric also analyzed and determined the characteristics of secondary rainbows.  Secondary rainbows appear fainter than primary rainbows due to a second reflection within the raindrop.  Theodoric's theory is very close to the modern explanation of rainbows.


Primary Sources



Key Terms and Definitions

kinematics: description of motion of moving objects

dynamics: description of the causes of various motions

impetus:  a quality that is imparted to objects that keeps them in motion after losing contact with the initial force

Forma Fluens:  The idea that motion is merely a term describing the moving body and the succession of places the body moves into

Fluxus Formae:  The idea that motion is a quality of an object that can be changed

Mean Speed Theorem:  a theorem that states that a body uniformly accelerating from rest, covers the same distance in the same amount of time as a body moving at a constant speed equal to half of the accelerated body's final speed.  Nicole Oresme provided a proof of this theorem.

Bradwardine's Law:  A law put forth by Thomas Bradwardine that relates an algebraic increase in the velocity of an object to a geometric increase of the ratio of force to resistance.  



Relevant Links


Comments (6)

Katie Cox said

at 5:23 pm on Oct 14, 2008

I missed class for a university sponsored event today, so Dr. Ramberg advised me to start this class notes page based on the reading assigned for today. I included a cursory description of each section of Lindberg ch 12, but I do not know for sure that it is exactly what was covered in class today. I did completely omit any discussion of optics, as Lindberg seemed wishy-washy about putting it into this chapter, and any information included in the chapter was already covered in class on September 30. Like I said, though, I'm guessing at the content of today's lecture.

Grant Berry said

at 9:10 pm on Oct 14, 2008

I talked about motion a little bit, mentioning Ockham and Buridan's arguments.

jgm829@... said

at 11:55 pm on Oct 14, 2008

I added some stuff on Aristotle's theory of motion and on how John Philoponus says motion acts otherwise.

liz mastroianni said

at 1:08 pm on Oct 15, 2008

just looked over it, didn't seem like there was anything that needed to be added. However, im going to look over it later and look over it again

Alyson Collins said

at 5:00 pm on Oct 15, 2008

Just added Merton College (kinematics vs. dynamics), and a bit about Brabwardine's Law, Still plenty to add though.

Garrett McCormack said

at 8:30 pm on Oct 16, 2008

i added some more definitions and some sentences here and there

You don't have permission to comment on this page.