The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics introduced to explain projectile motion against gravity, first by Hipparchus in antiquity and subsequently by Philoponus. A modified version was later developed by Avicenna and Jean Buridan which became the ancestor of the concepts of inertia and momentum in classical mechanics.

Hipparchan-Philoponan theory

The problem for Aristotelian dynamics posed by the continuation of projectile motion against the resistance of gravity post-projection, such as a stone thrown upwards, was the question of what the mover is that keeps it moving upwards against gravity after the original projector stops pushing it and releases it. Aristotelian dynamics presupposes that all motion against resistance requires a conjoined mover. But in 'detached motions' such as these, there is no visibly apparent mover.

Whereas Aristotle had tentatively suggested the auxiliary theory that the propellant is the medium which is endowed with an incorporeal motive force impressed within its parts by the original projector as they also excite the medium in the original action of throwing the projectile, impetus theoreticians found this theory empirically inadequate and refuted. So they replaced it with the alternative theory that the impressed motive force is impressed directly within the projectile itself by the original projector rather than in the medium. In the process they dispensed with the intermediary propelling agent of the medium in Aristotle's theory, deeming it redundant. Impetus dynamics was thus a secondary theory of Aristotelian dynamics that saved its core principle from refutation by projectile motion and observed it by identifying an internal impetus as its conjoined mover rather than the external medium. What all variants of impetus dynamics had in common was the theory that an incorporeal motive force - be it called an impressed force, mayl or impetus - is impressed within the projectile by some projector.

However, there were crucial differences and variations within Aristotelian impetus dynamics as it developed from its original Hipparchan version of antiquity as subsequently adopted by such as Galileo in his early Pisan dynamics of his 1590 De Motu and its scholastic Avicennan version adopted in the later impetus dynamics of his Dialogo and Discorsi. In the paradigm case of a projectile motion as a form of violent motion against gravity, that of a stone thrown vertically upwards against the downward force of gravity that then falls down again after reaching its zenith, according to Hipparchan impetus dynamics the projector impresses an upward motive force within the stone which is greater then the downward force of gravity or its weight (I > W) whereby the stone moves upwards as its gravity is overcome by its greater upward impetus. But this force of impetus was held to be essentially evanescent and starts to decay away to nothing just of its own accord from the moment the stone is released, rather than its decay being due to any external resistance or to the downward resistance of gravity. Thus the stone’s upward motion decelerates as its impetus decays and its excess over gravity diminishes. Then at the turning point or moment of stasis from upward to downward motion, the stone was said to be in dynamical equilibrium where the upward force of impetus equals the downward force of gravity or the stone’s weight (I = W). After this in the third phase of this projectile motion where I < W, the stone accelerates downwards as its impetus decays even further until it is wholly exhausted (I = 0) and the stone assumes a characteristic constant speed of natural motion proportional to its excess natural weight over that of the medium. Thus this theory predicts all natural motion (i.e. gravitational fall) has a terminal velocity, even in a vacuum.

Thus in its dynamical account of projectile motion, the Hipparchan impetus theory also offered an explanation of the acceleration of gravitational fall when it is the downward second stage of vertical projectile motion. Natural motion was already accepted by Aristotle as being swifter at the end than at the beginning. The Hipparchan impetus theory explained the acceleration as a case of dynamical de-retardation, the continual erosion of the power of a brake on the natural speed of natural motion according to the body's excess natural weight in the medium.

However, it also offered an explanation of the case of gravitational fall just from a state of rest, as when a stone is dropped from the hand. In this case the initial situation of the stone at rest before release was analysed as a state of dynamical equilibrium between the weight of the stone acting downwards and a counterbalancing equal upward force impressed within the stone by the hand pressing upwards. Then when the stone is released from the hand its counterbalancing impetus that was continually refreshed by the hand then immediately starts to decay without further refreshment, and thus becomes increasingly less than its weight and the stone moves downward since I < W, accelerating as a case of de-retardation until I = 0.

Avicennan-Buridan theory

In the 11th century, Avicenna developed an elaborate theory of motion, in which he made a distinction between the inclination and force of a projectile, and concluded that motion was a result of an inclination (mayl) transferred to the projectile by the thrower, and that projectile motion in a vacuum would not cease. He viewed inclination as a permanent force whose effect is dissipated by external forces such as air resistance. Avicenna also referred to mayl to as being proportional to weight times velocity, which was similar to Newton's theory of momentum. Avicenna's concept of mayl was also consistent with the concept of inertia roughly equivalent to Jean Buridan's concept of impetus.

In the 14th century, Jean Buridan rejected the Hipparchan-Philoponan notion that the motive force, which he named impetus, dissipated spontaneously, and adopted the Avicennian impetus theory in which (i) it is only corrupted by the resistances of the medium and of gravity in the case of anti-gravitational motion, but would otherwise be permanently conserved in the absence of any resistances to motion, and in which (ii) gravity is also a downward projector and creator of downward impetus, unlike in the radically different Hipparchan-Philoponan theory in which gravity neither creates not destroys impetus. This latter assimilation of the role of gravity in natural motion to the role of a projector that creates impetus in violent motion was explicitly expounded by Buridan's pupil Dominicus de Clavasio, in his 1357 De Caelo, as follows:

"When something moves a stone by violence, in addition to imposing on it an actual force, it impresses in it a certain impetus. In the same way gravity not only gives motion itself to a moving body, but also gives it a motive power and an impetus, ...".

Buridan's position was that a moving object would only be arrested by the resistance of the air and the weight of the body which would oppose its impetus. Buridan also maintained that impetus was proportional to speed; thus, his initial idea of impetus was similar in many ways to the modern concept of momentum. Despite the obvious similarities to more modern idea of momentum, Buridan saw his theory as only a modification to Aristotle's basic philosophy, maintaining many other peripatetic views, including the belief that there was still a fundamental difference between an object in motion and an object at rest. Buridan also maintained that impetus could be not only linear, but also circular in nature, causing objects (such as celestial bodies) to move in a circle.

In order to dispense with the need for positing continually moving intelligences or souls in the celestial spheres, which he pointed out are not posited by the Bible, he applied impetus theory to their endless rotation by extension of a terrestrial example of its application to rotary motion in the form of a rotating millwheel that continues rotating for a long time after the originally propelling hand is withdrawn, driven by the impetus impressed within it. He wrote on the celestial impetus of the spheres as follows:

"God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more...And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus.

However, having discounted the possibility of any resistance either due to a contrary inclination to move in any opposite direction or due to any external resistance, in concluding their impetus was therefore not corrupted by any resistance Buridan also discounted any inherent resistance to motion in the form of an inclination to rest within the spheres themselves, such as the inertia posited by Averroes and Aquinas. For otherwise that resistance would destroy their impetus, as the anti-Duhemian historian of science Annaliese Maier maintained the Parisian impetus dynamicists were forced to conclude because of their belief in an inherent inclinatio ad quietem or inertia in all bodies. But in fact contrary to that inertial variant of Aristotelian dynamics, according to Buridan prime matter does not resist motion.But this then raised the question within Aristotelian dynamics of why the motive force of impetus does not therefore move the spheres with infinite speed.

One impetus dynamics answer seemed to be that it was a secondary kind of motive force that produced uniform motion rather than infinite speed, just as it seemed Aristotle had supposed the spheres' moving souls do, or rather than producing uniformly accelerated motion like the primary force of gravity did by producing constantly increasing amounts of impetus. However in his Treatise on the heavens and the world in which the heavens are moved by inanimate inherent mechanical forces, Buridan's pupil Oresme offered an alternative 'Thomist'inertial response to this problem in that he did posit a resistance to motion inherent in the heavens (i.e. in the spheres), but which is only a resistance to acceleration beyond their natural speed, rather than to motion itself, and was thus a tendency to preserve their natural speed.This analysis of the dynamics of the motions of the spheres seems to have been a first anticipation of Newton's revised conception of inertia as only resisting accelerated motion but not resisting uniform motion.

Buridan's thought was followed up by his pupil Albert of Saxony (1316-1390) and the Oxford Calculators. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of graphs.

Shortly before Galileo's theory of impetus, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone:

Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion.

See also

• Conatus
• Inertia
• Momentum

References and footnotes

Bibliography

• Clagett, Marshall Science of Mechanics in the Middle Ages University of Wisconsin Press 1959
• Moody, E.A. Galileo and his precursors in Galileo Reappraised Golino (ed) University of California Press 1966
• Drake, Stillman & Drabkin, I.E. Mechanics in Sixteenth Century Italy The University of Wisconsin Press, 1969