The theory of impetus, developed in the Middle Ages, attempts to explain the forced motion of a body, what it is, and how it comes about or ceases. In ancient and medieval times, motion was always considered absolute, relative to the Earth as the center of the universe. The theory was introduced by John Philoponus in the 6th century, ISBN is for volume 7, not the set. Link to page 307 from Google's copy of 2008 reprint. expanded upon by Islamic scholars in the 11th and 12th centuries, and established in Western scientific thought in the 14th century, before ultimately being disproven in the 17th century. It is the intellectual precursor to the concepts of inertia, momentum and acceleration in classical mechanics.
The theory of impetus is an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain projectile motion against gravity. Aristotelian dynamics of forced (in antiquity called "unnatural") motion states that a body only moves when an external force is constantly driving it. The greater the force acting, the proportionally greater the speed of the body. If the force stops acting, the body immediately returns to the natural state of rest. It also states – as clearly formulated by John of Jadun in his work Quaestiones super 8 libros Physicorum Aristotelis – that both motion and force are transmitted to the medium,Thomas Aquinas in his Commentary on the Eight Books of Physics, Phys. VIII lect. 22, writes about Aristotle's Physics: "dicit quod si secundum movens movet motum a primo movente necesse est hoc dicere, quod primum movens, scilicet proiciens, det secundo moventi , scilicet aeri vel cuicumque tali corpori, quod est natum movere corpus proiectum, ut possit movere et ut possit moveri: utrumque enim habet aer vel aqua a proiciente; et quod moveat et quod moveatur." Translation: "He says, if the second mover transmits the motion of the first mover, then it must be said that the first mover, namely the thrower, transmits to the second mover, namely the air or any other medium which naturally moves the thrown body, something that can move and that can be moved: for air or water have both from the thrower: that which moves and that which is moved." such that this force propagates continuously from layer to layer of air, becoming weaker and weaker until it finally dies out. This is how the body finally comes to rest.
Although the medieval philosophers held to the intuitive idea that only a direct application of force could cause and maintain motion, they recognized that Aristotle's explanation of unnatural motion could not be correct. They therefore developed the concept of impetus. Impetus was understood to be a force inherent in a moving body that had previously been transferred to it by an external force during a previous direct contact.
Impetus as a force has no equivalence in modern mechanics, which provides a different explanation of objects in motion: Motion is not absolute but relative to a reference frame (observer), and the permanent state of an object is not rest but uniform motion. The continuity of motion does not require an external or internal force, being based on the inertia of the object. At most, impetus approaches the meaning of "linear momentum" of a mass, because it is linear momentum as the product of mass and velocity that maintains motion due to the inertia of the mass (conservation of linear momentum). But momentum is not a force; rather, a force is the cause of a change in the momentum of a body, and vice versa.
Aristotelian theory
Aristotelian physics is the form of natural philosophy described in the works of the Greek philosopher Aristotle (384–322 BC). In his work Physics, Aristotle intended to establish general principles of change that govern all natural bodies, both living and inanimate, celestial and terrestrial – including all motion, quantitative change, qualitative change, and substantial change.
Aristotle describes two kinds of motion: "violent" or "unnatural motion", such as that of a thrown stone, in Physics (254b10), and "natural motion", such as of a falling object, in On the Heavens (300a20). In violent motion, as soon as the agent stops causing it, the motion stops also: in other words, the natural state of an object is to be at rest. (Aristotle did not address friction.)
Hipparchus' theory
In the 2nd century, Hipparchus assumed that the throwing force is transferred to the body at the time of the throw, and that the body dissipates it during the subsequent up-and-down motion of free fall. This is according to the Neoplatonist Simplicius of Cilicia, who quotes Hipparchus in his book Aristotelis De Caelo commentaria 264, 25 as follows: "Hipparchus says in his book On Bodies Carried Down by Their Weight that the throwing force is the cause of the upward motion of [a lump of] earth thrown upward as long as this force is stronger than that of the thrown body; the stronger the throwing force, the faster the upward motion. Then, when the force decreases, the upward motion continues at a decreased speed until the body begins to move downward under the influence of its own weight, while the throwing force still continues in some way. As this decreases, the velocity of the fall increases and reaches its highest value when this force is completely dissipated." Thus, Hipparchus does not speak of a continuous contact between the moving force and the moving body, or of the function of air as an intermediate carrier of motion, as Aristotle claims.
Philoponan theory
In the 6th century, John Philoponus partly accepted Aristotle's theory that "continuation of motion depends on continued action of a force," but modified it to include his idea that the hurled body acquires a motive power or inclination for forced movement from the agent producing the initial motion and that this power secures the continuation of such motion. However, he argued that this impressed virtue was temporary: that it was a self-expending inclination, and thus the violent motion produced comes to an end, changing back into natural motion.Aydin Sayili (1987), "Ibn Sīnā and Buridan on the Motion of the Projectile", Annals of the New York Academy of Sciences 500 (1): 477–482
In his book On Aristotle Physics 641, 12; 641, 29; 642, 9 Philoponus first argues explicitly against Aristotle's explanation that a thrown stone, after leaving the hand, cannot be propelled any further by the air behind it. Then he continues: "Instead, some immaterial kinetic force must be imparted to the projectile by the thrower." He also held that an object thrown into empty space would continue moving without any air to push it, contrary to Aristotle's opinion. Philoponus uses two different expressions for impetus: kinetic capacity (dynamis) and kinetic force (energeia). Both expressions designate a concept similar to the modern concept of energy, distinct from the Aristotelian conceptions of potentiality and actuality.
Philoponus' theory of imparted force cannot be understood as a principle of inertia. For while he rightly says that the driving quality is no longer imparted externally but has become an internal property of the body, he still accepts the Aristotelian assertion that the driving quality is a force (power) that now acts internally and to which velocity is proportional.
Ockham's theory and Marchia's theory The first to describe persistent motion by itself was William of Ockham in 1318. He proposed a thought experiment in which two projectiles moving in different directions meet at a point; according to Aristotle, the same portion of air at that point would be moved simultaneously in two different directions. Ockham thought this absurd and that it invalidated the Aristotelian theory. "I say therefore that that which moves (ipsum movens) ... after the separation of the moving body from the original projector, is the body moved by itself (ipsum motum secundum se) and not by any power in it or relative to it (virtus absoluta in eo vel respectiva)".William of Ockham Commentary on the Sentences, Book 2, Question 26, M, 1318
Around 1320, Francis de Marchia developed a detailed and elaborate theory of his virtus derelicta. He described this as force impressed on a projectile that gradually passes away and is consumed by the movement it generates. It is a form that is "not simply permanent, nor simply fluent, but almost medial", staying for some time in the body, but then fading away.
Iranian theories
In the 11th century, Avicenna (Ibn Sīnā) discussed Philoponus' theory in The Book of Healing, in Physics IV.14 he says: "When we independently verify the issue (of projectile motion), we find the most correct doctrine is the doctrine of those who think that the moved object acquires an inclination from the mover."
Ibn Sīnā agreed that an impetus is imparted to a projectile by the thrower and viewed this as persistent, requiring external forces such as air resistance to dissipate it. Ibn Sīnā made distinction between 'force' and 'inclination' (called "mayl"), and argued that an object gained inclination when the object is in opposition to its natural motion. Therefore, he concluded that continuation of motion is attributed to the inclination that is transferred to the object, and that object will be in motion until the inclination is spent. He also claimed that a projectile in a vacuum would not stop unless it is acted upon.Espinoza, Fernando. "An Analysis of the Historical Development of Ideas About Motion and its Implications for Teaching". Physics Education. Vol. 40(2).
This idea was later described as "impetus" by Jean Buridan, who may have been influenced by Ibn Sina.Sayili, Aydin. "Ibn Sina and Buridan on the Motion the Projectile". Annals of the New York Academy of Sciences vol. 500(1). pp. 477–482.
Arabic theories In the 12th century, Hibat Allah Abu'l-Barakat al-Baghdaadi adopted Philoponus' theory of impetus. In his Kitab al-Mu'tabar, Abu'l-Barakat stated that the mover imparts a violent inclination (mayl qasri) on the moved and that this diminishes as the moving object distances itself from the mover. Like Philoponus, and unlike Ibn Sīnā, al-Baghdaadi believed that the inclination self-extinguishes.
He also proposed an explanation of the acceleration of falling bodies where inclination is successively applied, because it is the falling body itself which provides the inclination, as opposed to shooting a bow, where only one violent inclination is applied. According to Shlomo Pines, al-Baghdaadi's theory was:
the oldest negation of Aristotle's fundamental dynamic law [namely, that a constant force produces a uniform motion], [and is thus an] anticipation in a vague fashion of the fundamental law of classical mechanics [namely, that a force applied continuously produces acceleration].
Jean Buridan and Albert of Saxony later refer to Abu'l-Barakat in explaining that the acceleration of a falling body is a result of its increasing impetus.
Buridanist impetus In the 14th century, Jean Buridan postulated the notion of motive force, which he called impetus.
Buridan gives his theory a mathematical value: impetus = weight × velocity.
Buridan's pupil Dominicus de Clavasio in his 1357 De Caelo, states:
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. 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 angular in nature, causing objects (such as celestial bodies) to move in a circle.