Editing Momentum (section)

== History of the concept ==
=== Impetus ===
{{Main|Theory of impetus}}

==== John Philoponus ====
In about 530 AD, [[John Philoponus]] developed a concept of momentum in ''On Physics'', a commentary to [[Aristotle]]'s ''[[Physics (Aristotle)|Physics]]''. Aristotle claimed that everything that is moving must be kept moving by something. For example, a thrown ball must be kept moving by motions of the air. Philoponus pointed out the absurdity in Aristotle's claim that motion of an object is promoted by the same air that is resisting its passage. He proposed instead that an impetus was imparted to the object in the act of throwing it.<ref>{{cite encyclopedia |title=John Philoponus |encyclopedia=Stanford Encyclopedia of Philosophy |url=http://plato.stanford.edu/entries/philoponus/#2.1 |access-date=26 July 2012 |date=8 June 2007}}</ref>

==== Ibn Sīnā ====
[[File:1950 "Avicenna" stamp of Iran (cropped).jpg|alt=Engraving of Ibn Sīnā|thumb|195x195px|Ibn Sīnā<br/>(980–1037)]]
In 1020, [[Avicenna|Ibn Sīnā]] (also known by his [[Latinisation of names|Latinized]] name Avicenna) read Philoponus and published his own theory of motion in ''[[The Book of Healing]]''. He agreed that an impetus is imparted to a projectile by the thrower; but unlike Philoponus, who believed that it was a temporary virtue that would decline even in a vacuum, he viewed it as a persistent, requiring external forces such as [[air resistance]] to dissipate it.<ref name="Espinoza">{{cite journal |last1=Espinoza |first1=Fernando |date=2005 |title=An analysis of the historical development of ideas about motion and its implications for teaching |journal=Physics Education |volume=40 |issue=2 |page=141 |bibcode=2005PhyEd..40..139E |doi=10.1088/0031-9120/40/2/002 |s2cid=250809354}}</ref><ref name="Nasr">{{Cite book |last1=Nasr |first1=Seyyed Hossein |title=The Islamic intellectual tradition in Persia |last2=Razavi |first2=Mehdi Amin |date=1996 |publisher=[[Routledge]] |isbn=978-0-7007-0314-2 |page=72 |author1-link=Seyyed Hossein Nasr}}</ref><ref name="Sayili">{{cite journal |author=[[Aydin Sayili]] |date=1987 |title=Ibn Sīnā and Buridan on the Motion of the Projectile |journal=Annals of the New York Academy of Sciences |volume=500 |issue=1 |pages=477–482 |bibcode=1987NYASA.500..477S |doi=10.1111/j.1749-6632.1987.tb37219.x |s2cid=84784804}}</ref>

==== Peter Olivi, Jean Buridan ====
In the 13th and 14th century, [[Peter Olivi]] and [[Jean Buridan]] read and refined the work of Philoponus, and possibly that of Ibn Sīnā.<ref name="Sayili" /> Buridan, who in about 1350 was made rector of the University of Paris, referred to [[Theory of impetus|impetus]] being proportional to the weight times the speed. Moreover, Buridan's theory was different from his predecessor's in that he did not consider impetus to be self-dissipating, asserting that a body would be arrested by the forces of air resistance and gravity which might be opposing its impetus.<ref>{{cite encyclopedia |title=Buridian, John |encyclopedia=Medieval Science, Technology and Medicine:an Encyclopedia |page=107 |last2=Livesay |first2=S. J. |last3=Wallis |first3=F. |first1=T. F. |last1=Glick}}</ref><ref name="Park">{{cite book |last=Park |first=David |url=https://archive.org/details/howwhyessayonori0000park |title=The how and the why: an essay on the origins and development of physical theory |date=1990 |publisher=Princeton University Press |others=With drawings by Robin Brickman |isbn=978-0-691-02508-7 |edition=3rd print |location=Princeton, New Jersey |pages=[https://archive.org/details/howwhyessayonori0000park/page/139 139–141] |url-access=registration}}</ref>

=== Quantity of motion<span class="anchor" id="Quantity of motion"></span> ===

==== René Descartes ====
In ''[[Principles of Philosophy]]'' (''Principia Philosophiae'') from 1644, the French philosopher [[René Descartes]] defined "quantity of motion" (''[[Latin language|Latin]]: quantitas motus'') as the product of size and speed,<ref name=":0">{{Cite book |last=Descartes |first=R. |url=https://www.earlymoderntexts.com/assets/pdfs/descartes1644part2.pdf |title=Principles of philosophy |year=2008 |editor-last=Bennett |editor-first=J. |at=Part II, § 36. |orig-date=1644}}</ref> and claimed that the total quantity of motion in the universe is conserved.<ref name=":0" /><ref>Alexander Afriat (2004). [http://philsci-archive.pitt.edu/1699/1/Momentum3.pdf "Cartesian and Lagrangian Momentum"]. {{webarchive|url=https://web.archive.org/web/20170309014638/http://philsci-archive.pitt.edu/1699/1/Momentum3.pdf|date=2017-03-09}}.</ref>[[File:Frans Hals - Portret van René Descartes (cropped)2.jpg|alt=Portrait of René Descartes|thumb|153x153px|René Descartes<br/>(1596–1650)]]{{Blockquote|text=If x is twice the size of y, and is moving half as fast, then there's the same amount of motion in each.|author=|title=|source=}}{{Blockquote|text=[God] created matter, along with its motion ... merely by letting things run their course, he preserves the same amount of motion ... as he put there in the beginning.}}

This should not be read as a statement of the modern law of [[conservation of momentum]], since Descartes had no concept of mass as distinct from weight and size. (The concept of mass, as distinct from weight, was introduced by Newton in 1686.)<ref>{{Cite book |last=Newton |first=I |url=https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PP13 |title=The mathematical principles of natural philosophy |publisher=Printed for Benjamin Motte |year=1729 |pages=1–2 |translator-last=Motte |translator-first=A. |orig-date=Original work published 1686}}</ref> More important, he believed that it is speed rather than velocity that is conserved. So for Descartes, if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion.<ref>{{Cite book |last=Garber |first=Daniel |title=The Cambridge Companion to Descartes |date=1992 |publisher=Cambridge University Press |isbn=978-0-521-36696-0 |editor=John Cottingham |place=Cambridge |pages=310–319 |chapter=Descartes' Physics}}</ref><ref>{{cite book |last=Rothman |first=Milton A. |url=https://archive.org/details/discoveringnatur0000roth/page/83 |title=Discovering the natural laws: the experimental basis of physics |date=1989 |publisher=Dover |isbn=978-0-486-26178-2 |edition=2nd |location=New York |pages=[https://archive.org/details/discoveringnatur0000roth/page/83 83–88]}}</ref><ref>{{cite encyclopedia |title=Descartes' Physics |encyclopedia=The Stanford Encyclopedia of Philosophy |url=https://plato.stanford.edu/archives/fall2017/entries/descartes-physics/ |access-date=29 November 2019 |date=Fall 2017 |editor-last1=Zalta |editor-first1=Edward N. |first1=Edward |last1=Slowik}}</ref> [[Galileo]], in his ''[[Two New Sciences]]'' (published in 1638), used the [[Italian language|Italian]] word {{lang|it|impeto}} to similarly describe Descartes's quantity of motion.

==== Christiaan Huygens ====
[[File:Christiaan Huygens-painting (cropped).jpeg|alt=Portrait of Christiaan Huygens|thumb|155x155px|Christiaan Huygens<br/>(1629–1695)]]
In the 1600s, [[Christiaan Huygens]] concluded quite early that [[Cartesian laws of motion|Descartes's laws]] for the elastic collision of two bodies must be wrong, and he formulated the correct laws.<ref>{{cite book |title=The Beginnings of Modern Science |publisher=Basic Books |year=1964 |editor-last=Taton |editor-first=Rene |orig-date=1958}}</ref> An important step was his recognition of the [[Galilean invariance]] of the problems.<ref>Garber and Ayers, pp. 666–667.</ref> His views then took many years to be circulated. He passed them on in person to [[William Brouncker, 2nd Viscount Brouncker|William Brouncker]] and [[Christopher Wren]] in London, in 1661.<ref>Garber and Ayers, p. 689.</ref> What Spinoza wrote to [[Henry Oldenburg]] about them, in 1666 during the [[Second Anglo-Dutch War]], was guarded.<ref name="Israel2001">{{cite book |last=Israel |first=Jonathan I. |url=https://books.google.com/books?id=vMvlEweVPTsC&pg=RA3-PR62 |title=Radical Enlightenment: Philosophy and the Making of Modernity 1650–1750 |date=8 February 2001 |publisher=Oxford University Press |isbn=978-0-19-162287-8 |pages=lxii–lxiii |author-link=Jonathan I. Israel |access-date=11 May 2013}}</ref> Huygens had actually worked them out in a manuscript {{lang|la|De motu corporum ex percussione}} in the period 1652–1656. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He published them in the {{lang|fr|[[Journal des sçavans]]}} in 1669.<ref>Dictionary, p. 470.</ref>

=== Momentum ===

==== John Wallis ====
In 1670, [[John Wallis]], in {{lang|la|Mechanica sive De Motu, Tractatus Geometricus}}, stated the law of conservation of momentum: "the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result".<ref>{{cite book |last=Scott |first=J. F. |title=The Mathematical Work of John Wallis, D.D., F.R.S. |date=1981 |publisher=Chelsea Publishing Company |isbn=978-0-8284-0314-6 |page=111}}</ref> Wallis used ''momentum'' for quantity of motion, and {{lang|la|vis}} for force.

==== Gottfried Leibniz ====
In 1686, [[Gottfried Wilhelm Leibniz]], in ''[[Discourse on Metaphysics]]'', gave an argument against Descartes' construction of the conservation of the "quantity of motion" using an example of dropping blocks of different sizes different distances. He points out that force is conserved but quantity of motion, construed as the product of size and speed of an object, is not conserved.<ref>{{Cite book |last=Leibniz |first=G. W. |title=Philosophical Essays |date=1989 |publisher=Hackett |isbn=978-0-87220-062-3 |editor1-last=Ariew |editor1-first=Roger |place=Indianapolis, Indiana |pages=49–51 |chapter=Discourse on Metaphysics |editor2-last=Garber |editor2-first=Daniel}}</ref>

==== Isaac Newton ====
[[File:Isaac Newton by James Thronill, after Sir Godfrey Kneller.jpg|alt=Portrait of Isaac Newton by James Thronill, after Sir Godfrey Kneller|thumb|187x187px|Isaac Newton<br/>(1642–1727)]]
In 1687, [[Isaac Newton]], in {{lang|la|[[Philosophiæ Naturalis Principia Mathematica]]}}, just like Wallis, showed a similar casting around for words to use for the mathematical momentum. His Definition II defines {{lang|la|quantitas motus}}, "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum.<ref>{{cite book |last=Grimsehl |first=Ernst |title=A Textbook of Physics |date=1932 |publisher=Blackie & Son |location=London & Glasgow |page=78 |translator-last=Woodward |translator-first=Leonard Ary}}</ref> Thus when in Law II he refers to {{lang|la|mutatio motus}}, "change of motion", being proportional to the force impressed, he is generally taken to mean momentum and not motion.<ref>{{cite book |last=Rescigno |first=Aldo |title=Foundation of Pharmacokinetics |date=2003 |publisher=Kluwer Academic/Plenum |isbn=978-0-306-47704-1 |location=New York |page=19}}</ref>

==== John Jennings ====
In 1721, [[John Jennings (tutor)|John Jennings]] published ''Miscellanea'', where the momentum in its current mathematical sense is attested, five years before the final edition of Newton's {{lang|la|Principia Mathematica}}. ''Momentum'' {{math|M}} or "quantity of motion" was being defined for students as "a rectangle", the product of {{mvar|Q}} and {{mvar|V}}, where {{mvar|Q}} is "quantity of material" and {{mvar|V}} is "velocity", {{math|{{sfrac|{{var|s}}|{{var|t}}}}}}.<ref>{{cite book |last=Jennings |first=John |title=Miscellanea in Usum Juventutis Academicae |date=1721 |publisher=R. Aikes & G. Dicey |location=Northampton |page=67 |author-link=John Jennings (tutor) |lang=la}}</ref>

In 1728, the [[Cyclopædia, or an Universal Dictionary of Arts and Sciences|Cyclopedia]] states:

{{Blockquote
|text=The ''Momentum'', ''Impetus'', or Quantity of Motion of any Body, is the ''Factum'' [i.e., product] of its Velocity, (or the Space it moves in a given Time, see {{sc2|Motion}}) multiplied into its Mass.
}}