Editing Force (section)

== Pre-Newtonian concepts ==
{{see also|Aristotelian physics|Theory of impetus}}
[[File:Aristoteles Louvre2.jpg|thumb|upright|[[Aristotle]] famously described a force as anything that causes an object to undergo "unnatural motion"]]
Since antiquity the concept of force has been recognized as integral to the functioning of each of the [[simple machine]]s. The [[mechanical advantage]] given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of [[work (physics)|work]]. Analysis of the characteristics of forces ultimately culminated in the work of [[Archimedes]] who was especially famous for formulating a treatment of [[buoyant force]]s inherent in [[fluid]]s.<ref name="Archimedes"/>

[[Aristotle]] provided a [[philosophical]] discussion of the concept of a force as an integral part of [[Physics (Aristotle)|Aristotelian cosmology]]. In Aristotle's view, the terrestrial sphere contained four [[Classical element|elements]] that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of the elements earth and water, were in their natural place when on the ground, and that they stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force.<ref>{{cite book |last=Lang |first=Helen S. |title=The order of nature in Aristotle's physics : place and the elements |year=1998 |publisher=Cambridge Univ. Press |location=Cambridge |isbn=978-0521624534 |edition=}}</ref> This theory, based on the everyday experience of how objects move, such as the constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of [[projectile]]s, such as the flight of arrows. An archer causes the arrow to move at the start of the flight, and it then sails through the air even though no discernible efficient cause acts upon it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries the projectile to its target. This explanation requires a continuous medium such as air to sustain the motion.<ref name="Hetherington">{{cite book |first=Norriss S. |last=Hetherington |title=Cosmology: Historical, Literary, Philosophical, Religious, and Scientific Perspectives |page=[https://archive.org/details/cosmologyhistori0000unse/page/100 100] |publisher=Garland Reference Library of the Humanities |year=1993 |isbn=978-0-8153-1085-3 |url=https://archive.org/details/cosmologyhistori0000unse/page/100 }}</ref>

Though [[Aristotelian physics]] was criticized as early as the 6th century,<ref>{{cite book|first=Richard |last=Sorabji |chapter=John Philoponus |title=Philoponus and the Rejection of Aristotelian Science |jstor=44216227 |year=2010 |edition=2nd |publisher=Institute of Classical Studies, University of London |isbn=978-1-905-67018-5 |oclc=878730683 |page=47}}</ref><ref>{{cite book|first=Anneliese |last=Maier |author-link=Anneliese Maier |title=On the Threshold of Exact Science |publisher=University of Pennsylvania Press |year=1982 |editor-first=Steven D. |editor-last=Sargent |isbn=978-0-812-27831-6 |oclc=495305340 |page=79}}</ref> its shortcomings would not be corrected until the 17th century work of [[Galileo Galilei]], who was influenced by the late medieval idea that objects in forced motion carried an innate force of [[impetus theory|impetus]]. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the [[Aristotelian theory of gravity|Aristotelian theory of motion]]. He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their [[velocity]] unless acted on by a force, for example [[friction]].<ref name="Galileo">{{cite book|last=Drake |first=Stillman |year=1978 |title=Galileo At Work |location=Chicago |publisher=University of Chicago Press |isbn=0-226-16226-5}}</ref> Galileo's idea that force is needed to change motion rather than to sustain it, further improved upon by [[Isaac Beeckman]], [[René Descartes]], and [[Pierre Gassendi]], became a key principle of Newtonian physics.<ref>{{Cite book |last=LoLordo |first=Antonia |url=https://www.worldcat.org/oclc/182818133 |title=Pierre Gassendi and the Birth of Early Modern Philosophy |date=2007 |publisher=Cambridge University Press |isbn=978-0-511-34982-9 |location=New York |pages=175–180 |oclc=182818133}}</ref>

In the early 17th century, before Newton's ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'', the term "force" ({{langx|la|vis}}) was applied to many physical and non-physical phenomena, e.g., for an acceleration of a point. The product of a point mass and the square of its velocity was named {{lang|la|vis viva}} (live force) by [[Gottfried Wilhelm Leibniz|Leibniz]]. The modern concept of force corresponds to Newton's {{lang|la|vis motrix}} (accelerating force).<ref>{{Cite book |author-link1=Vladimir Arnold |first1=V. I. |last1=Arnold |first2=V. V. |last2=Kozlov |first3= A. I. |last3=Neĩshtadt |url=https://www.worldcat.org/oclc/16404140 |chapter=Mathematical aspects of classical and celestial mechanics |title=Encyclopaedia of Mathematical Sciences, Dynamical Systems III |volume=3 |date=1988 |publisher=Springer-Verlag |others=Anosov, D. V. |isbn=0-387-17002-2 |location=Berlin |oclc=16404140}}</ref>