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also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown 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href="https://cs.wikipedia.org/wiki/Vis_viva" title="Vis viva – Czech" lang="cs" hreflang="cs" data-title="Vis viva" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Vis_viva" title="Vis viva – German" lang="de" hreflang="de" data-title="Vis viva" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Vis_viva" title="Vis viva – Spanish" lang="es" hreflang="es" data-title="Vis viva" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Force_vive_(physique)" title="Force vive (physique) – French" lang="fr" hreflang="fr" data-title="Force vive (physique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%A5%D5%B6%D5%A4%D5%A1%D5%B6%D5%AB_%D5%B8%D6%82%D5%AA_(%D6%86%D5%AB%D5%A6%D5%AB%D5%AF%D5%A1)" title="Կենդանի ուժ (ֆիզիկա) – Armenian" lang="hy" hreflang="hy" data-title="Կենդանի ուժ (ֆիզիկա)" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Vis_viva" title="Vis viva – Indonesian" lang="id" hreflang="id" data-title="Vis viva" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%9B%D7%95%D7%97_%D7%94%D7%97%D7%99" title="הכוח החי – Hebrew" lang="he" hreflang="he" data-title="הכוח החי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vis_viva" title="Vis viva – Dutch" lang="nl" hreflang="nl" data-title="Vis viva" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Tirik_kuch_(fizika)" title="Tirik kuch (fizika) – Uzbek" lang="uz" hreflang="uz" data-title="Tirik kuch (fizika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Vis_viva" title="Vis viva – Portuguese" lang="pt" hreflang="pt" data-title="Vis viva" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Vis_viva" title="Vis viva – Romanian" lang="ro" hreflang="ro" data-title="Vis viva" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%96%D0%B8%D0%B2%D0%B0%D1%8F_%D1%81%D0%B8%D0%BB%D0%B0_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Живая сила (физика) – Russian" lang="ru" hreflang="ru" data-title="Живая сила (физика)" data-language-autonym="Русский" data-language-local-name="Russian" 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<a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> in an early formulation of the principle of <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vis_viva&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Proposed by <a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Gottfried Leibniz</a> over the period 1676–1689, the theory was controversial as it seemed to oppose the theory of conservation of quantity of motion advocated by <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Descartes' quantity of motion was different from <a href="/wiki/Momentum" title="Momentum">momentum</a>, but Newton defined the quantity of motion as the conjunction of the quantity of matter and velocity in Definition II of his <a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Principia.</a> In Definition III, he defined the force that resists a change in motion as the <i>vis inertia</i> of Descartes. <a href="/wiki/Newton%E2%80%99s_Third_Law_of_Motion" class="mw-redirect" title="Newton’s Third Law of Motion">Newton’s Third Law of Motion</a> (for every action there is an equal and opposite reaction) is also equivalent to the principle of <a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">conservation of momentum</a>. Leibniz accepted the principle of conservation of momentum, but rejected the Cartesian version of it.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The difference between these ideas was whether the quantity of motion was simply related to a body's resistance to a change in velocity (vis inertia) or whether a body's amount of force due to its motion (vis viva) was related to the square of its velocity. </p><p>The theory was eventually absorbed into the modern theory of <a href="/wiki/Energy" title="Energy">energy</a>, though the term still survives in the context of <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a> through the <a href="/wiki/Vis-viva_equation" title="Vis-viva equation"><i>vis viva</i> equation</a>. The English equivalent "living force" was also used, for example by <a href="/wiki/George_William_Hill" title="George William Hill">George William Hill</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The term is due to the <a href="/wiki/Germany" title="Germany">German</a> philosopher <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a>, who was the first to attempt a mathematical formulation from 1676 to 1689. Leibniz noticed that in many mechanical systems (of several <a href="/wiki/Mass" title="Mass">masses</a>, <i>m<sub>i</sub></i> each with <a href="/wiki/Velocity" title="Velocity">velocity</a> <i>v<sub>i</sub></i>) the quantity<sup id="cite_ref-:0_4-0" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}m_{i}v_{i}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i}m_{i}v_{i}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0369647e33f4ff129034584a5fa0a68e6bf7f6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:8.764ex; height:5.509ex;" alt="{\displaystyle \sum _{i}m_{i}v_{i}^{2}}"></span></div> <p>was conserved. He called this quantity the <i>vis viva</i> or "living force" of the system.<sup id="cite_ref-:0_4-1" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The principle represented an accurate statement of the conservation of <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> in <a href="/wiki/Elastic_collision" title="Elastic collision">elastic collisions</a> that was independent of the <a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">conservation of momentum</a>. </p><p>However, many <a href="/wiki/Physicist" title="Physicist">physicists</a> at the time were unaware of this fact and, instead, were influenced by the prestige of Sir <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> in <a href="/wiki/England" title="England">England</a> and of <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> in <a href="/wiki/France" title="France">France</a>, both of whom advanced the <a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">conservation of momentum</a> as a guiding principle. Thus the <a href="/wiki/Momentum" title="Momentum">momentum</a>:<sup id="cite_ref-:0_4-2" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,\!\sum _{i}m_{i}\mathbf {v} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,\!\sum _{i}m_{i}\mathbf {v} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a59f6fe47cc33ef3e75af9cd0ca7fe5420b1bbb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:8.793ex; height:5.509ex;" alt="{\displaystyle \,\!\sum _{i}m_{i}\mathbf {v} _{i}}"></span></div> <p>was held by the rival camp to be the conserved <i>vis viva</i>. It was largely <a href="/wiki/Engineer" title="Engineer">engineers</a> such as <a href="/wiki/John_Smeaton" title="John Smeaton">John Smeaton</a>, <a href="/wiki/Peter_Ewart" title="Peter Ewart">Peter Ewart</a>, <a href="/w/index.php?title=Karl_Holtzmann&action=edit&redlink=1" class="new" title="Karl Holtzmann (page does not exist)">Karl Holtzmann</a>, <a href="/wiki/Gustave-Adolphe_Hirn" title="Gustave-Adolphe Hirn">Gustave-Adolphe Hirn</a> and <a href="/wiki/Marc_Seguin" title="Marc Seguin">Marc Seguin</a> who objected that conservation of momentum alone was not adequate for practical calculation and who made use of Leibniz's principle. The principle was also championed by some <a href="/wiki/Chemist" title="Chemist">chemists</a> such as <a href="/wiki/William_Hyde_Wollaston" title="William Hyde Wollaston">William Hyde Wollaston</a>. </p><p>The French mathematician <a href="/wiki/%C3%89milie_du_Ch%C3%A2telet" title="Émilie du Châtelet">Émilie du Châtelet</a>, who had a sound grasp of Newtonian mechanics, developed Leibniz's concept and, combining it with the observations of <a href="/wiki/Willem_%27s_Gravesande" title="Willem 's Gravesande">Willem 's Gravesande</a>, showed that <i>vis viva</i> was dependent on the square of the velocities.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Members of the academic establishment such as <a href="/wiki/John_Playfair" title="John Playfair">John Playfair</a> were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a>, but in the 18th and 19th centuries, the fate of the lost energy was still unknown. Gradually it came to be suspected that the <a href="/wiki/Heat" title="Heat">heat</a> inevitably generated by motion was another form of <i>vis viva</i>. In 1783, <a href="/wiki/Antoine_Lavoisier" title="Antoine Lavoisier">Antoine Lavoisier</a> and <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Pierre-Simon Laplace</a> reviewed the two competing theories of <i>vis viva</i> and <a href="/wiki/Caloric_theory" title="Caloric theory">caloric theory</a>.<sup class="plainlinks nourlexpansion citation" id="ref_LL"><a class="external autonumber" href="https://en.wikipedia.org/wiki/Vis_viva#endnote_LL">[1]</a></sup> <a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Count Rumford</a>'s 1798 observations of heat generation during the <a href="/wiki/Boring_(manufacturing)" title="Boring (manufacturing)">boring</a> of <a href="/wiki/Cannon" title="Cannon">cannons</a> added more weight to the view that mechanical motion could be converted into heat. <i>Vis viva</i> began to be known as <i>energy</i> after <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a> first used the term in 1807. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bernoulli-vis-viva-with-0.5-multiplier-1736_(1741).gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Bernoulli-vis-viva-with-0.5-multiplier-1736_%281741%29.gif/220px-Bernoulli-vis-viva-with-0.5-multiplier-1736_%281741%29.gif" decoding="async" width="220" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Bernoulli-vis-viva-with-0.5-multiplier-1736_%281741%29.gif/330px-Bernoulli-vis-viva-with-0.5-multiplier-1736_%281741%29.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Bernoulli-vis-viva-with-0.5-multiplier-1736_%281741%29.gif/440px-Bernoulli-vis-viva-with-0.5-multiplier-1736_%281741%29.gif 2x" data-file-width="1326" data-file-height="264" /></a><figcaption>An excerpt from <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a>'s article, dated 1736,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> with the definition of vis viva with <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> multiplier.</figcaption></figure> <p>The recalibration of <i>vis viva</i> to include the coefficient of a half, namely: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E={\frac {1}{2}}\sum _{i}m_{i}v_{i}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {1}{2}}\sum _{i}m_{i}v_{i}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0c98e04749cc19d246335ac74e2c5eabeb0ebdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:16.024ex; height:6.343ex;" alt="{\displaystyle E={\frac {1}{2}}\sum _{i}m_{i}v_{i}^{2}}"></span></div> <p>was largely the result of the work of <a href="/wiki/Gaspard-Gustave_Coriolis" class="mw-redirect" title="Gaspard-Gustave Coriolis">Gaspard-Gustave Coriolis</a> and <a href="/wiki/Jean-Victor_Poncelet" title="Jean-Victor Poncelet">Jean-Victor Poncelet</a> over the period 1819–1839,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> although the present-day definition can occasionally be found earlier (e.g., in <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a>'s texts). The former called it the <i>quantité de travail</i> (quantity of work) and the latter, <i>travail mécanique</i> (mechanical work) and both championed its use in engineering calculation. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vis_viva&action=edit&section=2" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Conservation_of_energy#History" title="Conservation of energy">Conservation of energy: Historical development</a></li> <li><a href="/wiki/%C3%89lan_vital" title="Élan vital">Élan vital</a></li> <li><a href="/wiki/Kinetic_energy" title="Kinetic energy">Kinetic energy</a></li> <li><a href="/wiki/Orthogenesis" title="Orthogenesis">Orthogenesis</a></li> <li><a href="/wiki/Potentiality_and_actuality" title="Potentiality and actuality">Potentiality and actuality</a></li> <li><a href="/wiki/Vis-viva_equation" title="Vis-viva equation">Vis-viva equation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vis_viva&action=edit&section=3" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMcDonough2021" class="citation cs2">McDonough, Jeffrey K. (2021), <a rel="nofollow" class="external text" href="https://plato.stanford.edu/archives/fall2021/entries/leibniz-physics/">"Leibniz's Philosophy of Physics"</a>, in Zalta, Edward N. (ed.), <i>The Stanford Encyclopedia of Philosophy</i> (Fall 2021 ed.), Metaphysics Research Lab, Stanford University<span class="reference-accessdate">, retrieved <span class="nowrap">2021-08-28</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Leibniz%27s+Philosophy+of+Physics&rft.btitle=The+Stanford+Encyclopedia+of+Philosophy&rft.edition=Fall+2021&rft.pub=Metaphysics+Research+Lab%2C+Stanford+University&rft.date=2021&rft.aulast=McDonough&rft.aufirst=Jeffrey+K.&rft_id=https%3A%2F%2Fplato.stanford.edu%2Farchives%2Ffall2021%2Fentries%2Fleibniz-physics%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVis+viva" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcDonough2021" class="citation cs2">McDonough, Jeffrey K. (2021), <a rel="nofollow" class="external text" href="https://plato.stanford.edu/archives/fall2021/entries/leibniz-physics/">"Leibniz's Philosophy of Physics"</a>, in Zalta, Edward N. (ed.), <i>The Stanford Encyclopedia of Philosophy</i> (Fall 2021 ed.), Metaphysics Research Lab, Stanford University<span class="reference-accessdate">, retrieved <span class="nowrap">2021-08-28</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Leibniz%27s+Philosophy+of+Physics&rft.btitle=The+Stanford+Encyclopedia+of+Philosophy&rft.edition=Fall+2021&rft.pub=Metaphysics+Research+Lab%2C+Stanford+University&rft.date=2021&rft.aulast=McDonough&rft.aufirst=Jeffrey+K.&rft_id=https%3A%2F%2Fplato.stanford.edu%2Farchives%2Ffall2021%2Fentries%2Fleibniz-physics%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVis+viva" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">See <a rel="nofollow" class="external text" href="https://babel.hathitrust.org/cgi/pt?id=coo.31924064186772&view=1up&seq=209&skin=2021">"Remarks on the Stability of Planetary Systems"</a>, 1874.</span> </li> <li id="cite_note-:0-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_4-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith2006" class="citation journal cs1">Smith, George E. (October 2006). <a rel="nofollow" class="external text" href="http://physicstoday.scitation.org/doi/10.1063/1.2387086">"The vis viva dispute: A controversy at the dawn of dynamics"</a>. <i>Physics Today</i>. <b>59</b> (10): 31–36. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006PhT....59j..31S">2006PhT....59j..31S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.2387086">10.1063/1.2387086</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-9228">0031-9228</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=The+vis+viva+dispute%3A+A+controversy+at+the+dawn+of+dynamics&rft.volume=59&rft.issue=10&rft.pages=31-36&rft.date=2006-10&rft.issn=0031-9228&rft_id=info%3Adoi%2F10.1063%2F1.2387086&rft_id=info%3Abibcode%2F2006PhT....59j..31S&rft.aulast=Smith&rft.aufirst=George+E.&rft_id=http%3A%2F%2Fphysicstoday.scitation.org%2Fdoi%2F10.1063%2F1.2387086&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVis+viva" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMusielak2014" class="citation arxiv cs1">Musielak, Dora (2014). "The Marquise du Chatelet: A Controversial Woman of Science". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1406.7401">1406.7401</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/math.HO">math.HO</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=The+Marquise+du+Chatelet%3A+A+Controversial+Woman+of+Science&rft.date=2014&rft_id=info%3Aarxiv%2F1406.7401&rft.aulast=Musielak&rft.aufirst=Dora&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVis+viva" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBernoulli_D.1741" class="citation journal cs1">Bernoulli D. (1741). <a rel="nofollow" class="external text" href="https://www.biodiversitylibrary.org/page/10125763#page/124/mode/1up">"De legibus quibusdam mechanicis..."</a> <i>Commentarii Academiae Scientiarum Imperialis Petropolitanae (For the Year 1736)</i>. <b>8</b>: 99–127<span class="reference-accessdate">. Retrieved <span class="nowrap">18 November</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Commentarii+Academiae+Scientiarum+Imperialis+Petropolitanae+%28For+the+Year+1736%29&rft.atitle=De+legibus+quibusdam+mechanicis...&rft.volume=8&rft.pages=99-127&rft.date=1741&rft.au=Bernoulli+D.&rft_id=https%3A%2F%2Fwww.biodiversitylibrary.org%2Fpage%2F10125763%23page%2F124%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVis+viva" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCoriolis1829" class="citation book cs1">Coriolis, Gustave (1829). <a rel="nofollow" class="external text" href="https://gallica.bnf.fr/ark:/12148/bpt6k1068268/f27.item"><i>Du calcul de l'effet des machines, ou Considérations sur l'emploi des moteurs et sur leur évaluation : pour servir d'introduction à l'étude spéciale des machines</i></a>. Carilian-Goeury (Paris). p. 17<span class="reference-accessdate">. Retrieved <span class="nowrap">18 November</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Du+calcul+de+l%27effet+des+machines%2C+ou+Consid%C3%A9rations+sur+l%27emploi+des+moteurs+et+sur+leur+%C3%A9valuation+%3A+pour+servir+d%27introduction+%C3%A0+l%27%C3%A9tude+sp%C3%A9ciale+des+machines&rft.pages=17&rft.pub=Carilian-Goeury+%28Paris%29&rft.date=1829&rft.aulast=Coriolis&rft.aufirst=Gustave&rft_id=https%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k1068268%2Ff27.item&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVis+viva" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vis_viva&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>George E. Smith, <a rel="nofollow" class="external text" href="http://www.giovannibachelet.it/FG1-14-15/settimana_04/VisViva-PhysicsToday2006.pdf">"The Vis Viva Dispute: A Controversy at the Dawn of Dynamics"</a>, <i>Physics Today</i> <b>59</b> (October 2006) Issue 10 pp 31–36. <a rel="nofollow" class="external autonumber" href="http://ptonline.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTOAD000059000010000031000001&idtype=cvips">[2]</a> (see also <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070929102715/http://www.physicstoday.org/vol-59/iss-12/p16.html">erratum</a>)</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output 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style="padding:0 0.25em"> <ul><li><a href="/wiki/Alternating_series_test" title="Alternating series test">Alternating series test</a></li> <li><a href="/wiki/Best_of_all_possible_worlds" title="Best of all possible worlds">Best of all possible worlds</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Calculus controversy</a></li> <li><i><a href="/wiki/Calculus_ratiocinator" title="Calculus ratiocinator">Calculus ratiocinator</a></i></li> <li><i><a href="/wiki/Characteristica_universalis" title="Characteristica universalis">Characteristica universalis</a></i></li> <li><a href="/wiki/Compossibility" title="Compossibility">Compossibility</a></li> <li><a href="/wiki/Difference_(philosophy)" title="Difference (philosophy)">Difference</a></li> <li><a href="/wiki/Dynamism_(metaphysics)" title="Dynamism (metaphysics)">Dynamism</a></li> <li><a href="/wiki/Identity_of_indiscernibles" title="Identity of indiscernibles">Identity of indiscernibles</a></li> <li><a href="/wiki/Individuation" title="Individuation">Individuation</a></li> <li><a href="/wiki/Law_of_continuity" title="Law of continuity">Law of continuity</a></li> <li><a href="/wiki/Leibniz_wheel" title="Leibniz wheel">Leibniz wheel</a></li> <li><a href="/wiki/Leibniz%27s_gap" title="Leibniz's gap">Leibniz's gap</a></li> <li><a href="/wiki/Leibniz%27s_notation" title="Leibniz's notation">Leibniz's notation</a></li> <li><i><a href="/wiki/Lingua_generalis" title="Lingua generalis">Lingua generalis</a></i></li> <li><i><a href="/wiki/Mathesis_universalis" title="Mathesis universalis">Mathesis universalis</a></i></li> <li><a href="/wiki/Pre-established_harmony" class="mw-redirect" title="Pre-established harmony">Pre-established harmony</a></li> <li><a href="/wiki/Principle_of_plenitude" title="Principle of plenitude">Plenitude</a></li> <li><a href="/wiki/Principle_of_sufficient_reason" title="Principle of sufficient reason">Sufficient reason</a></li> <li><i><a href="/wiki/Salva_veritate" title="Salva veritate">Salva veritate</a></i></li> <li><a href="/wiki/Theodicy" title="Theodicy">Theodicy</a></li> <li><a href="/wiki/Transcendental_law_of_homogeneity" title="Transcendental law of homogeneity">Transcendental law of homogeneity</a></li> <li><a href="/wiki/Rationalism" title="Rationalism">Rationalism</a></li> <li><a href="/wiki/Universal_science" title="Universal science">Universal science</a></li> <li><i><a class="mw-selflink selflink">Vis viva</a></i></li> <li><a href="/wiki/Well-founded_phenomenon" class="mw-redirect" title="Well-founded phenomenon">Well-founded phenomenon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/De_Arte_Combinatoria" title="De Arte Combinatoria">De Arte Combinatoria</a></i> <span style="font-size:85%;">(1666)</span></li> <li><i><a href="/wiki/Discourse_on_Metaphysics" title="Discourse on Metaphysics">Discourse on Metaphysics</a></i> <span style="font-size:85%;">(1686)</span></li> <li><i><a href="/wiki/New_Essays_on_Human_Understanding" title="New Essays on Human Understanding">New Essays on Human Understanding</a></i> <span style="font-size:85%;">(1704)</span></li> <li><i><a href="/wiki/Th%C3%A9odic%C3%A9e" title="Théodicée">Théodicée</a></i> <span style="font-size:85%;">(1710)</span></li> <li><i><a href="/wiki/Monadology" title="Monadology">Monadology</a></i> <span style="font-size:85%;">(1714)</span></li> <li><a href="/wiki/Leibniz%E2%80%93Clarke_correspondence" title="Leibniz–Clarke correspondence">Leibniz–Clarke correspondence</a> <span style="font-size:85%;">(1715–1716)</span></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" 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