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href="https://es.wikipedia.org/wiki/Antoine_Parent" title="Antoine Parent – Spanish" lang="es" hreflang="es" data-title="Antoine Parent" 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/Antoine_Parent" title="Antoine Parent – French" lang="fr" hreflang="fr" data-title="Antoine Parent" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Antoine_Parent" title="Antoine Parent – Haitian Creole" lang="ht" hreflang="ht" data-title="Antoine Parent" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ja 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">French mathematician</div> <p><b>Antoine Parent</b> (September 16, 1666 – September 26, 1716) was a French <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, born in <a href="/wiki/Paris" title="Paris">Paris</a> and died there, who wrote in 1700 on <a href="/wiki/Analytical_geometry" class="mw-redirect" title="Analytical geometry">analytical geometry</a> of three dimensions. His works were collected and published in three volumes at Paris in 1713. </p><p>Parent had the idea to represent any surface by means of an equation between the three coordinates to any of its points. He derived the correct formula for bending of <a href="/wiki/Cantilever" title="Cantilever">cantilever beams</a>. He correctly assumed a central neutral axis and linear stress distribution from tensile at the top face to equal and opposite compression at the bottom, thus deriving a correct elastic section modulus of the cross sectional area times the section depth divided by six. Parent's work had little impact, and it was many more years before scientific principles were regularly applied to the analysis of the strength of beams in bending.<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> </p> <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=Antoine_Parent&action=edit&section=1" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <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">Loria, G. (1902). Sketch of the origin and development of geometry prior to 1850. The Monist (13)1 p. 101.</span> </li> </ol></div></div> <dl><dd><i>An original entry was based on the book</i> <a href="/wiki/Wikipedia:Rouse_History_of_Mathematics" title="Wikipedia:Rouse History of Mathematics"><i>A Short Account of the History of Mathematics</i></a> (4th edition, 1908) by W. W. 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href="https://viaf.org/viaf/68971371">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJmXQbWP43gJ8q83FpqbBP">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/105511131X">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/no97034228">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb103679948">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb103679948">BnF data</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Parent, Antoine <1666-1716>"><a rel="nofollow" class="external text" href="https://opac.sbn.it/nome/UBOV400380">Italy</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/14403327">Belgium</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:parent.antoine.1">zbMATH</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd105511131X.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/105511131X">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/097646431">IdRef</a></span></li></ul></div></td></tr></tbody></table></div> <p><br /> </p> <style data-mw-deduplicate="TemplateStyles:r1012311289">.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .asbox table{background:transparent}.mw-parser-output .asbox p{margin:0}.mw-parser-output .asbox p+p{margin-top:0.25em}.mw-parser-output .asbox-body{font-style:italic}.mw-parser-output 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