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href="#Theorem_4"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Theorem 4</span> </div> </a> <ul id="toc-Theorem_4-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Commentaries_on_the_contents" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Commentaries_on_the_contents"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Commentaries on the contents</span> </div> </a> <ul id="toc-Commentaries_on_the_contents-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Halley's_question" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Halley's_question"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Halley's question</span> </div> </a> <ul id="toc-Halley's_question-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Role_of_Robert_Hooke" 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<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">1684 document by Isaac Newton containing mathematical derivations of Kepler's laws</div> <p class="mw-empty-elt"> </p><p><b><span title="Latin-language text"><i lang="la">De motu corporum in gyrum</i></span></b><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> (from <a href="/wiki/Latin" title="Latin">Latin</a>: "On the motion of bodies in an orbit"; abbreviated <span title="Latin-language text"><i lang="la">De Motu</i></span><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup>) is the presumed title of a manuscript by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> sent to <a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a> in November 1684. The manuscript was prompted by a visit from Halley earlier that year when he had questioned Newton about problems then occupying the minds of Halley and his scientific circle in London, including Sir <a href="/wiki/Christopher_Wren" title="Christopher Wren">Christopher Wren</a> and <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a>. </p><p>This manuscript gave important mathematical derivations relating to the three <a href="/wiki/Relation_(mathematics)" title="Relation (mathematics)">relations</a> now known as "<a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a>" (before Newton's work, these had not been generally regarded as <a href="/wiki/Scientific_law" title="Scientific law">scientific laws</a>).<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Halley reported the communication from Newton to the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> on 10 December 1684 (<a href="/wiki/Old_Style" class="mw-redirect" title="Old Style">Old Style</a>).<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> After further encouragement from Halley, Newton developed the ideas outlined by <span title="Latin-language text"><i lang="la">De Motu</i></span> into his book <span title="Latin-language text"><i lang="la"><a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Philosophiæ Naturalis Principia Mathematica</a></i></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Contents">Contents</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=1" title="Edit section: Contents"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Centripetal_force_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Centripetal_force_diagram.svg/220px-Centripetal_force_diagram.svg.png" decoding="async" width="220" height="185" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Centripetal_force_diagram.svg/330px-Centripetal_force_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Centripetal_force_diagram.svg/440px-Centripetal_force_diagram.svg.png 2x" data-file-width="596" data-file-height="500" /></a><figcaption>Diagram illustrating <a href="/wiki/Centripetal_force" title="Centripetal force">centripetal force</a></figcaption></figure> <p>One of the surviving copies of <i>De Motu</i> was made by being entered in the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a>'s register book, and its (Latin) text is available online.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>For ease of cross-reference to the contents of <i>De Motu</i> that appeared again in the <i>Principia</i>, there are online sources for the <i>Principia</i> in English translation,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> as well as in Latin.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p><i>De motu corporum in gyrum</i> is short enough to set out here the contents of its different sections. It contains 11 propositions, labelled as 'theorems' and 'problems', some with corollaries. Before reaching this core subject-matter, Newton begins with some preliminaries: </p> <ul><li><b>3 Definitions</b>:</li></ul> <dl><dd>1: '<a href="/wiki/Centripetal_force" title="Centripetal force">Centripetal force</a>' (Newton originated this term, and its first occurrence is in this document) impels or attracts a body to some point regarded as a center. (This reappears in Definition 5 of the <i>Principia</i>.)</dd> <dd>2: 'Inherent force' of a body is defined in a way that prepares for the idea of <a href="/wiki/Inertia" title="Inertia">inertia</a> and of Newton's first law (in the absence of external force, a body continues in its state of motion either at rest or in uniform motion along a straight line). (Definition 3 of the <i>Principia</i> is to similar effect.)</dd> <dd>3: 'Resistance': the property of a medium that regularly impedes motion.</dd></dl> <ul><li><b>4 Hypotheses</b>:</li></ul> <dl><dd>1: Newton indicates that in the first 9 propositions below, resistance is assumed nil, then for the remaining (2) propositions, resistance is assumed proportional both to the speed of the body and to the density of the medium.</dd> <dd>2: By its intrinsic force (alone) every body would progress uniformly in a straight line to infinity unless something external hinders that.</dd></dl> <p>(Newton's later first law of motion is to similar effect, Law 1 in the <i>Principia</i>.) </p> <dl><dd>3: Forces combine by a <a href="/wiki/Parallelogram_of_force" title="Parallelogram of force">parallelogram rule</a>. Newton treats them in effect as we now treat vectors. This point reappears in Corollaries 1 and 2 to the third law of motion, Law 3 in the <i>Principia</i>.</dd> <dd>4: In the initial moments of effect of a centripetal force, the distance is proportional to the square of the time. (The context indicates that Newton was dealing here with <a href="/wiki/Infinitesimals" class="mw-redirect" title="Infinitesimals">infinitesimals</a> or their limiting ratios.) This reappears in Book 1, Lemma 10 in the <i>Principia</i>.</dd></dl> <p>Then follow two more preliminary points: </p> <ul><li><b>2 Lemmas</b>:</li></ul> <dl><dd>1: Newton briefly sets out continued products of proportions involving differences:</dd> <dd>if A/(A–B) = B/(B–C) = C/(C–D) etc., then A/B = B/C = C/D etc.</dd> <dd>2: All parallelograms touching a given <a href="/wiki/Ellipse" title="Ellipse">ellipse</a> (to be understood: at the endpoints of <a href="/wiki/Conjugate_diameters" title="Conjugate diameters">conjugate diameters</a>) are equal in area.</dd></dl> <p>Then follows Newton's main subject-matter, labelled as theorems, problems, <a href="/wiki/Corollaries" class="mw-redirect" title="Corollaries">corollaries</a> and <a href="/wiki/Scholia" title="Scholia">scholia</a>: </p> <div class="mw-heading mw-heading3"><h3 id="Theorem_1">Theorem 1</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=2" title="Edit section: Theorem 1"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Theorem 1</b> demonstrates that where an orbiting body is subject only to a centripetal force, it follows that a radius vector, drawn from the body to the attracting center, sweeps out equal areas in equal times (no matter how the centripetal force varies with distance). (Newton uses for this derivation – as he does in later proofs in this <i>De Motu</i>, as well as in many parts of the later <i>Principia</i> – a limit argument of infinitesimal calculus in geometric form,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> in which the area swept out by the radius vector is divided into triangle-sectors. They are of small and decreasing size considered to tend towards zero individually, while their number increases without limit.) This theorem appears again, with expanded explanation, as Proposition 1, Theorem 1, of the <i>Principia</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Theorem_2">Theorem 2</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=3" title="Edit section: Theorem 2"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Theorem 2</b> considers a body moving uniformly in a <a href="/wiki/Circular_orbit" title="Circular orbit">circular orbit</a>, and shows that for any given time-segment, the centripetal force (directed towards the center of the circle, treated here as a center of attraction) is proportional to the square of the arc-length traversed, and inversely proportional to the radius. (This subject reappears as Proposition 4, Theorem 4 in the <i>Principia</i>, and the corollaries here reappear also.) </p><p><b>Corollary 1</b> then points out that the centripetal force is proportional to V<sup>2</sup>/R, where V is the orbital speed and R the circular radius. </p><p><b>Corollary 2</b> shows that, putting this in another way, the centripetal force is proportional to (1/P<sup>2</sup>) * R where P is the orbital period. </p><p><b>Corollary 3</b> shows that if P<sup>2</sup> is proportional to R, then the centripetal force would be independent of R. </p><p><b>Corollary 4</b> shows that if P<sup>2</sup> is proportional to R<sup>2</sup>, then the centripetal force would be proportional to 1/R. </p><p><b>Corollary 5</b> shows that if P<sup>2</sup> is proportional to R<sup>3</sup>, then the centripetal force would be proportional to 1/(R<sup>2</sup>). </p><p>A <b>scholium</b> then points out that the Corollary 5 relation (square of orbital period proportional to cube of orbital size) is observed to apply to the planets in their orbits around the Sun, and to the Galilean satellites orbiting Jupiter. </p> <div class="mw-heading mw-heading3"><h3 id="Theorem_3">Theorem 3</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=4" title="Edit section: Theorem 3"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Theorem 3</b> now evaluates the centripetal force in a non-circular orbit, using another geometrical limit argument, involving ratios of vanishingly small line-segments. The demonstration comes down to evaluating the curvature of the orbit as if it were made of infinitesimal arcs, and the centripetal force at any point is evaluated from the speed and the curvature of the local infinitesimal arc. This subject reappears in the <i>Principia</i> as Proposition 6 of Book 1. </p><p>A <b>corollary</b> then points out how it is possible in this way to determine the centripetal force for any given shape of orbit and center. </p><p><b>Problem </b>1 then explores the case of a circular orbit, assuming the center of attraction is on the circumference of the circle. A scholium points out that if the orbiting body were to reach such a center, it would then depart along the <a href="/wiki/Tangent" title="Tangent">tangent</a>. (Proposition 7 in the <i>Principia</i>.) </p><p><b>Problem 2</b> explores the case of an ellipse, where the center of attraction is at its center, and finds that the centripetal force to produce motion in that configuration would be directly proportional to the radius vector. (This material becomes Proposition 10, Problem 5 in the <i>Principia</i>.) </p><p><b>Problem 3</b> again explores the ellipse, but now treats the further case where the center of attraction is at one of its <a href="/wiki/Focus_(geometry)" title="Focus (geometry)">foci</a>. "A body orbits in an <a href="/wiki/Ellipse" title="Ellipse">ellipse</a>: there is required the law of centripetal force tending to a focus of the ellipse." Here Newton finds the centripetal force to produce motion in this configuration would be inversely proportional to the square of the radius vector. (Translation: 'Therefore, the centripetal force is reciprocally as L X SP², that is, (reciprocally) in the doubled ratio [i.e., square] of the distance ... .') This becomes Proposition 11 in the <i>Principia</i>. </p><p>A <b>scholium</b> then points out that this Problem 3 proves that the planetary orbits are ellipses with the Sun at one focus. (Translation: 'The major planets orbit, therefore, in ellipses having a focus at the center of the Sun, and with their <i>radii</i> (<i>vectores</i>) drawn to the Sun describe areas proportional to the times, altogether (Latin: 'omnino') as <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a> supposed.') (This conclusion is reached after taking as initial fact the observed proportionality between square of <a href="/wiki/Orbital_period" title="Orbital period">orbital period</a> and cube of <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">orbital size</a>, considered in corollary 5 to Theorem 1.) (A controversy over the cogency of the conclusion is described below.) The subject of Problem 3 becomes Proposition 11, Problem 6, in the <i>Principia</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Theorem_4">Theorem 4</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=5" title="Edit section: Theorem 4"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Theorem 4</b> shows that with a centripetal force inversely proportional to the square of the radius vector, the time of revolution of a body in an elliptical orbit with a given major axis is the same as it would be for the body in a circular orbit with the same diameter as that major axis. (Proposition 15 in the <i>Principia</i>.) </p><p>A <b>scholium</b> points out how this enables determining the planetary ellipses and the locations of their foci by indirect measurements. </p><p><b>Problem 4</b> then explores, for the case of an <a href="/wiki/Inverse-square_law" title="Inverse-square law">inverse-square law</a> of centripetal force, how to determine the orbital ellipse for a given starting position, speed, and direction of the orbiting body. Newton points out here, that if the speed is high enough, the orbit is no longer an ellipse, but is instead a <a href="/wiki/Parabola" title="Parabola">parabola</a> or <a href="/wiki/Hyperbola" title="Hyperbola">hyperbola</a>. He also identifies a geometrical criterion for distinguishing between the elliptical case and the others, based on the calculated size of the <a href="/wiki/Latus_rectum" class="mw-redirect" title="Latus rectum">latus rectum</a>, as a proportion to the distance the orbiting body at closest approach to the center. (Proposition 17 in the <i>Principia</i>.) </p><p>A <b>scholium</b> then remarks that a bonus of this demonstration is that it allows definition of the orbits of comets and enables an estimation of their periods and returns where the orbits are elliptical. Some practical difficulties of implementing this are also discussed. </p><p>Finally in the series of propositions based on zero resistance from any medium, <b>Problem 5</b> discusses the case of a degenerate elliptical orbit, amounting to a straight-line fall towards or ejection from the attracting center. (Proposition 32 in the <i>Principia</i>.) </p><p>A <b>scholium</b> points out how problems 4 and 5 would apply to projectiles in the atmosphere and to the fall of heavy bodies, if the atmospheric resistance could be assumed nil. </p><p>Lastly, Newton attempts to extend the results to the case where there is <a href="/wiki/Drag_(physics)" title="Drag (physics)">atmospheric resistance</a>, considering first (<b>Problem 6</b>) the effects of resistance on inertial motion in a straight line, and then (<b>Problem 7</b>) the combined effects of resistance and a uniform centripetal force on motion towards/away from the center in a homogeneous medium. Both problems are addressed geometrically using hyperbolic constructions. These last two 'Problems' reappear in Book 2 of the <i>Principia</i> as Propositions 2 and 3. </p><p>Then a final <b>scholium</b> points out how problems 6 and 7 apply to the horizontal and vertical components of the motion of projectiles in the atmosphere (in this case neglecting earth curvature). </p> <div class="mw-heading mw-heading2"><h2 id="Commentaries_on_the_contents">Commentaries on the contents</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=6" title="Edit section: Commentaries on the contents"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At some points in 'De Motu', Newton depends on matters proved being used in practice as a basis for regarding their <a href="/wiki/Converse_(logic)" title="Converse (logic)">converses</a> as also proved. This has been seen as especially so in regard to 'Problem 3'. Newton's style of demonstration in all his writings was rather brief in places; he appeared to assume that certain steps would be found self-evident or obvious. In 'De Motu', as in the first edition of the <i>Principia</i>, Newton did not specifically state a basis for extending the proofs to the converse. The proof of the converse here depends on its being apparent that there is a unique relation, i.e., that in any given setup, only one orbit corresponds to one given and specified set of force/velocity/starting position. Newton added a mention of this kind into the second edition of the <i>Principia</i>, as a Corollary to Propositions 11–13, in response to criticism of this sort made during his lifetime.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>A significant scholarly controversy has existed over the question whether and how far these extensions to the converse, and the associated uniqueness statements, are self-evident and obvious or not. (There is no suggestion that the converses are not true, or that they were not stated by Newton, the argument has been over whether Newton's proofs were satisfactory or not.)<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Halley's_question"><span id="Halley.27s_question"></span>Halley's question</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=7" title="Edit section: Halley's question"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The details of <a href="/wiki/Edmund_Halley" class="mw-redirect" title="Edmund Halley">Edmund Halley</a>'s visit to Newton in 1684 are known to us only from reminiscences of thirty to forty years later. According to one of these reminiscences, Halley asked Newton, "what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it."<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Another version of the question was given by Newton himself, but also about thirty years after the event: he wrote that Halley, asking him "if I knew what figure the Planets described in their Orbs about the Sun was very desirous to have my Demonstration"<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In light of these differing reports, both produced from old memories, it is hard to know exactly what words Halley used. </p> <div class="mw-heading mw-heading2"><h2 id="Role_of_Robert_Hooke">Role of Robert Hooke</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=8" title="Edit section: Role of Robert Hooke"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Newton acknowledged in 1686 that an initial stimulus on him in 1679/80 to extend his investigations of the movements of heavenly bodies had arisen from correspondence with <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a> in 1679/80.<sup id="cite_ref-1679letters_16-0" class="reference"><a href="#cite_note-1679letters-16"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Hooke had started an exchange of correspondence in November 1679 by writing to Newton, to tell Newton that Hooke had been appointed to manage the Royal Society's correspondence.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Hooke therefore wanted to hear from members about their researches, or their views about the researches of others; and as if to whet Newton's interest, he asked what Newton thought about various matters, and then gave a whole list, mentioning "compounding the celestial motions of the planetts of a direct motion by the tangent and an attractive motion towards the central body", and "my hypothesis of the lawes or causes of springinesse", and then a new hypothesis from Paris about planetary motions (which Hooke described at length), and then efforts to carry out or improve national surveys, the difference of latitude between London and Cambridge, and other items. Newton replied with "a fansy of my own" about determining the Earth's motion, using a falling body. Hooke disagreed with Newton's idea of how the falling body would move, and a short correspondence developed. </p><p>Later, in 1686, when Newton's <i>Principia</i> had been presented to the Royal Society, Hooke claimed from this correspondence the credit for some of Newton's content in the <i>Principia</i>, and said Newton owed the idea of an inverse-square law of attraction to him – although at the same time, Hooke disclaimed any credit for the curves and trajectories that Newton had demonstrated on the basis of the inverse square law.<sup id="cite_ref-1686letters_18-0" class="reference"><a href="#cite_note-1686letters-18"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Newton, who heard of this from Halley, rebutted Hooke's claim in letters to Halley, acknowledging only an occasion of reawakened interest.<sup id="cite_ref-1686letters_18-1" class="reference"><a href="#cite_note-1686letters-18"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Newton did acknowledge some prior work of others, including <a href="/wiki/Isma%C3%ABl_Bullialdus" title="Ismaël Bullialdus">Ismaël Bullialdus</a>, who suggested (but without demonstration) that there was an attractive force from the Sun in the inverse square proportion to the distance, and <a href="/wiki/Giovanni_Alfonso_Borelli" title="Giovanni Alfonso Borelli">Giovanni Alfonso Borelli</a>, who suggested (again without demonstration) that there was a tendency towards the Sun like gravity or magnetism that would make the planets move in ellipses; but that the elements Hooke claimed were due either to Newton himself, or to other predecessors of them both such as Bullialdus and Borelli, but not Hooke. Wren and Halley were both skeptical of Hooke's claims, recalling an occasion when Hooke had claimed to have a derivation of planetary motions under an inverse square law, but had failed to produce it even under the incentive of a prize.<sup id="cite_ref-1686letters_18-2" class="reference"><a href="#cite_note-1686letters-18"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>There has been scholarly controversy over exactly what if anything Newton really gained from Hooke, apart from the stimulus that Newton acknowledged.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>About thirty years after Newton's death in 1727, <a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Alexis Clairaut</a>, one of Newton's early and eminent successors in the field of gravitational studies, wrote after reviewing Hooke's work that it showed "what a distance there is between a truth that is glimpsed and a truth that is demonstrated".<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </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=De_motu_corporum_in_gyrum&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Galileo" class="mw-redirect" title="Galileo">Galileo</a>, <a href="/wiki/Descartes" class="mw-redirect" title="Descartes">Descartes</a>, and <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a></li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li></ul> <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=De_motu_corporum_in_gyrum&action=edit&section=10" 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 reflist-columns references-column-width" style="column-width: 30em;"> <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">D T Whiteside (ed.), Mathematical Papers of Isaac newton, vol. 6 (1684–1691), (Cambridge University Press, 1974), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=lIZ0v23iqRgC&pg=PA30">pp. 30</a>–91.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Curtis Wilson: "From Kepler's Laws, so-called, to Universal Gravitation: Empirical Factors", in <i>Archives for History of the Exact Sciences</i>, 6 (1970), pp. 89–170.</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"><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="CITEREFGondhalekar2005" class="citation book cs1">Gondhalekar, Prabhakar (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fqx5-t_DjYQC&q=De+motu+corporum+in+gyrum+10+december+1684&pg=PA89"><i>The Grip of Gravity: The Quest to Understand the Laws of Motion and Gravitation</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0521018678" title="Special:BookSources/978-0521018678"><bdi>978-0521018678</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Grip+of+Gravity%3A+The+Quest+to+Understand+the+Laws+of+Motion+and+Gravitation&rft.pub=Cambridge+University+Press&rft.date=2005&rft.isbn=978-0521018678&rft.aulast=Gondhalekar&rft.aufirst=Prabhakar&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dfqx5-t_DjYQC%26q%3DDe%2Bmotu%2Bcorporum%2Bin%2Bgyrum%2B10%2Bdecember%2B1684%26pg%3DPA89&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADe+motu+corporum+in+gyrum" 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">The surviving copy in the Royal Society's register book was printed in S P Rigaud's 'Historical Essay' of 1838 (in the original Latin), but note that the title was added by Rigaud, and the original copy had no title: online, it is <a rel="nofollow" class="external text" href="https://archive.org/details/historicalessay00newtgoog/page/n122">available here as <i>Isaaci Newtoni Propositiones De Motu</i></a>.</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">English translations are based on the third (1726) edition, and the first English translation, of 1729, as far as Book 1, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA65">is available here</a>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Newton's <i>Principia</i> in its original 1687 edition is online in text-searchable form (in the original Latin) <a rel="nofollow" class="external text" href="https://www.gutenberg.org/ebooks/28233">here</a>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">The content of infinitesimal calculus in the <i>Principia</i> was recognized, both in Newton's lifetime and later, among others by the <a href="/wiki/Guillaume_de_l%27H%C3%B4pital" title="Guillaume de l'Hôpital">Marquis de l'Hospital</a>, whose 1696 book "Analyse des infiniment petits" (Infinitesimal analysis) stated in its preface, about the <i>Principia</i>, that 'nearly all of it is of this calculus' ('lequel est presque tout de ce calcul'). See also D T Whiteside (1970), "The mathematical principles underlying Newton's <i>Principia Mathematica</i>", <i>Journal for the History of Astronomy</i>, vol. 1 (1970), 116–138 [120].</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">See D T Whiteside (ed.), <i>Mathematical Papers of Isaac Newton</i>, vol. 6 (1684–1691), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=lIZ0v23iqRgC&pg=PA56">pp. 56</a>–57, footnote 73.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">The criticism is recounted by C Wilson in "Newton's Orbit Problem, A Historian's Response", <i>College Mathematics Journal</i> (1994) 25(3), pp. 193–200 [195–196]</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">For further discussion of the point see Curtis Wilson, in "Newton's Orbit Problem, A Historian's Response", <i>College Mathematics Journal</i> (1994) 25(3), pp. 193–200 [196], concurring that Newton had given the outline of an argument; also D T Whiteside, Math. Papers vol. 6, p. 57; and Bruce Pourciau, "On Newton's proof that inverse-square orbits must be conics", <i>Annals of Science 48</i> (1991) 159–172; but the point was disagreed by R. Weinstock, who called it a 'petitio principii', see e.g. "Newton's <i>Principia</i> and inverse-square orbits: the flaw reexamined", <i>Historia Math</i>. 19(1) (1992), pp. 60–70.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">The argument is also spelled out by Bruce Pourciau in "From centripetal forces to conic orbits: a path through the early sections of Newton's Principia", <i>Studies in the History and Philosophy of Science</i>, 38 (2007), pp. 56–83.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Quoted in Richard S. Westfall's <i>Never at Rest</i>, Chapter 10, p. 403; giving the version of the question in John Conduitt's report.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Newton's note is now in the Cambridge University Library at MS Add.3968, f.101; and printed by I Bernard Cohen, in "Introduction to Newton's <i>Principia</i>", 1971, at p. 293.</span> </li> <li id="cite_note-1679letters-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-1679letters_16-0">^</a></b></span> <span class="reference-text">H W Turnbull (ed.), <i>Correspondence of Isaac Newton, Vol 2</i> (1676–1687), (Cambridge University Press, 1960), giving the Hooke-Newton correspondence (of November 1679 to January 1679|80) at pp. 297–314, and the 1686 correspondence at pp. 431–448.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><i>Correspondence</i> vol. 2 already cited, at p. 297.</span> </li> <li id="cite_note-1686letters-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-1686letters_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-1686letters_18-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-1686letters_18-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">H W Turnbull (ed.), <i>Correspondence of Isaac Newton, Vol 2</i> (1676–1687), (Cambridge University Press, 1960), giving the Halley-Newton correspondence of May to July 1686 about Hooke's claims at pp. 431–448.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">Aspects of the controversy can be seen for example in the following papers: N Guicciardini, "Reconsidering the Hooke-Newton debate on Gravitation: Recent Results", in <i>Early Science and Medicine</i>, 10 (2005), 511–517; Ofer Gal, "The Invention of Celestial Mechanics", in <i>Early Science and Medicine</i>, 10 (2005), 529–534; M Nauenberg, "Hooke's and Newton's Contributions to the Early Development of Orbital mechanics and Universal Gravitation", in <i>Early Science and Medicine</i>, 10 (2005), 518–528.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink">'<i><a href="#cite_ref-20">^</a><b></b></i></span><i><b> <span class="reference-text">W.W. Rouse Ball, </span></b></i><b>An Essay on Newton's 'Principia</b> (London and New York: Macmillan, 1893), p. 69. </li> </ol></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">they found the original document documents, Only <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></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">not to be confused with several other Newtonian papers carrying titles that start with these words</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=De_motu_corporum_in_gyrum&action=edit&section=11" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Never at rest: a biography of Isaac Newton</i>, by R. S. Westfall, Cambridge University Press, 1980 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-23143-4" title="Special:BookSources/0-521-23143-4">0-521-23143-4</a></li> <li><i>The Mathematical Papers of Isaac Newton</i>, Vol. 6, pp. 30–91, ed. by D. T. Whiteside, Cambridge University Press, 1974 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-08719-8" title="Special:BookSources/0-521-08719-8">0-521-08719-8</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 .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul 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.div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style></div><div role="navigation" class="navbox" aria-labelledby="Sir_Isaac_Newton" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output 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navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Isaac_Newton" title="Template:Isaac Newton"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Isaac_Newton" title="Template talk:Isaac Newton"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Isaac_Newton" title="Special:EditPage/Template:Isaac Newton"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Sir_Isaac_Newton" style="font-size:114%;margin:0 4em"><a href="/wiki/Isaac_Newton" title="Isaac Newton">Sir Isaac Newton</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Publications</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Method_of_Fluxions" title="Method of Fluxions">Fluxions</a></i> (1671)</li> <li><i><a class="mw-selflink selflink">De Motu</a></i> (1684)</li> <li><i><a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Principia</a></i> (1687)</li> <li><i><a href="/wiki/Opticks" title="Opticks">Opticks</a></i> (1704)</li> <li><i><a href="/wiki/The_Queries" class="mw-redirect" title="The Queries">Queries</a></i> (1704)</li> <li><i><a href="/wiki/Arithmetica_Universalis" title="Arithmetica Universalis">Arithmetica</a></i> (1707)</li> <li><i><a href="/wiki/De_analysi_per_aequationes_numero_terminorum_infinitas" title="De analysi per aequationes numero terminorum infinitas">De Analysi</a></i> (1711)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Other writings</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Quaestiones_quaedam_philosophicae" title="Quaestiones quaedam philosophicae">Quaestiones</a></i> (1661–1665)</li> <li>"<a href="/wiki/Standing_on_the_shoulders_of_giants" title="Standing on the shoulders of giants">standing on the shoulders of giants</a>" (1675)</li> <li><i><a href="/wiki/Notes_on_the_Jewish_Temple" title="Notes on the Jewish Temple">Notes on the Jewish Temple</a></i> (c. 1680)</li> <li>"<a href="/wiki/General_Scholium" title="General Scholium">General Scholium</a>" (1713; <i>"<a href="/wiki/Hypotheses_non_fingo" title="Hypotheses non fingo">hypotheses non fingo</a>"</i> )</li> <li><i><a href="/wiki/The_Chronology_of_Ancient_Kingdoms_Amended" title="The Chronology of Ancient Kingdoms Amended">Ancient Kingdoms Amended</a></i> (1728)</li> <li><i><a href="/wiki/An_Historical_Account_of_Two_Notable_Corruptions_of_Scripture" title="An Historical Account of Two Notable Corruptions of Scripture">Corruptions of Scripture</a></i> (1754)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Contributions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Calculus" title="Calculus">Calculus</a> <ul><li><a href="/wiki/Fluxion" title="Fluxion">fluxion</a></li></ul></li> <li><a href="/wiki/Impact_depth" title="Impact depth">Impact depth</a></li> <li><a href="/wiki/Inertia" title="Inertia">Inertia</a></li> <li><a href="/wiki/Newton_disc" title="Newton disc">Newton disc</a></li> <li><a href="/wiki/Newton_polygon" title="Newton polygon">Newton polygon</a> <ul><li><a href="/wiki/Newton%E2%80%93Okounkov_body" title="Newton–Okounkov body">Newton–Okounkov body</a></li></ul></li> <li><a href="/wiki/Newton%27s_reflector" title="Newton's reflector">Newton's reflector</a></li> <li><a href="/wiki/Newtonian_telescope" title="Newtonian telescope">Newtonian telescope</a></li> <li><a href="/wiki/Newton_scale" title="Newton scale">Newton scale</a></li> <li><a href="/wiki/Newton%27s_metal" title="Newton's metal">Newton's metal</a></li> <li><a href="/wiki/Spectrum" title="Spectrum">Spectrum</a></li> <li><a href="/wiki/Structural_coloration" title="Structural coloration">Structural coloration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/Newtonianism" title="Newtonianism">Newtonianism</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bucket_argument" title="Bucket argument">Bucket argument</a></li> <li><a href="/wiki/Newton%27s_inequalities" title="Newton's inequalities">Newton's inequalities</a></li> <li><a href="/wiki/Newton%27s_law_of_cooling" title="Newton's law of cooling">Newton's law of cooling</a></li> <li><a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a> <ul><li><a href="/wiki/Post-Newtonian_expansion" title="Post-Newtonian expansion">post-Newtonian expansion</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">parameterized</a></li> <li><a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a></li></ul></li> <li><a href="/wiki/Newton%E2%80%93Cartan_theory" title="Newton–Cartan theory">Newton–Cartan theory</a></li> <li><a href="/wiki/Schr%C3%B6dinger%E2%80%93Newton_equation" title="Schrödinger–Newton equation">Schrödinger–Newton equation</a></li> <li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a> <ul><li><a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws</a></li></ul></li> <li><a href="/wiki/Newtonian_dynamics" title="Newtonian dynamics">Newtonian dynamics</a></li> <li><a href="/wiki/Newton%27s_method_in_optimization" title="Newton's method in optimization">Newton's method in optimization</a> <ul><li><a href="/wiki/Problem_of_Apollonius" title="Problem of Apollonius">Apollonius's problem</a></li> <li><a href="/wiki/Truncated_Newton_method" title="Truncated Newton method">truncated Newton method</a></li></ul></li> <li><a href="/wiki/Gauss%E2%80%93Newton_algorithm" title="Gauss–Newton algorithm">Gauss–Newton algorithm</a></li> <li><a href="/wiki/Newton%27s_rings" title="Newton's rings">Newton's rings</a></li> <li><a href="/wiki/Newton%27s_theorem_about_ovals" title="Newton's theorem about ovals">Newton's theorem about ovals</a></li> <li><a href="/wiki/Newton%E2%80%93Pepys_problem" title="Newton–Pepys problem">Newton–Pepys problem</a></li> <li><a href="/wiki/Newtonian_potential" title="Newtonian potential">Newtonian potential</a></li> <li><a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian fluid</a></li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Corpuscular_theory_of_light" title="Corpuscular theory of light">Corpuscular theory of light</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Leibniz–Newton calculus controversy</a></li> <li><a href="/wiki/Newton%27s_notation" class="mw-redirect" title="Newton's notation">Newton's notation</a></li> <li><a href="/wiki/Rotating_spheres" title="Rotating spheres">Rotating spheres</a></li> <li><a href="/wiki/Newton%27s_cannonball" title="Newton's cannonball">Newton's cannonball</a></li> <li><a href="/wiki/Newton%E2%80%93Cotes_formulas" title="Newton–Cotes formulas">Newton–Cotes formulas</a></li> <li><a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a> <ul><li><a href="/wiki/Generalized_Gauss%E2%80%93Newton_method" title="Generalized Gauss–Newton method">generalized Gauss–Newton method</a></li></ul></li> <li><a href="/wiki/Newton_fractal" title="Newton fractal">Newton fractal</a></li> <li><a href="/wiki/Newton%27s_identities" title="Newton's identities">Newton's identities</a></li> <li><a href="/wiki/Newton_polynomial" title="Newton polynomial">Newton polynomial</a></li> <li><a href="/wiki/Newton%27s_theorem_of_revolving_orbits" title="Newton's theorem of revolving orbits">Newton's theorem of revolving orbits</a></li> <li><a href="/wiki/Newton%E2%80%93Euler_equations" title="Newton–Euler equations">Newton–Euler equations</a></li> <li><a href="/wiki/Power_number" title="Power number">Newton number</a> <ul><li><a href="/wiki/Kissing_number" title="Kissing number">kissing number problem</a></li></ul></li> <li><a href="/wiki/Difference_quotient" title="Difference quotient">Newton's quotient</a></li> <li><a href="/wiki/Parallelogram_of_force" title="Parallelogram of force">Parallelogram of force</a></li> <li><a href="/wiki/Puiseux_series" title="Puiseux series">Newton–Puiseux theorem</a></li> <li><a href="/wiki/Absolute_space_and_time#Newton" title="Absolute space and time">Absolute space and time</a></li> <li><a href="/wiki/Luminiferous_aether" title="Luminiferous aether">Luminiferous aether</a></li> <li><a href="/wiki/Finite_difference" title="Finite difference">Newtonian series</a> <ul><li><a href="/wiki/Table_of_Newtonian_series" title="Table of Newtonian series">table</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Personal life</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Woolsthorpe_Manor" title="Woolsthorpe Manor">Woolsthorpe Manor</a> (birthplace)</li> <li><a href="/wiki/Cranbury_Park" title="Cranbury Park">Cranbury Park</a> (home)</li> <li><a href="/wiki/Early_life_of_Isaac_Newton" title="Early life of Isaac Newton">Early life</a></li> <li><a href="/wiki/Later_life_of_Isaac_Newton" title="Later life of Isaac Newton">Later life</a></li> <li><a href="/wiki/Isaac_Newton%27s_apple_tree" title="Isaac Newton's apple tree">Apple tree</a></li> <li><a href="/wiki/Religious_views_of_Isaac_Newton" title="Religious views of Isaac Newton">Religious views</a></li> <li><a href="/wiki/Isaac_Newton%27s_occult_studies" title="Isaac Newton's occult studies">Occult studies</a></li> <li><a href="/wiki/Scientific_Revolution" title="Scientific Revolution">Scientific Revolution</a></li> <li><a href="/wiki/Copernican_Revolution" title="Copernican Revolution">Copernican Revolution</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Relations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Catherine_Barton" title="Catherine Barton">Catherine Barton</a> (niece)</li> <li><a href="/wiki/John_Conduitt" title="John Conduitt">John Conduitt</a> (nephew-in-law)</li> <li><a href="/wiki/Isaac_Barrow" title="Isaac Barrow">Isaac Barrow</a> (professor)</li> <li><a href="/wiki/William_Clarke_(apothecary)" title="William Clarke (apothecary)">William Clarke</a> (mentor)</li> <li><a href="/wiki/Benjamin_Pulleyn" title="Benjamin Pulleyn">Benjamin Pulleyn</a> (tutor)</li> <li><a href="/wiki/Roger_Cotes" title="Roger Cotes">Roger Cotes</a> (student)</li> <li><a href="/wiki/William_Whiston" title="William Whiston">William Whiston</a> (student)</li> <li><a href="/wiki/John_Keill" title="John Keill">John Keill</a> (disciple)</li> <li><a href="/wiki/William_Stukeley" title="William Stukeley">William Stukeley</a> (friend)</li> <li><a href="/wiki/William_Jones_(mathematician)" title="William Jones (mathematician)">William Jones</a> (friend)</li> <li><a href="/wiki/Abraham_de_Moivre" title="Abraham de Moivre">Abraham de Moivre</a> (friend)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/Isaac_Newton_in_popular_culture" title="Isaac Newton in popular culture">Depictions</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Newton_(Blake)" title="Newton (Blake)"><i>Newton</i> by Blake</a> (monotype)</li> <li><a href="/wiki/Newton_(Paolozzi)" title="Newton (Paolozzi)"><i>Newton</i> by Paolozzi</a> (sculpture)</li> <li><i><a href="/wiki/Isaac_Newton_Gargoyle" title="Isaac Newton Gargoyle">Isaac Newton Gargoyle</a></i></li> <li><i><a href="/wiki/Astronomers_Monument" title="Astronomers Monument">Astronomers Monument</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/List_of_things_named_after_Isaac_Newton" title="List of things named after Isaac Newton">Namesake</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Newton_(unit)" title="Newton (unit)">Newton (unit)</a></li> <li><a href="/wiki/Newton%27s_cradle" title="Newton's cradle">Newton's cradle</a></li> <li><a href="/wiki/Isaac_Newton_Institute" title="Isaac Newton Institute">Isaac Newton Institute</a></li> <li><a href="/wiki/Institute_of_Physics_Isaac_Newton_Medal" class="mw-redirect" title="Institute of Physics Isaac Newton Medal">Isaac Newton Medal</a></li> <li><a href="/wiki/Isaac_Newton_Telescope" title="Isaac Newton Telescope">Isaac Newton Telescope</a></li> <li><a href="/wiki/Isaac_Newton_Group_of_Telescopes" title="Isaac Newton Group of Telescopes">Isaac Newton Group of Telescopes</a></li> <li><a href="/wiki/XMM-Newton" title="XMM-Newton">XMM-Newton</a></li> <li><a href="/wiki/Sir_Isaac_Newton_Sixth_Form" title="Sir Isaac Newton Sixth Form">Sir Isaac Newton Sixth Form</a></li> <li><a href="/wiki/Statal_Institute_of_Higher_Education_Isaac_Newton" title="Statal Institute of Higher Education Isaac Newton">Statal Institute of Higher Education Isaac Newton</a></li> <li><a href="/wiki/Newton_International_Fellowship" title="Newton International Fellowship">Newton International Fellowship</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Categories</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"><div class="div-col"> <div class="CategoryTreeTag" data-ct-options="{"mode":20,"hideprefix":20,"showcount":false,"namespaces":false,"notranslations":false}"><div class="CategoryTreeSection"><div class="CategoryTreeItem"><span class="CategoryTreeBullet"><a class="CategoryTreeToggle" data-ct-title="Isaac_Newton" aria-expanded="false"></a> </span> <bdi dir="ltr"><a href="/wiki/Category:Isaac_Newton" title="Category:Isaac Newton">Isaac Newton</a></bdi></div><div class="CategoryTreeChildren" 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