616:
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.
638:, 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.
113:
421:: 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 of the distance ... .') This becomes Proposition 11 in the
576:, 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
297:– a limit argument of infinitesimal calculus in geometric form, 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
596:'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."
316:, 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
468:
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
369:
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
615:
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. Hooke therefore wanted to hear from members about their researches, or their views about the researches of others; and as
583:
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
288:
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
599:
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" In light of these differing reports, both
571:
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
402:
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
548:) 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
514:
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.
152:
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:
490:
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
627:, 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.
741:
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
648:, 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".
432:
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
387:
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
357:
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.
851:(1994) 25(3), pp. 193–200 , 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",
200:
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
46:
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
630:
Newton, who heard of this from Halley, rebutted Hooke's claim in letters to Halley, acknowledging only an occasion of reawakened interest. Newton did acknowledge some prior work of others, including
1792:
915:(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.
180:
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
453:, 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
169:' (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
1207:
227:
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
608:
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
559:
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).
800:, 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
954:
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
533:
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.
1142:
522:
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
872:
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",
641:
There has been scholarly controversy over exactly what if anything Newton really gained from Hooke, apart from the stimulus that Newton acknowledged.
1772:
962:, 10 (2005), 529–534; M Nauenberg, "Hooke's and Newton's Contributions to the Early Development of Orbital mechanics and Universal Gravitation", in
634:, who suggested (but without demonstration) that there was an attractive force from the Sun in the inverse square proportion to the distance, and
945:(1676–1687), (Cambridge University Press, 1960), giving the Halley-Newton correspondence of May to July 1686 about Hooke's claims at pp. 431–448.
499:. He also identifies a geometrical criterion for distinguishing between the elliptical case and the others, based on the calculated size of the
1110:
716:
81:
898:
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
220:. 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
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2: By its intrinsic force (alone) every body would progress uniformly in a straight line to infinity unless something external hinders that.
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1827:
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had been presented to the Royal Society, Hooke claimed from this correspondence the credit for some of Newton's content in the
1359:
381:
then points out how it is possible in this way to determine the centripetal force for any given shape of orbit and center.
332:
shows that, putting this in another way, the centripetal force is proportional to (1/P) * R where P is the orbital period.
326:
then points out that the centripetal force is proportional to V/R, where V is the orbital speed and R the circular radius.
63:
758:
English translations are based on the third (1726) edition, and the first English translation, of 1729, as far as Book 1,
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1169:
480:
points out how this enables determining the planetary ellipses and the locations of their foci by indirect measurements.
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1043:
1030:
855:(1991) 159–172; but the point was disagreed by R. Weinstock, who called it a 'petitio principii', see e.g. "Newton's
567:
At some points in 'De Motu', Newton depends on matters proved being used in practice as a basis for regarding their
445:
supposed.') (This conclusion is reached after taking as initial fact the observed proportionality between square of
1757:
1582:
688:
D T Whiteside (ed.), Mathematical Papers of Isaac newton, vol. 6 (1684–1691), (Cambridge University Press, 1974),
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point is evaluated from the speed and the curvature of the local infinitesimal arc. This subject reappears in the
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1679:
1577:
1398:
1842:
450:
503:, as a proportion to the distance the orbiting body at closest approach to the center. (Proposition 17 in the
1662:
847:
For further discussion of the point see Curtis Wilson, in "Newton's Orbit Problem, A Historian's Response",
796:, whose 1696 book "Analyse des infiniment petits" (Infinitesimal analysis) stated in its preface, about the
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again explores the ellipse, but now treats the further case where the center of attraction is at one of its
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580:, as a Corollary to Propositions 11–13, in response to criticism of this sort made during his lifetime.
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not to be confused with several other Newtonian papers carrying titles that start with these words
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350:
shows that if P is proportional to R, then the centripetal force would be proportional to 1/(R).
701:
Curtis Wilson: "From Kepler's Laws, so-called, to Universal Gravitation: Empirical Factors", in
1822:
1752:
1742:
1507:
1470:
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shows that if P is proportional to R, then the centripetal force would be proportional to 1/R.
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441:) drawn to the Sun describe areas proportional to the times, altogether (Latin: 'omnino') as
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The criticism is recounted by C Wilson in "Newton's Orbit Problem, A Historian's Response",
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shows that if P is proportional to R, then the centripetal force would be independent of R.
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8:
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78:). After further encouragement from Halley, Newton went on to develop and write his book
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in its original 1687 edition is online in text-searchable form (in the original Latin)
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1038:, Vol. 6, pp. 30–91, ed. by D. T. Whiteside, Cambridge University Press, 1974
889:, Chapter 10, p. 403; giving the version of the question in John Conduitt's report.
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1: Newton briefly sets out continued products of proportions involving differences:
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16:
1684 document by Isaac Newton containing mathematical derivations of Kepler's laws
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442:
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Finally in the series of propositions based on zero resistance from any medium,
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2: 'Inherent force' of a body is defined in a way that prepares for the idea of
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718:
The Grip of Gravity: The Quest to Understand the Laws of Motion and Gravitation
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produced from old memories, it is hard to know exactly what words Halley used.
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313:
228:
67:
58:
This manuscript gave important mathematical derivations relating to the three
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544:) the effects of resistance on inertial motion in a straight line, and then (
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958:, 10 (2005), 511–517; Ofer Gal, "The Invention of Celestial Mechanics", in
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269:
Then follows Newton's main subject-matter, labelled as theorems, problems,
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39:
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argument has been over whether Newton's proofs were satisfactory or not.)
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was recognized, both in Newton's lifetime and later, among others by the
776:
536:
Lastly, Newton attempts to extend the results to the case where there is
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3: 'Resistance': the property of a medium that regularly impedes motion.
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208:(Newton's later first law of motion is to similar effect, Law 1 in the
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or their limiting ratios.) This reappears in Book 1, Lemma 10 in the
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66:" (before Newton's work, these had not been generally regarded as
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if A/(A–B) = B/(B–C) = C/(C–D) etc., then A/B = B/C = C/D etc.
29:
131:'s register book, and its (Latin) text is available online.
98:– of which nearly all of the content also reappears in the
70:). Halley reported the communication from Newton to the
1025:, by R. S. Westfall, Cambridge University Press, 1980
32:: "On the motion of bodies in an orbit"; abbreviated
1000:they found the original document documents, Only
1773:Statal Institute of Higher Education Isaac Newton
859:and inverse-square orbits: the flaw reexamined",
644:About thirty years after Newton's death in 1727,
1814:
874:Studies in the History and Philosophy of Science
987:(London and New York: Macmillan, 1893), p. 69.
562:
134:For ease of cross-reference to the contents of
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933:
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788:The content of infinitesimal calculus in the
146:in English translation, as well as in Latin.
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320:, and the corollaries here reappear also.)
99:
93:
87:
82:Philosophiæ Naturalis Principia Mathematica
79:
38:) is the presumed title of a manuscript by
33:
22:
1071:
1057:
1023:Never at rest: a biography of Isaac Newton
703:Archives for History of the Exact Sciences
239:Then follow two more preliminary points:
293:, as well as in many parts of the later
111:
1036:The Mathematical Papers of Isaac Newton
603:
312:considers a body moving uniformly in a
261:(to be understood: at the endpoints of
257:2: All parallelograms touching a given
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1323:Newton's law of universal gravitation
1052:
943:Correspondence of Isaac Newton, Vol 2
913:Correspondence of Isaac Newton, Vol 2
92:) from a nucleus that can be seen in
1481:Newton's theorem of revolving orbits
1078:
806:Journal for the History of Astronomy
746:Isaaci Newtoni Propositiones De Motu
587:
1429:Leibniz–Newton calculus controversy
1170:standing on the shoulders of giants
819:Mathematical Papers of Isaac Newton
142:, there are online sources for the
13:
486:then explores, for the case of an
14:
1864:
127:was made by being entered in the
64:Kepler's laws of planetary motion
1758:Isaac Newton Group of Telescopes
927:vol. 2 already cited, at p. 297.
885:Quoted in Richard S. Westfall's
1828:Historical physics publications
1778:Newton International Fellowship
1459:generalized Gauss–Newton method
1372:Newton's method in optimization
1016:
985:An Essay on Newton's 'Principia
969:
948:
918:
892:
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715:Gondhalekar, Prabhakar (2005).
123:One of the surviving copies of
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721:. Cambridge University Press.
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695:
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619:Later, in 1686, when Newton's
1:
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289:does in later proofs in this
1399:Newton's theorem about ovals
563:Commentaries on the contents
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374:as Proposition 6 of Book 1.
361:
304:
280:
7:
1768:Sir Isaac Newton Sixth Form
1424:Corpuscular theory of light
1350:Schrödinger–Newton equation
849:College Mathematics Journal
836:College Mathematics Journal
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138:that appeared again in the
107:
10:
1869:
1177:Notes on the Jewish Temple
964:Early Science and Medicine
960:Early Science and Medicine
956:Early Science and Medicine
863:. 19(1) (1992), pp. 60–70.
838:(1994) 25(3), pp. 193–200
808:, vol. 1 (1970), 116–138 .
1786:
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1678:
1601:
1543:
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817:See D T Whiteside (ed.),
552:as Propositions 2 and 3.
150:De motu corporum in gyrum
24:De motu corporum in gyrum
1328:post-Newtonian expansion
1208:Corruptions of Scripture
1200:Ancient Kingdoms Amended
636:Giovanni Alfonso Borelli
417:. "A body orbits in an
392:. (Proposition 7 in the
1518:Absolute space and time
1382:truncated Newton method
1355:Newton's laws of motion
1318:Newton's law of cooling
876:, 38 (2007), pp. 56–83.
705:, 6 (1970), pp. 89–170.
216:3: Forces combine by a
86:(commonly known as the
1753:Isaac Newton Telescope
1743:Isaac Newton Institute
1513:Newton–Puiseux theorem
1508:Parallelogram of force
1496:kissing number problem
1486:Newton–Euler equations
1389:Gauss–Newton algorithm
1338:gravitational constant
821:, vol. 6 (1684–1691),
538:atmospheric resistance
184:is to similar effect.)
120:
100:
94:
88:
80:
34:
23:
1843:Works by Isaac Newton
1707:Isaac Newton Gargoyle
1617: (nephew-in-law)
1593:Copernican Revolution
1588:Scientific Revolution
1449:Newton–Cotes formulas
1313:Newton's inequalities
1290:Structural coloration
966:, 10 (2005), 518–528.
802:Principia Mathematica
794:Marquis de l'Hospital
540:, considering first (
116:Diagram illustrating
115:
74:on 10 December 1684 (
1714:Astronomers Monument
1404:Newton–Pepys problem
1377:Apollonius's problem
1345:Newton–Cartan theory
1258:Newton–Okounkov body
1191:hypotheses non fingo
1180: (c. 1680)
941:H W Turnbull (ed.),
911:H W Turnbull (ed.),
853:Annals of Science 48
604:Role of Robert Hooke
265:) are equal in area.
1523:Luminiferous aether
1471:Newton's identities
1444:Newton's cannonball
1419:Classical mechanics
1409:Newtonian potential
1270:Newtonian telescope
902:", 1971, at p. 293.
671:Classical mechanics
263:conjugate diameters
1748:Isaac Newton Medal
1553: (birthplace)
1367:Newtonian dynamics
1265:Newton's reflector
744:available here as
666:Christiaan Huygens
488:inverse-square law
218:parallelogram rule
121:
1810:
1809:
1702: (sculpture)
1669:Abraham de Moivre
1623: (professor)
1551:Woolsthorpe Manor
1503:Newton's quotient
1476:Newton polynomial
1434:Newton's notation
1165: (1661–1665)
980:W.W. Rouse Ball,
825:–57, footnote 73.
760:is available here
632:Ismaël Bullialdus
588:Halley's question
167:Centripetal force
118:centripetal force
1860:
1838:1680s in science
1798:
1693: (monotype)
1657:William Stukeley
1653: (disciple)
1633:Benjamin Pulleyn
1609:Catherine Barton
1528:Newtonian series
1439:Rotating spheres
1185:General Scholium
1080:Sir Isaac Newton
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1738:Newton's cradle
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1645:William Whiston
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1578:Religious views
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1454:Newton's method
1414:Newtonian fluid
1308:Bucket argument
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68:scientific laws
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1627:William Clarke
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1478:
1473:
1468:
1466:Newton fractal
1463:
1462:
1461:
1451:
1446:
1441:
1436:
1431:
1426:
1421:
1416:
1411:
1406:
1401:
1396:
1394:Newton's rings
1391:
1386:
1385:
1384:
1379:
1369:
1364:
1363:
1362:
1352:
1347:
1342:
1341:
1340:
1335:
1330:
1320:
1315:
1310:
1304:
1302:
1296:
1295:
1293:
1292:
1287:
1282:
1280:Newton's metal
1277:
1272:
1267:
1262:
1261:
1260:
1253:Newton polygon
1250:
1245:
1240:
1235:
1234:
1233:
1222:
1220:
1216:
1215:
1213:
1212:
1204:
1196:
1187:" (1713;
1181:
1173:
1166:
1157:
1155:
1154:Other writings
1151:
1150:
1148:
1147:
1139:
1131:
1123:
1115:
1107:
1099:
1090:
1088:
1084:
1083:
1076:
1075:
1068:
1061:
1053:
1047:
1046:
1033:
1018:
1015:
1012:
1011:
1002:
992:
991:
989:
988:
968:
947:
929:
925:Correspondence
917:
904:
891:
878:
865:
840:
827:
810:
781:
764:
751:
734:
728:978-0521018678
727:
707:
694:
680:
678:
675:
674:
673:
668:
653:
650:
605:
602:
589:
586:
564:
561:
462:
459:
447:orbital period
363:
360:
314:circular orbit
306:
303:
282:
279:
267:
266:
255:
252:
248:
247:
237:
236:
229:infinitesimals
225:
206:
205:
202:
197:
196:
189:
188:
185:
174:
162:
161:
109:
106:
62:now known as "
15:
9:
6:
4:
3:
2:
1865:
1854:
1851:
1849:
1846:
1844:
1841:
1839:
1836:
1834:
1831:
1829:
1826:
1824:
1823:Physics books
1821:
1820:
1818:
1801:
1797:
1789:
1785:
1779:
1776:
1774:
1771:
1769:
1766:
1764:
1761:
1759:
1756:
1754:
1751:
1749:
1746:
1744:
1741:
1739:
1736:
1734:
1733:Newton (unit)
1731:
1730:
1728:
1726:
1722:
1716:
1715:
1711:
1709:
1708:
1704:
1701:
1699:
1695:
1692:
1690:
1686:
1685:
1683:
1681:
1677:
1670:
1667:
1664:
1663:William Jones
1661:
1658:
1655:
1652:
1649:
1646:
1643:
1640:
1637:
1635: (tutor)
1634:
1631:
1628:
1625:
1622:
1619:
1616:
1615:John Conduitt
1613:
1611: (niece)
1610:
1607:
1606:
1604:
1600:
1594:
1591:
1589:
1586:
1584:
1581:
1579:
1576:
1574:
1571:
1569:
1566:
1564:
1561:
1558:
1557:Cranbury Park
1555:
1552:
1549:
1548:
1546:
1544:Personal life
1542:
1534:
1531:
1530:
1529:
1526:
1524:
1521:
1519:
1516:
1514:
1511:
1509:
1506:
1504:
1501:
1497:
1494:
1493:
1492:
1491:Newton number
1489:
1487:
1484:
1482:
1479:
1477:
1474:
1472:
1469:
1467:
1464:
1460:
1457:
1456:
1455:
1452:
1450:
1447:
1445:
1442:
1440:
1437:
1435:
1432:
1430:
1427:
1425:
1422:
1420:
1417:
1415:
1412:
1410:
1407:
1405:
1402:
1400:
1397:
1395:
1392:
1390:
1387:
1383:
1380:
1378:
1375:
1374:
1373:
1370:
1368:
1365:
1361:
1360:Kepler's laws
1358:
1357:
1356:
1353:
1351:
1348:
1346:
1343:
1339:
1336:
1334:
1333:parameterized
1331:
1329:
1326:
1325:
1324:
1321:
1319:
1316:
1314:
1311:
1309:
1306:
1305:
1303:
1301:
1297:
1291:
1288:
1286:
1283:
1281:
1278:
1276:
1273:
1271:
1268:
1266:
1263:
1259:
1256:
1255:
1254:
1251:
1249:
1246:
1244:
1241:
1239:
1236:
1232:
1229:
1228:
1227:
1224:
1223:
1221:
1219:Contributions
1217:
1210:
1209:
1205:
1202:
1201:
1197:
1194:
1192:
1186:
1182:
1179:
1178:
1174:
1172:" (1675)
1171:
1167:
1164:
1163:
1159:
1158:
1156:
1152:
1145:
1144:
1140:
1137:
1136:
1132:
1129:
1128:
1124:
1121:
1120:
1116:
1113:
1112:
1108:
1105:
1104:
1100:
1097:
1096:
1092:
1091:
1089:
1085:
1081:
1074:
1069:
1067:
1062:
1060:
1055:
1054:
1051:
1045:
1044:0-521-08719-8
1041:
1037:
1034:
1032:
1031:0-521-23143-4
1028:
1024:
1021:
1020:
1006:
997:
993:
986:
983:
982:
975:
974:
965:
961:
957:
951:
944:
938:
936:
934:
926:
921:
914:
908:
901:
895:
888:
887:Never at Rest
882:
875:
869:
862:
861:Historia Math
858:
854:
850:
844:
837:
831:
824:
820:
814:
807:
803:
799:
795:
791:
785:
778:
774:
768:
761:
755:
748:
747:
738:
730:
724:
720:
719:
711:
704:
698:
691:
685:
681:
672:
669:
667:
663:
659:
656:
655:
649:
647:
642:
639:
637:
633:
628:
626:
622:
617:
613:
611:
601:
597:
595:
594:Edmund Halley
585:
581:
579:
575:
570:
560:
558:
555:Then a final
553:
551:
547:
543:
539:
534:
532:
527:
525:
521:
516:
513:
508:
506:
502:
498:
494:
489:
485:
481:
479:
474:
472:
467:
458:
456:
452:
448:
444:
440:
436:
431:
426:
424:
420:
416:
412:
408:
406:
401:
397:
395:
391:
386:
382:
380:
375:
373:
368:
359:
356:
351:
349:
345:
343:
339:
337:
333:
331:
327:
325:
321:
319:
315:
311:
302:
300:
296:
292:
287:
278:
276:
272:
264:
260:
256:
253:
250:
249:
245:
242:
241:
240:
234:
230:
226:
223:
219:
215:
214:
213:
211:
203:
199:
198:
194:
191:
190:
186:
183:
179:
175:
172:
168:
164:
163:
159:
158:3 Definitions
156:
155:
154:
151:
147:
145:
141:
137:
132:
130:
129:Royal Society
126:
119:
114:
105:
102:
96:
90:
84:
83:
77:
73:
72:Royal Society
69:
65:
61:
56:
54:
50:
45:
44:Edmond Halley
41:
36:
31:
27:
25:
19:
1800:Isaac Newton
1712:
1705:
1697:
1688:
1621:Isaac Barrow
1559: (home)
1300:Newtonianism
1275:Newton scale
1238:Impact depth
1211: (1754)
1206:
1203: (1728)
1198:
1188:
1175:
1160:
1146: (1711)
1141:
1138: (1707)
1133:
1130: (1704)
1125:
1122: (1704)
1117:
1114: (1687)
1109:
1106: (1684)
1102:
1101:
1098: (1671)
1093:
1087:Publications
1035:
1022:
1017:Bibliography
1005:
996:
984:
978:
977:
973:
972:
963:
959:
955:
950:
942:
924:
920:
912:
907:
899:
894:
886:
881:
873:
868:
860:
856:
852:
848:
843:
835:
830:
818:
813:
805:
801:
797:
789:
784:
772:
767:
754:
745:
737:
717:
710:
702:
697:
684:
643:
640:
629:
624:
620:
618:
614:
612:in 1679/80.
610:Robert Hooke
607:
598:
591:
582:
577:
573:
566:
556:
554:
549:
545:
541:
535:
530:
528:
523:
519:
517:
511:
509:
504:
501:latus rectum
483:
482:
477:
475:
470:
465:
464:
454:
451:orbital size
449:and cube of
438:
434:
429:
427:
422:
410:
409:
404:
399:
398:
393:
384:
383:
378:
376:
371:
366:
365:
354:
352:
347:
346:
341:
340:
335:
334:
329:
328:
323:
322:
317:
309:
308:
298:
294:
290:
285:
284:
268:
243:
238:
232:
221:
209:
207:
193:4 Hypotheses
192:
181:
170:
157:
149:
148:
143:
139:
135:
133:
124:
122:
57:
53:Robert Hooke
40:Isaac Newton
21:
20:
18:
1700:by Paolozzi
1639:Roger Cotes
1248:Newton disc
1162:Quaestiones
1135:Arithmetica
348:Corollary 5
342:Corollary 4
336:Corollary 3
330:Corollary 2
324:Corollary 1
271:corollaries
1833:1684 works
1817:Categories
1787:Categories
1763:XMM-Newton
1680:Depictions
1651:John Keill
1573:Apple tree
1568:Later life
1563:Early life
1143:De Analysi
677:References
1602:Relations
1111:Principia
900:Principia
857:Principia
798:Principia
790:Principia
773:Principia
771:Newton's
662:Descartes
625:Principia
621:Principia
578:Principia
574:Principia
569:converses
550:Principia
546:Problem 7
542:Problem 6
524:Principia
520:Problem 5
505:Principia
497:hyperbola
484:Problem 4
471:Principia
466:Theorem 4
461:Theorem 4
455:Principia
423:Principia
411:Problem 3
405:Principia
400:Problem 2
394:Principia
379:corollary
372:Principia
367:Theorem 3
362:Theorem 3
318:Principia
310:Theorem 2
305:Theorem 2
299:Principia
295:Principia
286:Theorem 1
281:Theorem 1
233:Principia
222:Principia
210:Principia
182:Principia
171:Principia
144:Principia
140:Principia
101:Principia
89:Principia
76:Old Style
60:relations
1725:Namesake
1691:by Blake
1285:Spectrum
1226:Calculus
1195: )
1095:Fluxions
652:See also
557:scholium
531:scholium
512:scholium
493:parabola
478:scholium
439:vectores
430:scholium
385:Problem
355:scholium
244:2 Lemmas
108:Contents
42:sent to
1243:Inertia
1231:fluxion
1127:Queries
1119:Opticks
1103:De Motu
658:Galileo
419:ellipse
390:tangent
291:De Motu
275:scholia
259:ellipse
201:medium.
178:inertia
136:De Motu
125:De Motu
95:De Motu
35:De Motu
1698:Newton
1689:Newton
1042:
1029:
823:pp. 56
725:
690:pp. 30
664:, and
443:Kepler
28:(from
1533:table
435:radii
30:Latin
1040:ISBN
1027:ISBN
777:here
723:ISBN
692:–91.
415:foci
273:and
165:1: '
51:and
804:",
526:.)
507:.)
495:or
473:.)
407:.)
396:.)
212:.)
1819::
932:^
660:,
529:A
510:A
476:A
457:.
428:A
425:.
377:A
353:A
301:.
277::
173:.)
104:.
55:.
1193:"
1189:"
1183:"
1168:"
1072:e
1065:t
1058:v
971:'
779:.
762:.
749:.
731:.
437:(
246::
235:.
224:.
195::
160::
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