983:
1403:
1599:
1201:
3219:
136:
1720:. He believed this put fluxions back on safe ground. By this time, Leibniz's derivative (and his notation) had largely replaced Newton's fluxions and fluents, and remains in use today.
3154:
1681:. Berkeley referred to them as "ghosts of departed quantities", a statement which unnerved mathematicians of the time and led to the eventual disuse of infinitesimals in calculus.
2934:
3784:
2922:
1143:
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2016:
3334:
2204:
3440:
1053:
3759:
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2897:
3492:
3344:
3082:
1528:
1398:{\displaystyle {\dot {y}}={\frac {\Delta y}{\Delta t}}={\frac {(2+o)^{2}-2^{2}}{(2+o)-2}}={\frac {4+4o+o^{2}-4}{2+o-2}}={\frac {4o+o^{2}}{o}}}
2514:
2268:
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211:
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2426:
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2146:
1064:
I cannot proceed with the explanations of the fluxions now, I have preferred to conceal it thus: 6accdæ13eff7i3l9n4o4qrr4s8t12vx.
478:
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3589:
3410:
3007:
2939:
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2419:
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483:
463:
145:
1963:
Kitcher, Philip (March 1973). "Fluxions, Limits, and
Infinite Littlenesse. A Study of Newton's Presentation of the Calculus".
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2463:
2337:
2009:
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538:
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3844:
3584:
3039:
2216:
2194:
1080:, meaning: "Given an equation that consists of any number of flowing quantities, to find the fluxions: and vice versa".
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1941:
318:
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2715:
2263:
2002:
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31:
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3146:
2710:
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1911:
926:
718:
607:
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2489:
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2211:
2184:
2156:
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323:
284:
190:
3276:
2199:
1677:. He did not believe it could be ignored and pointed out that if it was zero, the consequence would be
3725:
3445:
3202:
2780:
2399:
2246:
1745:
1734:
1011:
941:
921:
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328:
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3514:
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3420:
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2800:
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2124:
2111:
2071:
2051:
1729:
1717:
1650:, published in 1734. Berkeley refused to believe that they were accurate because of the use of the
916:
886:
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275:
158:
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2529:
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2414:
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2119:
1980:
1036:
881:
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768:
708:
662:
543:
467:
373:
368:
172:
3749:
3465:
2524:
2519:
2315:
2086:
703:
698:
167:
1768:
The Method of
Fluxions and Infinite Series: With Its Application to the Geometry of Curve-lines
3708:
3680:
3562:
3539:
3487:
3405:
3291:
3029:
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2607:
2584:
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2451:
2354:
2169:
2061:
1866:
1837:
1791:
1498:
because of its second order infinite smallness comparing to first order infinite smallness of
955:
789:
567:
450:
403:
260:
255:
1628:
as a non-zero quantity by stating that fluxions were a consequence of movement by an object.
1115:
3668:
3644:
3620:
3450:
3196:
2987:
2770:
2683:
2663:
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2504:
2446:
2438:
2372:
2285:
2046:
2041:
1972:
1940:
1739:
1678:
1078:
Data æqvatione qvotcvnqve flventes qvantitates involvente, flvxiones invenire: et vice versa
799:
693:
667:
528:
445:
409:
1472:
1441:
3656:
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3319:
3049:
3034:
2818:
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1936:
1637:
1023:
931:
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1859:
1689:
1658:
1609:
1503:
1413:
1150:
1093:
814:
622:
394:
1030:
with respect to time). Newton introduced the concept in 1665 and detailed them in his
3828:
3744:
3626:
3568:
2833:
2688:
2574:
2278:
2253:
1984:
1814:
1709:
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1433:
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313:
270:
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3311:
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3249:
3091:
2843:
2813:
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2241:
1019:
548:
298:
1887:
1060:
explaining them, but concealing his words in code due to his suspicion. He wrote:
3650:
3259:
3138:
2091:
2033:
1646:
1641:
1031:
911:
1836:(Digitally printed version, pbk. re-issue. ed.). Cambridge : Univ. Press.
1742:: A modern formalization of the reals that includes infinity and infinitesimals
1467:
is second order infinite small term and according to Newton, we can now ignore
3774:
3662:
2808:
2740:
2494:
2367:
2231:
2221:
2164:
1949:
1027:
657:
581:
308:
303:
207:
1794:
3002:
2750:
2745:
2056:
1799:
1069:
586:
576:
3296:
3237:
2997:
2499:
2377:
2025:
1594:{\displaystyle {\dot {y}}={\frac {\Delta y}{\Delta t}}={\frac {4o}{o}}=4}
1041:
1007:
652:
399:
356:
45:
17:
3254:
3130:
2101:
3017:
2081:
30:
This article is about the mathematical concept. For other uses, see
3060:
1976:
2096:
1073:
1684:
Towards the end of his life Newton revised his interpretation of
1713:
3064:
1998:
1861:
A brief history of infinity: the quest to think the unthinkable
1943:
The
Analyst: a Discourse addressed to an Infidel Mathematician
1994:
1644:
of the time, denounced Newton's fluxions in his essay
1692:
1661:
1612:
1531:
1506:
1475:
1444:
1416:
1204:
1175:
1153:
1118:
1096:
58:
3798:
3735:
3690:
3613:
3555:
3310:
3230:
3165:
3098:
2977:
2888:
2881:
2799:
2761:
2633:
2540:
2472:
2353:
2155:
2110:
2032:
27:
Historical mathematical concept; form of derivative
1858:
1698:
1667:
1618:
1593:
1512:
1488:
1457:
1422:
1397:
1187:
1159:
1137:
1102:
1072:(by denoting the frequency of each letter) of the
130:
3785:Statal Institute of Higher Education Isaac Newton
1018:) at a given point. Fluxions were introduced by
131:{\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}
1716:, using a similar definition to the concept of
1062:
1040:. Fluxions and fluents made up Newton's early
3076:
2010:
963:
8:
1832:Turnbull, Isaac Newton. Ed. by H.W. (2008).
3083:
3069:
3061:
2885:
2017:
2003:
1995:
970:
956:
836:
742:
646:
522:
362:
196:
36:
3045:Regiomontanus' angle maximization problem
1771:. Henry Woodfall; and sold by John Nourse
1712:, preferring to define it as approaching
1691:
1660:
1611:
1570:
1547:
1533:
1532:
1530:
1505:
1480:
1474:
1449:
1443:
1415:
1383:
1367:
1332:
1310:
1275:
1262:
1243:
1220:
1206:
1205:
1203:
1174:
1152:
1129:
1117:
1095:
91:
68:
63:
57:
1522:. So, the final equation gets the form:
981:
2393:Differentiating under the integral sign
1757:
776:
745:
685:
566:
494:Differentiating under the integral sign
432:
386:
283:
242:
199:
44:
3335:Newton's law of universal gravitation
2269:Inverse functions and differentiation
1169:is time) the fluxion (derivative) at
986:Newton's introduction of the notions
7:
3493:Newton's theorem of revolving orbits
3441:Leibniz–Newton calculus controversy
3182:standing on the shoulders of giants
1068:The gibberish string was in fact a
1054:Leibniz–Newton calculus controversy
3808:
2067:Free variables and bound variables
1834:The correspondence of Isaac Newton
1558:
1550:
1231:
1223:
40:Part of a series of articles about
25:
2872:The Method of Mechanical Theorems
1948:. London. p. 25 – via
3770:Isaac Newton Group of Telescopes
2427:Partial fractions in integration
2343:Stochastic differential equation
3790:Newton International Fellowship
3471:generalized Gauss–Newton method
3384:Newton's method in optimization
2565:Jacobian matrix and determinant
2420:Tangent half-angle substitution
2388:Fundamental theorem of calculus
1056:, when Newton sent a letter to
2641:Arithmetico-geometric sequence
2333:Ordinary differential equation
1295:
1283:
1259:
1246:
125:
119:
110:
104:
88:
82:
1:
2464:Integro-differential equation
2338:Partial differential equation
1436:amount of time. So, the term
1052:Fluxions were central to the
1014:(a time-varying quantity, or
425:Integral of inverse functions
3411:Newton's theorem about ovals
1004:instantaneous rate of change
3780:Sir Isaac Newton Sixth Form
3436:Corpuscular theory of light
3362:Schrödinger–Newton equation
2618:Generalized Stokes' theorem
2405:Integration by substitution
843:Calculus on Euclidean space
266:Logarithmic differentiation
3861:
3189:Notes on the Jewish Temple
2147:(ε, δ)-definition of limit
1912:"Isaac Newton (1642-1727)"
1765:Newton, Sir Isaac (1736).
1022:to describe his form of a
29:
3040:Proof that 22/7 exceeds π
2955:
2829:Gottfried Wilhelm Leibniz
2776:e (mathematical constant)
1058:Gottfried Wilhelm Leibniz
577:Summand limit (term test)
3340:post-Newtonian expansion
3220:Corruptions of Scripture
3212:Ancient Kingdoms Amended
2791:Stirling's approximation
2264:Implicit differentiation
2212:Rules of differentiation
1888:"History of Mathematics"
1604:He justified the use of
261:Implicit differentiation
251:Differentiation notation
178:Inverse function theorem
32:Fluxion (disambiguation)
3530:Absolute space and time
3394:truncated Newton method
3367:Newton's laws of motion
3330:Newton's law of cooling
3025:Euler–Maclaurin formula
2930:trigonometric functions
2383:Constant of integration
1820:Encyclopædia Britannica
1138:{\displaystyle y=t^{2}}
719:Helmholtz decomposition
3765:Isaac Newton Telescope
3755:Isaac Newton Institute
3525:Newton–Puiseux theorem
3520:Parallelogram of force
3508:kissing number problem
3498:Newton–Euler equations
3401:Gauss–Newton algorithm
3350:gravitational constant
2994:Differential geometry
2839:Infinitesimal calculus
2542:Multivariable calculus
2490:Directional derivative
2296:Second derivative test
2274:Logarithmic derivative
2247:General Leibniz's rule
2142:Order of approximation
1700:
1669:
1620:
1595:
1514:
1490:
1459:
1424:
1399:
1189:
1161:
1139:
1104:
1066:
995:
853:Limit of distributions
673:Directional derivative
334:FaĂ di Bruno's formula
132:
3840:Differential calculus
3835:Mathematical analysis
3719:Isaac Newton Gargoyle
3629: (nephew-in-law)
3605:Copernican Revolution
3600:Scientific Revolution
3461:Newton–Cotes formulas
3325:Newton's inequalities
3302:Structural coloration
2913:logarithmic functions
2908:exponential functions
2824:Generality of algebra
2702:Tests of convergence
2328:Differential equation
2312:Further applications
2301:Extreme value theorem
2291:First derivative test
2185:Differential operator
2157:Differential calculus
1865:. London: Constable.
1857:Clegg, Brian (2003).
1701:
1670:
1621:
1596:
1515:
1491:
1489:{\displaystyle o^{2}}
1460:
1458:{\displaystyle o^{2}}
1425:
1400:
1190:
1162:
1140:
1105:
985:
937:Mathematical analysis
848:Generalized functions
533:arithmetico-geometric
379:Leibniz integral rule
133:
3726:Astronomers Monument
3416:Newton–Pepys problem
3389:Apollonius's problem
3357:Newton–Cartan theory
3270:Newton–Okounkov body
3203:hypotheses non fingo
3192: (c. 1680)
2978:Miscellaneous topics
2918:hyperbolic functions
2903:irrational functions
2781:Exponential function
2634:Sequences and series
2400:Integration by parts
1746:Nonstandard analysis
1690:
1659:
1610:
1529:
1504:
1473:
1442:
1414:
1202:
1173:
1151:
1116:
1094:
942:Nonstandard analysis
415:Lebesgue integration
285:Rules and identities
56:
3845:History of calculus
3535:Luminiferous aether
3483:Newton's identities
3456:Newton's cannonball
3431:Classical mechanics
3421:Newtonian potential
3282:Newtonian telescope
2965:List of derivatives
2801:History of calculus
2716:Cauchy condensation
2613:Exterior derivative
2570:Lagrange multiplier
2306:Maximum and minimum
2137:Limit of a sequence
2125:Limit of a function
2072:Graph of a function
2052:Continuous function
1730:History of calculus
1188:{\displaystyle t=2}
613:Cauchy condensation
420:Contour integration
146:Fundamental theorem
73:
3760:Isaac Newton Medal
3565: (birthplace)
3379:Newtonian dynamics
3277:Newton's reflector
2898:rational functions
2865:Method of Fluxions
2711:Alternating series
2608:Differential forms
2590:Partial derivative
2550:Divergence theorem
2432:Quadratic integral
2200:Leibniz's notation
2190:Mean value theorem
2175:Partial derivative
2120:Indeterminate form
1792:Weisstein, Eric W.
1696:
1665:
1616:
1591:
1510:
1486:
1455:
1420:
1395:
1185:
1157:
1135:
1100:
1037:Method of Fluxions
996:
785:Partial derivative
714:generalized Stokes
608:Alternating series
489:Reduction formulae
464:tangent half-angle
451:Cylindrical shells
374:Integral transform
369:Lists of integrals
173:Mean value theorem
128:
59:
3822:
3821:
3714: (sculpture)
3681:Abraham de Moivre
3635: (professor)
3563:Woolsthorpe Manor
3515:Newton's quotient
3488:Newton polynomial
3446:Newton's notation
3177: (1661–1665)
3058:
3057:
2984:Complex calculus
2973:
2972:
2854:Law of Continuity
2786:Natural logarithm
2771:Bernoulli numbers
2762:Special functions
2721:Direct comparison
2585:Multiple integral
2459:Integral equation
2355:Integral calculus
2286:Stationary points
2260:Other techniques
2205:Newton's notation
2170:Second derivative
2062:Finite difference
1735:Newton's notation
1699:{\displaystyle o}
1668:{\displaystyle o}
1619:{\displaystyle o}
1583:
1565:
1541:
1513:{\displaystyle o}
1423:{\displaystyle o}
1393:
1362:
1305:
1238:
1214:
1160:{\displaystyle t}
1103:{\displaystyle y}
980:
979:
860:
859:
822:
821:
790:Multiple integral
726:
725:
630:
629:
597:Direct comparison
568:Convergence tests
506:
505:
479:Partial fractions
346:
345:
256:Second derivative
16:(Redirected from
3852:
3810:
3705: (monotype)
3669:William Stukeley
3665: (disciple)
3645:Benjamin Pulleyn
3621:Catherine Barton
3540:Newtonian series
3451:Rotating spheres
3197:General Scholium
3092:Sir Isaac Newton
3085:
3078:
3071:
3062:
2988:Contour integral
2886:
2736:Limit comparison
2645:Types of series
2604:Advanced topics
2595:Surface integral
2439:Trapezoidal rule
2378:Basic properties
2373:Riemann integral
2321:Taylor's theorem
2047:Concave function
2042:Binomial theorem
2019:
2012:
2005:
1996:
1989:
1988:
1960:
1954:
1953:
1947:
1937:Berkeley, George
1933:
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1902:
1901:
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1829:
1823:
1812:
1806:
1805:
1804:
1787:
1781:
1780:
1778:
1776:
1762:
1740:Hyperreal number
1710:infinitely small
1707:
1705:
1703:
1702:
1697:
1679:division by zero
1676:
1674:
1672:
1671:
1666:
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1492:
1487:
1485:
1484:
1466:
1464:
1462:
1461:
1456:
1454:
1453:
1434:infinitely small
1431:
1429:
1427:
1426:
1421:
1404:
1402:
1401:
1396:
1394:
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1311:
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1158:
1144:
1142:
1141:
1136:
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1133:
1111:
1109:
1107:
1106:
1101:
994:in his 1736 book
972:
965:
958:
906:
871:
837:
833:
800:Surface integral
743:
739:
647:
643:
603:Limit comparison
523:
519:
410:Riemann integral
363:
359:
319:L'HĂ´pital's rule
276:Taylor's theorem
197:
193:
137:
135:
134:
129:
81:
72:
67:
37:
21:
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3807:
3794:
3750:Newton's cradle
3731:
3686:
3659: (student)
3657:William Whiston
3653: (student)
3609:
3590:Religious views
3551:
3466:Newton's method
3426:Newtonian fluid
3320:Bucket argument
3306:
3226:
3161:
3094:
3089:
3059:
3054:
3050:Steinmetz solid
3035:Integration Bee
2969:
2951:
2877:
2819:Colin Maclaurin
2795:
2763:
2757:
2629:
2623:Tensor calculus
2600:Volume integral
2536:
2511:Basic theorems
2474:Vector calculus
2468:
2349:
2316:Newton's method
2151:
2130:One-sided limit
2106:
2087:Rolle's theorem
2077:Linear function
2028:
2023:
1993:
1992:
1962:
1961:
1957:
1935:
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1930:
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1918:
1910:
1909:
1905:
1895:
1893:
1890:
1886:Buckmire, Ron.
1885:
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1759:
1754:
1726:
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1685:
1657:
1656:
1654:
1638:George Berkeley
1634:
1608:
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1605:
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1501:
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1471:
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1437:
1412:
1411:
1409:
1379:
1369:
1345:
1328:
1312:
1282:
1271:
1258:
1245:
1230:
1222:
1200:
1199:
1171:
1170:
1149:
1148:
1146:
1125:
1114:
1113:
1092:
1091:
1089:
1086:
1050:
1024:time derivative
976:
947:
946:
932:Integration Bee
907:
904:
897:
896:
872:
869:
862:
861:
834:
831:
824:
823:
805:Volume integral
740:
735:
728:
727:
644:
639:
632:
631:
601:
520:
515:
508:
507:
499:Risch algorithm
474:Euler's formula
360:
355:
348:
347:
329:General Leibniz
212:generalizations
194:
189:
182:
168:Rolle's theorem
163:
138:
74:
54:
53:
35:
28:
23:
22:
15:
12:
11:
5:
3858:
3856:
3848:
3847:
3842:
3837:
3827:
3826:
3820:
3819:
3806:
3805:
3804:
3803:
3802:
3800:
3796:
3795:
3793:
3792:
3787:
3782:
3777:
3772:
3767:
3762:
3757:
3752:
3747:
3741:
3739:
3733:
3732:
3730:
3729:
3722:
3715:
3706:
3696:
3694:
3688:
3687:
3685:
3684:
3683: (friend)
3678:
3677: (friend)
3672:
3671: (friend)
3666:
3660:
3654:
3648:
3642:
3641: (mentor)
3639:William Clarke
3636:
3630:
3624:
3617:
3615:
3611:
3610:
3608:
3607:
3602:
3597:
3595:Occult studies
3592:
3587:
3582:
3577:
3572:
3566:
3559:
3557:
3553:
3552:
3550:
3549:
3548:
3547:
3537:
3532:
3527:
3522:
3517:
3512:
3511:
3510:
3500:
3495:
3490:
3485:
3480:
3478:Newton fractal
3475:
3474:
3473:
3463:
3458:
3453:
3448:
3443:
3438:
3433:
3428:
3423:
3418:
3413:
3408:
3406:Newton's rings
3403:
3398:
3397:
3396:
3391:
3381:
3376:
3375:
3374:
3364:
3359:
3354:
3353:
3352:
3347:
3342:
3332:
3327:
3322:
3316:
3314:
3308:
3307:
3305:
3304:
3299:
3294:
3292:Newton's metal
3289:
3284:
3279:
3274:
3273:
3272:
3265:Newton polygon
3262:
3257:
3252:
3247:
3246:
3245:
3234:
3232:
3228:
3227:
3225:
3224:
3216:
3208:
3199:" (1713;
3193:
3185:
3178:
3169:
3167:
3166:Other writings
3163:
3162:
3160:
3159:
3151:
3143:
3135:
3127:
3119:
3111:
3102:
3100:
3096:
3095:
3090:
3088:
3087:
3080:
3073:
3065:
3056:
3055:
3053:
3052:
3047:
3042:
3037:
3032:
3030:Gabriel's horn
3027:
3022:
3021:
3020:
3015:
3010:
3005:
3000:
2992:
2991:
2990:
2981:
2979:
2975:
2974:
2971:
2970:
2968:
2967:
2962:
2960:List of limits
2956:
2953:
2952:
2950:
2949:
2948:
2947:
2942:
2937:
2927:
2926:
2925:
2915:
2910:
2905:
2900:
2894:
2892:
2883:
2879:
2878:
2876:
2875:
2868:
2861:
2859:Leonhard Euler
2856:
2851:
2846:
2841:
2836:
2831:
2826:
2821:
2816:
2811:
2805:
2803:
2797:
2796:
2794:
2793:
2788:
2783:
2778:
2773:
2767:
2765:
2759:
2758:
2756:
2755:
2754:
2753:
2748:
2743:
2738:
2733:
2728:
2723:
2718:
2713:
2708:
2700:
2699:
2698:
2693:
2692:
2691:
2686:
2676:
2671:
2666:
2661:
2656:
2651:
2643:
2637:
2635:
2631:
2630:
2628:
2627:
2626:
2625:
2620:
2615:
2610:
2602:
2597:
2592:
2587:
2582:
2577:
2572:
2567:
2562:
2560:Hessian matrix
2557:
2552:
2546:
2544:
2538:
2537:
2535:
2534:
2533:
2532:
2527:
2522:
2517:
2515:Line integrals
2509:
2508:
2507:
2502:
2497:
2492:
2487:
2478:
2476:
2470:
2469:
2467:
2466:
2461:
2456:
2455:
2454:
2449:
2441:
2436:
2435:
2434:
2424:
2423:
2422:
2417:
2412:
2402:
2397:
2396:
2395:
2385:
2380:
2375:
2370:
2365:
2363:Antiderivative
2359:
2357:
2351:
2350:
2348:
2347:
2346:
2345:
2340:
2335:
2325:
2324:
2323:
2318:
2310:
2309:
2308:
2303:
2298:
2293:
2283:
2282:
2281:
2276:
2271:
2266:
2258:
2257:
2256:
2251:
2250:
2249:
2239:
2234:
2229:
2224:
2219:
2209:
2208:
2207:
2202:
2192:
2187:
2182:
2177:
2172:
2167:
2161:
2159:
2153:
2152:
2150:
2149:
2144:
2139:
2134:
2133:
2132:
2122:
2116:
2114:
2108:
2107:
2105:
2104:
2099:
2094:
2089:
2084:
2079:
2074:
2069:
2064:
2059:
2054:
2049:
2044:
2038:
2036:
2030:
2029:
2024:
2022:
2021:
2014:
2007:
1999:
1991:
1990:
1977:10.1086/351042
1955:
1928:
1903:
1878:
1871:
1849:
1842:
1824:
1807:
1782:
1756:
1755:
1753:
1750:
1749:
1748:
1743:
1737:
1732:
1725:
1722:
1695:
1664:
1640:, a prominent
1633:
1630:
1615:
1602:
1601:
1590:
1587:
1582:
1578:
1575:
1569:
1563:
1560:
1555:
1552:
1546:
1540:
1537:
1509:
1483:
1479:
1452:
1448:
1419:
1406:
1405:
1392:
1386:
1382:
1378:
1375:
1372:
1366:
1360:
1357:
1354:
1351:
1348:
1343:
1340:
1335:
1331:
1327:
1324:
1321:
1318:
1315:
1309:
1303:
1300:
1297:
1294:
1291:
1288:
1285:
1278:
1274:
1270:
1265:
1261:
1257:
1254:
1251:
1248:
1242:
1236:
1233:
1228:
1225:
1219:
1213:
1210:
1184:
1181:
1178:
1156:
1132:
1128:
1124:
1121:
1112:is defined as
1099:
1088:If the fluent
1085:
1082:
1049:
1046:
978:
977:
975:
974:
967:
960:
952:
949:
948:
945:
944:
939:
934:
929:
927:List of topics
924:
919:
914:
908:
903:
902:
899:
898:
895:
894:
889:
884:
879:
873:
868:
867:
864:
863:
858:
857:
856:
855:
850:
845:
835:
830:
829:
826:
825:
820:
819:
818:
817:
812:
807:
802:
797:
792:
787:
779:
778:
774:
773:
772:
771:
766:
761:
756:
748:
747:
741:
734:
733:
730:
729:
724:
723:
722:
721:
716:
711:
706:
701:
696:
688:
687:
683:
682:
681:
680:
675:
670:
665:
660:
655:
645:
638:
637:
634:
633:
628:
627:
626:
625:
620:
615:
610:
605:
599:
594:
589:
584:
579:
571:
570:
564:
563:
562:
561:
556:
551:
546:
541:
536:
521:
514:
513:
510:
509:
504:
503:
502:
501:
496:
491:
486:
484:Changing order
481:
476:
471:
453:
448:
443:
435:
434:
433:Integration by
430:
429:
428:
427:
422:
417:
412:
407:
397:
395:Antiderivative
389:
388:
384:
383:
382:
381:
376:
371:
361:
354:
353:
350:
349:
344:
343:
342:
341:
336:
331:
326:
321:
316:
311:
306:
301:
296:
288:
287:
281:
280:
279:
278:
273:
268:
263:
258:
253:
245:
244:
240:
239:
238:
237:
236:
235:
230:
225:
215:
202:
201:
195:
188:
187:
184:
183:
181:
180:
175:
170:
164:
162:
161:
156:
150:
149:
148:
140:
139:
127:
124:
121:
118:
115:
112:
109:
106:
103:
100:
97:
94:
90:
87:
84:
80:
77:
71:
66:
62:
52:
49:
48:
42:
41:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3857:
3846:
3843:
3841:
3838:
3836:
3833:
3832:
3830:
3813:
3809:
3801:
3797:
3791:
3788:
3786:
3783:
3781:
3778:
3776:
3773:
3771:
3768:
3766:
3763:
3761:
3758:
3756:
3753:
3751:
3748:
3746:
3745:Newton (unit)
3743:
3742:
3740:
3738:
3734:
3728:
3727:
3723:
3721:
3720:
3716:
3713:
3711:
3707:
3704:
3702:
3698:
3697:
3695:
3693:
3689:
3682:
3679:
3676:
3675:William Jones
3673:
3670:
3667:
3664:
3661:
3658:
3655:
3652:
3649:
3647: (tutor)
3646:
3643:
3640:
3637:
3634:
3631:
3628:
3627:John Conduitt
3625:
3623: (niece)
3622:
3619:
3618:
3616:
3612:
3606:
3603:
3601:
3598:
3596:
3593:
3591:
3588:
3586:
3583:
3581:
3578:
3576:
3573:
3570:
3569:Cranbury Park
3567:
3564:
3561:
3560:
3558:
3556:Personal life
3554:
3546:
3543:
3542:
3541:
3538:
3536:
3533:
3531:
3528:
3526:
3523:
3521:
3518:
3516:
3513:
3509:
3506:
3505:
3504:
3503:Newton number
3501:
3499:
3496:
3494:
3491:
3489:
3486:
3484:
3481:
3479:
3476:
3472:
3469:
3468:
3467:
3464:
3462:
3459:
3457:
3454:
3452:
3449:
3447:
3444:
3442:
3439:
3437:
3434:
3432:
3429:
3427:
3424:
3422:
3419:
3417:
3414:
3412:
3409:
3407:
3404:
3402:
3399:
3395:
3392:
3390:
3387:
3386:
3385:
3382:
3380:
3377:
3373:
3372:Kepler's laws
3370:
3369:
3368:
3365:
3363:
3360:
3358:
3355:
3351:
3348:
3346:
3345:parameterized
3343:
3341:
3338:
3337:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3317:
3315:
3313:
3309:
3303:
3300:
3298:
3295:
3293:
3290:
3288:
3285:
3283:
3280:
3278:
3275:
3271:
3268:
3267:
3266:
3263:
3261:
3258:
3256:
3253:
3251:
3248:
3244:
3241:
3240:
3239:
3236:
3235:
3233:
3231:Contributions
3229:
3222:
3221:
3217:
3214:
3213:
3209:
3206:
3204:
3198:
3194:
3191:
3190:
3186:
3184:" (1675)
3183:
3179:
3176:
3175:
3171:
3170:
3168:
3164:
3157:
3156:
3152:
3149:
3148:
3144:
3141:
3140:
3136:
3133:
3132:
3128:
3125:
3124:
3120:
3117:
3116:
3112:
3109:
3108:
3104:
3103:
3101:
3097:
3093:
3086:
3081:
3079:
3074:
3072:
3067:
3066:
3063:
3051:
3048:
3046:
3043:
3041:
3038:
3036:
3033:
3031:
3028:
3026:
3023:
3019:
3016:
3014:
3011:
3009:
3006:
3004:
3001:
2999:
2996:
2995:
2993:
2989:
2986:
2985:
2983:
2982:
2980:
2976:
2966:
2963:
2961:
2958:
2957:
2954:
2946:
2943:
2941:
2938:
2936:
2933:
2932:
2931:
2928:
2924:
2921:
2920:
2919:
2916:
2914:
2911:
2909:
2906:
2904:
2901:
2899:
2896:
2895:
2893:
2891:
2887:
2884:
2880:
2874:
2873:
2869:
2867:
2866:
2862:
2860:
2857:
2855:
2852:
2850:
2847:
2845:
2842:
2840:
2837:
2835:
2834:Infinitesimal
2832:
2830:
2827:
2825:
2822:
2820:
2817:
2815:
2812:
2810:
2807:
2806:
2804:
2802:
2798:
2792:
2789:
2787:
2784:
2782:
2779:
2777:
2774:
2772:
2769:
2768:
2766:
2760:
2752:
2749:
2747:
2744:
2742:
2739:
2737:
2734:
2732:
2729:
2727:
2724:
2722:
2719:
2717:
2714:
2712:
2709:
2707:
2704:
2703:
2701:
2697:
2694:
2690:
2687:
2685:
2682:
2681:
2680:
2677:
2675:
2672:
2670:
2667:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2646:
2644:
2642:
2639:
2638:
2636:
2632:
2624:
2621:
2619:
2616:
2614:
2611:
2609:
2606:
2605:
2603:
2601:
2598:
2596:
2593:
2591:
2588:
2586:
2583:
2581:
2578:
2576:
2575:Line integral
2573:
2571:
2568:
2566:
2563:
2561:
2558:
2556:
2553:
2551:
2548:
2547:
2545:
2543:
2539:
2531:
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2512:
2510:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2482:
2480:
2479:
2477:
2475:
2471:
2465:
2462:
2460:
2457:
2453:
2450:
2448:
2447:Washer method
2445:
2444:
2442:
2440:
2437:
2433:
2430:
2429:
2428:
2425:
2421:
2418:
2416:
2413:
2411:
2410:trigonometric
2408:
2407:
2406:
2403:
2401:
2398:
2394:
2391:
2390:
2389:
2386:
2384:
2381:
2379:
2376:
2374:
2371:
2369:
2366:
2364:
2361:
2360:
2358:
2356:
2352:
2344:
2341:
2339:
2336:
2334:
2331:
2330:
2329:
2326:
2322:
2319:
2317:
2314:
2313:
2311:
2307:
2304:
2302:
2299:
2297:
2294:
2292:
2289:
2288:
2287:
2284:
2280:
2279:Related rates
2277:
2275:
2272:
2270:
2267:
2265:
2262:
2261:
2259:
2255:
2252:
2248:
2245:
2244:
2243:
2240:
2238:
2235:
2233:
2230:
2228:
2225:
2223:
2220:
2218:
2215:
2214:
2213:
2210:
2206:
2203:
2201:
2198:
2197:
2196:
2193:
2191:
2188:
2186:
2183:
2181:
2178:
2176:
2173:
2171:
2168:
2166:
2163:
2162:
2160:
2158:
2154:
2148:
2145:
2143:
2140:
2138:
2135:
2131:
2128:
2127:
2126:
2123:
2121:
2118:
2117:
2115:
2113:
2109:
2103:
2100:
2098:
2095:
2093:
2090:
2088:
2085:
2083:
2080:
2078:
2075:
2073:
2070:
2068:
2065:
2063:
2060:
2058:
2055:
2053:
2050:
2048:
2045:
2043:
2040:
2039:
2037:
2035:
2031:
2027:
2020:
2015:
2013:
2008:
2006:
2001:
2000:
1997:
1986:
1982:
1978:
1974:
1970:
1966:
1959:
1956:
1951:
1946:
1944:
1938:
1932:
1929:
1917:
1913:
1907:
1904:
1889:
1882:
1879:
1874:
1872:9781841196503
1868:
1863:
1862:
1853:
1850:
1845:
1843:9780521737821
1839:
1835:
1828:
1825:
1822:
1821:
1816:
1811:
1808:
1802:
1801:
1796:
1793:
1786:
1783:
1770:
1769:
1761:
1758:
1751:
1747:
1744:
1741:
1738:
1736:
1733:
1731:
1728:
1727:
1723:
1721:
1719:
1715:
1711:
1693:
1682:
1680:
1662:
1653:
1652:infinitesimal
1649:
1648:
1643:
1639:
1631:
1629:
1613:
1588:
1585:
1580:
1576:
1573:
1567:
1561:
1553:
1544:
1538:
1535:
1525:
1524:
1523:
1507:
1481:
1477:
1450:
1446:
1435:
1417:
1390:
1384:
1380:
1376:
1373:
1370:
1364:
1358:
1355:
1352:
1349:
1346:
1341:
1338:
1333:
1329:
1325:
1322:
1319:
1316:
1313:
1307:
1301:
1298:
1292:
1289:
1286:
1276:
1272:
1268:
1263:
1255:
1252:
1249:
1240:
1234:
1226:
1217:
1211:
1208:
1198:
1197:
1196:
1182:
1179:
1176:
1154:
1130:
1126:
1122:
1119:
1097:
1083:
1081:
1079:
1075:
1071:
1065:
1061:
1059:
1055:
1047:
1045:
1043:
1039:
1038:
1033:
1029:
1025:
1021:
1017:
1013:
1009:
1005:
1001:
993:
989:
984:
973:
968:
966:
961:
959:
954:
953:
951:
950:
943:
940:
938:
935:
933:
930:
928:
925:
923:
920:
918:
915:
913:
910:
909:
901:
900:
893:
890:
888:
885:
883:
880:
878:
875:
874:
866:
865:
854:
851:
849:
846:
844:
841:
840:
839:
838:
828:
827:
816:
813:
811:
808:
806:
803:
801:
798:
796:
795:Line integral
793:
791:
788:
786:
783:
782:
781:
780:
775:
770:
767:
765:
762:
760:
757:
755:
752:
751:
750:
749:
744:
738:
737:Multivariable
732:
731:
720:
717:
715:
712:
710:
707:
705:
702:
700:
697:
695:
692:
691:
690:
689:
684:
679:
676:
674:
671:
669:
666:
664:
661:
659:
656:
654:
651:
650:
649:
648:
642:
636:
635:
624:
621:
619:
616:
614:
611:
609:
606:
604:
600:
598:
595:
593:
590:
588:
585:
583:
580:
578:
575:
574:
573:
572:
569:
565:
560:
557:
555:
552:
550:
547:
545:
542:
540:
537:
534:
530:
527:
526:
525:
524:
518:
512:
511:
500:
497:
495:
492:
490:
487:
485:
482:
480:
477:
475:
472:
469:
465:
461:
460:trigonometric
457:
454:
452:
449:
447:
444:
442:
439:
438:
437:
436:
431:
426:
423:
421:
418:
416:
413:
411:
408:
405:
401:
398:
396:
393:
392:
391:
390:
385:
380:
377:
375:
372:
370:
367:
366:
365:
364:
358:
352:
351:
340:
337:
335:
332:
330:
327:
325:
322:
320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
291:
290:
289:
286:
282:
277:
274:
272:
271:Related rates
269:
267:
264:
262:
259:
257:
254:
252:
249:
248:
247:
246:
241:
234:
231:
229:
228:of a function
226:
224:
223:infinitesimal
221:
220:
219:
216:
213:
209:
206:
205:
204:
203:
198:
192:
186:
185:
179:
176:
174:
171:
169:
166:
165:
160:
157:
155:
152:
151:
147:
144:
143:
142:
141:
122:
116:
113:
107:
101:
98:
95:
92:
85:
78:
75:
69:
64:
60:
51:
50:
47:
43:
39:
38:
33:
19:
3812:Isaac Newton
3724:
3717:
3709:
3700:
3633:Isaac Barrow
3571: (home)
3312:Newtonianism
3287:Newton scale
3250:Impact depth
3242:
3223: (1754)
3218:
3215: (1728)
3210:
3200:
3187:
3172:
3158: (1711)
3153:
3150: (1707)
3145:
3142: (1704)
3137:
3134: (1704)
3129:
3126: (1687)
3121:
3118: (1684)
3113:
3110: (1671)
3105:
3099:Publications
2945:Secant cubed
2870:
2863:
2848:
2844:Isaac Newton
2814:Brook Taylor
2481:Derivatives
2452:Shell method
2180:Differential
1971:(1): 33–49.
1968:
1964:
1958:
1942:
1931:
1919:. Retrieved
1916:www.mhhe.com
1915:
1906:
1894:. Retrieved
1881:
1860:
1852:
1833:
1827:
1818:
1810:
1798:
1785:
1773:. Retrieved
1767:
1760:
1683:
1645:
1635:
1603:
1407:
1087:
1077:
1067:
1063:
1051:
1035:
1032:mathematical
1020:Isaac Newton
999:
997:
991:
987:
456:Substitution
218:Differential
191:Differential
3712:by Paolozzi
3651:Roger Cotes
3260:Newton disc
3174:Quaestiones
3147:Arithmetica
3013:of surfaces
2764:and numbers
2726:Dirichlet's
2696:Telescoping
2649:Alternating
2237:L'HĂ´pital's
2034:Precalculus
1647:The Analyst
1642:philosopher
912:Precalculus
905:Miscellanea
870:Specialized
777:Definitions
544:Alternating
387:Definitions
200:Definitions
3829:Categories
3799:Categories
3775:XMM-Newton
3692:Depictions
3663:John Keill
3585:Apple tree
3580:Later life
3575:Early life
3155:De Analysi
2809:Adequality
2495:Divergence
2368:Arc length
2165:Derivative
1950:Wikisource
1896:28 January
1752:References
1034:treatise,
1028:derivative
892:Variations
887:Stochastic
877:Fractional
746:Formalisms
709:Divergence
678:Identities
658:Divergence
208:Derivative
159:Continuity
3614:Relations
3123:Principia
3008:of curves
3003:Curvature
2890:Integrals
2684:Maclaurin
2664:Geometric
2555:Geometric
2505:Laplacian
2217:linearity
2057:Factorial
1985:121774892
1800:MathWorld
1795:"Fluxion"
1632:Criticism
1559:Δ
1551:Δ
1539:˙
1356:−
1339:−
1299:−
1269:−
1232:Δ
1224:Δ
1212:˙
1070:hash code
992:"fluxion"
882:Malliavin
769:Geometric
668:Laplacian
618:Dirichlet
529:Geometric
114:−
61:∫
3737:Namesake
3703:by Blake
3297:Spectrum
3238:Calculus
3207: )
3107:Fluxions
2998:Manifold
2731:Integral
2674:Infinite
2669:Harmonic
2654:Binomial
2500:Gradient
2443:Volumes
2254:Quotient
2195:Notation
2026:Calculus
1939:(1734).
1724:See also
1042:calculus
1016:function
1008:gradient
988:"fluent"
922:Glossary
832:Advanced
810:Jacobian
764:Exterior
694:Gradient
686:Theorems
653:Gradient
592:Integral
554:Binomial
539:Harmonic
404:improper
400:Integral
357:Integral
339:Reynolds
314:Quotient
243:Concepts
79:′
46:Calculus
18:Fluxions
3255:Inertia
3243:fluxion
3139:Queries
3131:Opticks
3115:De Motu
2935:inverse
2923:inverse
2849:Fluxion
2659:Fourier
2525:Stokes'
2520:Green's
2242:Product
2102:Tangent
1921:6 March
1817:at the
1815:Fluxion
1775:6 March
1706:
1686:
1675:
1655:
1636:Bishop
1626:
1606:
1520:
1500:
1496:
1469:
1465:
1438:
1430:
1410:
1167:
1147:
1145:(where
1110:
1090:
1084:Example
1076:phrase
1048:History
1010:, of a
1002:is the
1000:fluxion
917:History
815:Hessian
704:Stokes'
699:Green's
531: (
458: (
402: (
324:Inverse
299:Product
210: (
3710:Newton
3701:Newton
3018:Tensor
2940:Secant
2706:Abel's
2689:Taylor
2580:Matrix
2530:Gauss'
2112:Limits
2092:Secant
2082:Radian
1983:
1945:
1869:
1840:
1432:is an
1012:fluent
759:Tensor
754:Matrix
641:Vector
559:Taylor
517:Series
154:Limits
3545:table
2882:Lists
2741:Ratio
2679:Power
2415:Euler
2232:Chain
2222:Power
2097:Slope
1981:S2CID
1891:(PDF)
1718:limit
1408:Here
1074:Latin
1006:, or
582:Ratio
549:Power
468:Euler
446:Discs
441:Parts
309:Power
304:Chain
233:total
2751:Term
2746:Root
2485:Curl
1965:Isis
1923:2017
1898:2017
1867:ISBN
1838:ISBN
1777:2017
1714:zero
1195:is:
990:and
663:Curl
623:Abel
587:Root
2227:Sum
1973:doi
1708:as
1026:(a
294:Sum
3831::
1979:.
1969:64
1967:.
1914:.
1797:.
1044:.
998:A
466:,
462:,
3205:"
3201:"
3195:"
3180:"
3084:e
3077:t
3070:v
2018:e
2011:t
2004:v
1987:.
1975::
1952:.
1925:.
1900:.
1875:.
1846:.
1803:.
1779:.
1694:o
1663:o
1614:o
1589:4
1586:=
1581:o
1577:o
1574:4
1568:=
1562:t
1554:y
1545:=
1536:y
1508:o
1482:2
1478:o
1451:2
1447:o
1418:o
1391:o
1385:2
1381:o
1377:+
1374:o
1371:4
1365:=
1359:2
1353:o
1350:+
1347:2
1342:4
1334:2
1330:o
1326:+
1323:o
1320:4
1317:+
1314:4
1308:=
1302:2
1296:)
1293:o
1290:+
1287:2
1284:(
1277:2
1273:2
1264:2
1260:)
1256:o
1253:+
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1247:(
1241:=
1235:t
1227:y
1218:=
1209:y
1183:2
1180:=
1177:t
1155:t
1131:2
1127:t
1123:=
1120:y
1098:y
971:e
964:t
957:v
535:)
470:)
406:)
214:)
126:)
123:a
120:(
117:f
111:)
108:b
105:(
102:f
99:=
96:t
93:d
89:)
86:t
83:(
76:f
70:b
65:a
34:.
20:)
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