# Isaac Newton

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## Newton, Isaac

(1800–67) agriculturalist; born in Burlington County, N.J. By his mid-20s he was managing two farms in Springfield, Pa., so successfully that he opened a confectionery shop and sold ice cream made from his dairy surplus. Active in the state and national Agricultural Society, he urged Congress to establish a department of agriculture. In 1861 President Lincoln appointed him supervisor of the agricultural division of the Patent Office. In 1862 Congress created the Department of Agriculture with Newton as its first commissioner. In his annual reports he emphasized the importance of weather and climate to agriculture. He died from the effects of a sunstroke he received while working in the department's experimental field.*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Newton, Isaac

Born Dec. 25, 1642 (Jan. 4, 1643), in Woolsthorpe, near Grantham; died Mar. 20 (31), 1727, in Kensington. English physicist and mathematician. Creator of the theoretical foundations of mechanics and astronomy and discoverer of the law of universal gravitation and (independently of G. W. Leibniz) the differential and integral calculus. Inventor of the reflecting telescope and author of very important experimental works on optics.

Newton’s father, a farmer, died shortly before the birth of his son. At the age of 12, Newton began studying at the school in Grantham. In 1661 he entered Trinity College of Cambridge University as a subsizar (a poor student who worked as a servant in the college to support himself), where the prominent mathematician I. Barrow was his mentor. Newton graduated from the university in 1665, receiving the bachelor’s degree. He spent the period from 1665 to 1667, the time of the Great Plague, in his native village of Woolsthorpe. These were Newton’s most productive years. Here he developed the ideas that led to the invention of the differential and integral calculus and the reflecting telescope (he constructed the first reflecting telescope in 1668) and to the discovery of the law of universal gravitation. He also conducted experiments on the dispersion of light. In 1668 he received the master’s degree, and in 1669, after Barrow resigned his chair, Newton was appointed Lucasian Professor of Mathematics, a position that he held until 1701. In 1671, Newton constructed a second reflecting telescope—of larger size and better quality. The demonstration of the telescope made a strong impression on his contemporaries, and soon afterward, in January 1672, Newton was elected a fellow of the Royal Society of London, becoming the society’s president in 1703. In 1687 he published his monumental work *Philosophiae naturalis principia mathematica* (Mathematical Principles of Natural Philosophy), which, for brevity, is referred to as the *Principia*. In 1695 he was appointed warden of the mint. (Newton’s study of the properties of metals apparently was a factor in this appointment.) Newton’s work included a complete reform of the coinage of all British currency. He succeeded in placing in order the British currency system, and in 1699 he was promoted to the highly paid lifetime position of master of the mint. That same year, Newton was elected a foreign member of the Paris Academy of Sciences. In 1705 he was knighted for his scientific achievements. Newton was buried in Westminster Abbey.

The fundamental questions in mechanics, physics, and mathematics that were worked on by Newton were closely related to the scientific problems of the time. Newton became interested in optics while still a student, and his investigations in this field were connected with a desire to eliminate the deficiencies of optical instruments. In his first work dealing with optics, *New Theory About Light and Colors*, which he presented at the Royal Society of London in 1672, Newton advanced his views on the corpuscular hypothesis of light. This work generated a heated controversy in which R. Hooke opposed Newton’s corpuscular views of the nature of light; at that time, the wave hypothesis of light predominated. In answer to Hooke, Newton offered a hypothesis that combined corpuscular and wave conceptions of light. Newton later developed this hypothesis in *Theory About Light and Colors*, in which he also described the experiment on Newton’s rings and established the periodicity of light. When this work was read at a meeting of the Royal Society, Hooke claimed priority; as a result, the exasperated Newton decided not to publish his works on optics.

Newton’s optical studies, conducted over many years, were finally published in the fundamental work *Opticks*, in 1704, after Hooke’s death. A consistent opponent of unsubstantiated and arbitrary hypotheses, Newton opens *Opticks* with the words: “My design in this book is not to explain the properties of light by hypotheses but to propose and prove them by reason and experiments” (I. Newton, *Optika*, Moscow, 1954, p. 9). In *Opticks*, Newton described the meticulous experiments he had conducted to detect the dispersion of light, that is, the separation of white light by a prism into individual components of different colors and refrangibility; he also showed that dispersion causes chromatic aberration, a type of distortion in optical systems that use lenses. Erroneously believing that the distortion induced by this aberration could not be eliminated, Newton designed the reflecting telescope. In addition to carrying out experiments on the dispersion of light, Newton described the interference of light in thin plates and the change in the colors of interference bands as a function of the plate thickness in Newton’s rings. Newton was essentially the first to measure the wavelength of light. He also described his experiments on the diffraction of light.

*Opticks* concludes with a special appendix called “Queries,” in which Newton expressed his views on the nature of the universe. In particular, he sets forth his views on the structure of matter, in which not only the concept of the atom but also that of the molecule are implied. Moreover, Newton expounds the idea of the hierarchic structure of matter: he assumes that the “particles of bodies” (atoms) are separated by intervals of empty space and that these particles consist of smaller particles, which are also separated by empty space and consist of still smaller particles, and so forth, until solid indivisible particles are reached. Here, Newton considers anew the hypothesis that light may represent a combination of the motion of material particles and the propagation of ether waves.

The culmination of Newton’s scientific work was the *Principia*. in which Newton generalized his own investigations and the results of his predecessors, including Galileo, J. Kepler, R. Descartes, C. Huygens, G. Borelli, R. Hooke and E. Halley, and first created a unified orderly system of terrestrial and celestial mechanics, which became the foundation of all classical physics. Here Newton gave definitions of basic concepts—quantity of matter (equivalent to mass), density, quantity of motion (equivalent to momentum), and various types of forces. In formulating the concept of quantity of matter, he proceeded from the idea that atoms consist of some single type of primary matter; he interpreted density as the degree to which unit volume of a body is filled with primary matter. Newton was the first to consider the fundamental method of describing phenomenologically any physical effect by the agency of a force. In defining the concepts of space and time, he distinguished “absolute stationary space” from a bounded moving space, calling the latter “relative.” He also distinguished uniformly progressing, absolute, true time, called “duration,” from relative, apparent time, which serves as a measure of a “period of time.” These concepts of time and space were the basis of classical mechanics. Newton then formulated his three remarkable “axioms, or laws of motion”: the law of inertia, which is called Newton’s first law although it was discovered by Galileo; the law of proportionality of the change in momentum and force, called Newton’s second law; and the law of equal and opposite action and reaction, called Newton’s third law. From the second and third laws, he derived the law of conservation of momentum for a closed system.

Newton examined the motion of bodies under the action of central forces and proved that the trajectories of such motions are conic sections—ellipses, hyperbolas, or parabolas. He proposed his law of universal gravitation and concluded that all planets and comets are attracted to the sun and all satellites are attracted to the planets with a force inversely proportional to the square of the distance. Newton also developed the theory of the motion of celestial bodies and showed that Kepler’s laws and the most important deviations from the laws follow from the law of universal gravitation. For example, he explained the peculiarities of lunar motion, such as the variation of the motion and the regression of the nodes; he also explained the phenomenon of precession and the flattening of Jupiter, considered problems of the attraction of continuous masses and the theory of tides, and offered a theory of the figure of the earth.

In the *Principia*, Newton investigated the motion of a body in a continuous medium (a gas or a liquid) as a function of the velocity of the body and presented the results of his experiments on the oscillations of a pendulum in air and liquids. He also considered the velocity of propagation of sound in elastic media. Newton proved, by mathematical computations, the total untenability of Descartes’s hypothesis, which explained the motion of celestial bodies by using the concept of vortices of different types in the ether that fills the universe. Newton discovered the law governing the cooling of a heated body. In the *Principia* he also devoted much attention to the principle of dynamical similitude, on the basis of which similarity theory was developed.

Thus, the general outline for a rigorous mathematical approach to the solution of any specific problem in terrestrial or celestial mechanics was first given in the *Principia*. However, further application of these methods required detailed development of analytical mechanics (L. Euler, J. D’Alembert, J. Lagrange, W. R. Hamilton) and hydromechanics (Euler and D. Bernoulli). Subsequent developments in physics, such as relativity theory and quantum mechanics, revealed the limits of applicability of Newtonian mechanics.

The problems of natural science posed by Newton required the development of fundamentally new mathematical methods. For Newton, mathematics was the principal tool in physical investigation, and he emphasized that mathematical concepts are adopted from other fields and arise as an abstraction of phenomena and processes of the physical world. To Newton, mathematics was essentially a part of natural science.

The development of the differential and the integral calculus was an important landmark in the development of mathematics. Newton’s works on algebra, interpolation theory, and geometry were also of great importance. In 1665 and 1666, Newton developed the fundamental ideas of the method of fluxions under the influence of works by his teacher Barrow and by P. Fermat and J. Wallis. Also in the same period were Newton’s discovery of the inverse relation between the operations of differentiation and integration and his fundamental discoveries concerning infinite series, in particular, his inductive generalization of the binomial theorem to the case of any real exponent. Soon after, Newton’s main works on analysis were written, but they were not published until much later. Some of Newton’s mathematical discoveries became known as early as the 1670’s through his manuscripts and correspondence.

A profound relationship between Newton’s mathematical and mechanical investigations was clearly reflected in the concepts and terminology of the method of fluxions. Newton introduced the concept of a continuous mathematical quantity as an abstraction of various types of continuous mechanical motions. Curves are generated by the motion of points; surfaces, by the motion of curves; solids, by the motion of surfaces; angles, by the rotation of sides; and so on. Variable quantities were called fluents, or flowing quantities, by Newton; the common argument of fluents, to which other, dependent variables are referred, was called absolute time; the rates of change of fluents were called fluxions; and the infinitesimally small changes in fluents necessary for calculating fluxions were called moments (Leibniz called them differentials). Thus, Newton took as fundamental concepts the concepts of fluxion (derivative) and fluent (primitive, or indefinite, integral).

In the work *De analysi per equationes numero terminorum infinitas* (On Analysis by Infinite Series, 1669, published 1711), Newton calculated the derivative and integral of any power function. He expressed, by means of infinite power series, various rational, irrational, and fractional rational functions, as well as certain transcendental functions, such as logarithmic, exponential, sine, cosine, and arc sine functions. In the same work, he presented a method for the numerical solution of algebraic equations and a method for finding an expansion of implicit functions in a series in fractional powers of the independent variable. The method of calculating and studying functions by approximating them as infinite series assumed enormous significance for all analysis and for its applications.

The most complete discussion of the differential and integral calculus is contained in *De methodis serierum et fluxionum* (On the Methods of Series and Fluxions; 1670–71, published 1736). Here, Newton formulated the two fundamental inverse problems of analysis. The first problem consists in determining the rate of motion at a given instant from a known path, or determining the relation between fluxions from a given relation between fluents (the problem of differentiation). The second problem consists in determining the path traversed in a given period of time from a known rate of motion, or to determine the relation between fluents from a given relation between fluxions (the problem of integrating a differential equation and, in particular, the problem of finding antiderivatives). The method of fluxions was applied here to a large number of geometrical problems, such as the problems of tangents, curvature, extrema, quadratures, and squaring. In addition, a number of integrals of functions containing the square root of a quadratic trinomial are expressed in elementary functions. In *De methodis serierum et fluxionum*, much attention is paid to the integration of ordinary differential equations, with the primary role being played by the representation of a solution in the form of an infinite power series. Newton also solved some problems of the calculus of variations.

In the Introduction to *Tractatus de quadratura curvarum* (Quadrature of Curves; basic text written 1665–66 and introduction and final version 1670; published 1704) and in the *Principia*, Newton outlined a program for constructing the method of fluxions on the basis of the study of limits and the “ultimate ratios of the evanescent parts” or the “first ratios of the nascent augments,” without giving, however, a formal definition of limit and considering his definition of limit as an initial one. Newton’s study of limits, continued through a number of intermediate links (D’Alembert, Euler), was extensively developed in 19th-century mathematics by A. L. Cauchy and others.

In *Methodus differentialis* (Method of Differences; published 1711), Newton gave a solution for the problem of drawing a parabolic curve of order *n* through *n* + 1 given points with equidistant or nonequidistant abscissas and proposed an interpolation formula. In the *Principia* he gave a theory of conic sections. In *Enumeratio linearum tertii ordinis* (Enumeration of Lines of the Third Order; published 1704), Newton gave a classification of these curves, generalized the concepts of diameter and center, and indicated methods of constructing second- and third-order curves under various conditions. This work played a major part in the development of analytic geometry and some aspects of projective geometry. *Arithmetica universalis* … (Universal Arithmetic; published 1707; based on lectures of the 1670’s) contains important theorems on various topics in mathematics, such as symmetric functions of the roots of algebraic equations, dividing out of roots, and reducibility of equations. Algebra was finally liberated from its geometric form by Newton, and Newton’s definition of a number as the ratio of the length of any segment to a segment taken as unity, rather than as an accumulation of units, was an important step in the development of the study of real numbers.

Newton’s theory of the motion of celestial bodies, which was based on the law of universal gravitation, was recognized by major contemporary British scientists but was rejected on the European continent. The Cartesians, whose views predominated in Europe, particularly in France, in the first half of the 18th century, opposed Newton’s views, especially in regard to the question of gravitation. Newton predicted the flattening of the earth at the poles from calculations. The detection of such a flattening, as opposed to the bulges expected from the teachings of Descartes, was a convincing argument in support of Newton’s theory. The work of A. C. Clairaut in calculating the perturbing action of Jupiter and Saturn on the motion of Halley’s comet played an exceptional role in bolstering the stature of Newton’s theory. The crowning success of Newton’s theory in solving problems of celestial mechanics was the discovery of the planet Neptune in 1846 by U. Leverrier and J. Adams on the basis of calculations of perturbations of the orbit of Jupiter.

In Newton’s time, the problem of the nature of gravitation reduced essentially to the problem of interaction, that is, to the question of whether a material intermediary is present in the phenomenon of the mutual attraction of masses. Although Newton did not recognize Cartesian ideas on the nature of gravitation, he avoided making any explanations, believing that there were insufficient theoretical scientific or experimental grounds to do so. A scientific-philosophical doctrine called Newtonianism emerged after Newton’s death. Its most characteristic feature was the absolutization and development of Newton’s statement “I frame no hypotheses” (*Hypotheses non fingo*) and a call for the phenomenological study of events while ignoring fundamental scientific hypotheses.

The powerful apparatus of Newtonian mechanics had the universality and capability necessary to explain and describe a very broad range of natural phenomena, especially astronomical phenomena, and had an enormous influence on many branches of physics and chemistry. Newton wrote that it would be desirable to derive from the principles of mechanics all other natural phenomena, and he himself used mechanical models to explain certain optical and chemical phenomena. His views had an enormous influence on the subsequent development of physics. “Newton forced physics to think in his way, ‘classically,’ as we now say. … It may be asserted that his thoughts left their mark on the whole of physics; without Newton, science would have developed differently” (S. I. Vavilov, *Isaak N’iuton*, 1961, pp. 194 and 196).

Newton combined materialist views of natural science with a religious outlook. Toward the end of his life he wrote a paper on the Prophet Daniel and an interpretation of the Apocalypse. However, Newton clearly distinguished science from religion. “Newton granted him (god) the ‘first push,’ but denied him any subsequent intervention in the solar system” (F. Engels, *Dialektika prirody*, 1969, p. 171).

All of Newton’s principal works have been translated into Russian, largely owing to the efforts of A. N. Krylov and S. I. Vavilov.

### WORKS

*Opera quae extant omnia: Commentariis illustravit S. Horsley*, vols. 1–5. London, 1779–85.

*In Russian translation:*

“Matematicheskie nachala natural’noi filosofii. s primechaniiami i poiasneniiami A. N. Krylova.” In A. N. Krylov,

*Sobr. trudov*, vol. 7. Moscow-Leningrad, 1936.

*Lektsii po optike*. [Moscow] 1946. (Translated by S. I. Vavilov.)

*Optika ili traktat ob otrazheniiakh, prelomleniiakh, izgibaniiakh i tsvetakh sveta*, 2nd ed. Moscow, 1954. (Translated and annotated by S. I. Vavilov.)

*Matematicheskie raboty*. Moscow-Leningrad, 1937. (Translated from Latin by D. D. Mordukhai-Boltovskii.)

*Vseobshchaia arifmetika Hi kniga ob arifmeticheskom sinteze i analize*. Moscow-Leningrad, 1948. (Translated by A. P. Iushkevich.)

### REFERENCES

Vavilov, S. I.*Isaak N’iuton*. Moscow, 1961.

*Isaak N’iuton, 1643–1727*(a collection of articles commemorating Newton’s 300th birthday). Edited by S. I. Vavilov. Moscow-Leningrad, 1943.

## Newton, Isaac

*EB*, 13: 16–21]