# Soviet Literature on Newton

# SOVIET LITERATURE ON NEWTON

A profound and manifold study of Newton’s life and work began in Russia at the beginning of the twentieth century; for earlier works see the article by T. P. Kravets, cited below.

The foundation of Soviet studies on Newton was laid by A. N. Krylov, who in 1915–1916 published the complete *Principia* in Russian, with more than 200 notes and supplements of a historical, philological, and mathematical nature. More than a third of the volume is devoted to supplements that present a complete, modern analytic exposition of various theorems and proofs of the original text, the clear understanding of which is often too difficult for the modern reader: “Matematicheskie nachala naturalnoy estestvennoy filosofii” (“The Mathematical Principles of Natural Philosophy”), in *Izvestiya Nikolaevskoi morskoi akademii*, **4–5** (1915–1916); 2nd ed. in *Sobranie trudov akademika* A. N. *Krylova* (“Collected Works of Academician A. N. Krylov”), **VII** (Moscow-Leningrad, 1936). Krylov devoted special attention to certain of Newton’s methods and demonstrated that after suitable modification and development they could still be of use. Works on this subject include “Besedy o sposobakh opredelenia orbit komet i planet po malomu chislu nabludenii” (“Discourse on Methods of Determining Planetary and Cometary Orbits Based on a Limited Number of Observations”) *ibid.*, **VI** , 1–149; a series of papers, *ibid.*, V, 227–298; and “Nyutonova teoria astronomicheskoy refraktsii” (“Newton’s Theory of Astronomical Refraction”), *ibid.*, **V,** 151–225; see also his “On a Theorem of Sir Isaac Newton,” in *Monthly Notices of the Royal Astronomical Society*, **84** (1924), 392–395. On Kryiov’s work, see A. T. Grigorian, “Les etudes Newtoniennes de A. N. Krylov,” in I. B. Cohen and R. Taton, eds., *Mélanges Alexandre Koyré*, II (Paris, 1964), 198–207.

A Russian translation of Newton’s *Observations on the Prophecies & of Daniel and the Apocalypse of St. John was* published simultaneously with the first Russian edition of *Principia as Zamechania na knigu Prorok Daniil i Apokalipsis sv. loanna* (Petrograd, 1916); the translator’s name is not given.

An elaborately annotated translation of Newton’s works on optics is S. I. Vavilov, ed., *Optika Hi traktat oh otrozheniakh, pre/omleniakh, izgihaniakh i tsvetakh sveta* (“Optics” Moscow-Leningrad, 1927; 2nd ed., Moscow, 1954). Vavilov also published Russian translations of two of Newton’s essays, “Novaya teoria sveta, i tsvetov” (“A New Theory of Light and Colors”) and “Odna gipotesa, obyasnyayushchaya svoystva sveta, izlozhennaya v neskolkikh moikh statyakh” (“A Hypothesis Explaining the Properties of Light Presented in Several of My Papers”), *in Uspekhi fizicheskikh nauk*, **2** (1927), 121–163; and *Lektsti po optike* (“Lectiones opticae” Leningrad, 1946). Vavilov was the first to study thoroughly the significance of the last work in the development of physics.

Newton’s mathematical works published by Castillon in vol.**1** of *Opuscula mathematica* (1744) were translated by D. D. Mordukhay-Boltovskoy as *Matematicheskie raboty*(“Mathematical Works” Moscow-Leningrad, 1937); the editor’s 336 notes constitute nearly a third of the volume. *Arithmetica universalis* was translated by A. P. Youschkevitch with commentary as *Vseobshchaya arifmetika Hi kniga ob arifmeticheskikh sintese i analise* (Moscow, 1948).

Many works dedicated to various aspects of Newton’s scientific activity and to his role in the development of science were included in the tercentenary volumes *Isaak Nyuum. 1643–1727*. *Shornik statey k trekhsotletiyu so dnya rozhdenia*, S. I. Vavilov, ed. (Moscow-Leningrad, 1943); and *Moskovsky universitet—pamyati Nyutona—sbornik statey* (Moscow, 1946). These works are cited below as *Symposium I* and *Symposium II*, respectively.

Z. A. Zeitlin, in *Nauka i gipotesa* (“Science and Hypothesis” Moscow-Leningrad, 1926), studied the problem of Newton’s methodology, particularly the roles of Bentley and Cotes in preparing the 2nd ed. of the *Principia* and emphasized that both scientists had falsified Newtonian methods; the majority of other authors did not share his viewpoint. In “Efir, svet i veshchestvo v fisike Nyutona” (“Ether, Light, and Matter in Newton’s Physics”), in *Symposium* I, 33–52, S. I. Vavilov traced the evolution of Newton’s views on the hypothesis of the ether, the theory of light, and the structure of matter. Vavilov also dealt with Newton’s methods and the role of hypothesis in ch. 10 of his biography *Isaak Nyuton* (Moscow-Leningrad, 1943; 2nd ed., rev. and enl., 1945; 3rd ed., 1961). The 3rd ed., of this work appeared in vol. III of Vavilov’s *Sobranie sochinenii* (“Selected Works” Moscow, 1956), which contains all of Vavilov’s papers on Newton. The biography also appeared in German trans. (Vienna, 1948; Berlin, 1951).

B. M. Hessen in *Sotsialno-ekonomicheskie korni mekhaniki Nyutona* (“The Socioeconomic Roots of Newton’s Mechanics”), presented to the Second International Congress of the History of Science and Technology held in London in 1931 (Moscow-Leningrad, 1933), attempted to analyze the origin and development of Newton’s work in Marxist terms. Hessen examined the *Principia* in the light of contemporary economic and technological problems and in the context of the political, philosophical, and religious views which reflected the social conflict occurring during the period of revolution in England. His essay appeared in English as *Science at the Crossroads* (London, 1931), which is reprinted in facsimile with a foreword by Joseph Needham and an introduction by P. G. Werskey (London, 1971) and with a foreword by Robert S. Cohen (New York, 1971).

In his report on Newton’s atomism, “Newton on the Atomic Theory,” in Royal Society, *Newton Tercentenary Celebrations:* 15–19 *July, 1946* (Cambridge, 1947), Vavilov compared Newtonian chemical ideas with the development of chemistry in the nineteenth and twentieth centuries and, in particular, with the work of Mendeleev. The latter topic was also discussed in T. I. Raynov, “Nyuton i russkoe estestvoznanie” (“Newton and Russian Natural Science”), in *Symposium I*, 329–344, which also examined Lomonosov’s attitude toward Newton. See also P. S. Kudriavtsev, “Lomonosov i Nyuton,” in *Trudy Instituta istorii estestvoznaniya i teklniki. Akademiya naut SSSR*, **5** (1955), 33–51. On Newton’s role in the development of chemistry see also N. I. Flerov, “Vlianie Nyutona na razvitie khimii” (“Newton’s Influence on the Development of Chemistry”), in *Symposium II*, 101–106.

For detailed comments on some important problems of the *Principia*, see L. N. Sretensky, “Nyutonova teoria prilivov i figury zemli” (“Newton’s Theory of Tides and of the Figure of the Earth”), in *Symposium* I, 211–234; and A. D. Dubyago, “Komety i ikh znachenie v obshchey sisteme Nyutonovykh Nachal (“Comets and Their Significance in the General System of Newton’s Prineipia”). *ibid.*, 235–263. N. I. Idelson dealt with the history of the theory of lunar motion and presented a detailed study of the St. Petersburg competition of 1751, through which the theory of universal gravitation received lasting recognition. in “Zakon vsemirnogo tyagotenia i teoria dvizhenia luny” (“The Law of ’ Universal Gravitation and the Theory of Lunar Motion”), *ibid.*, 161–210. See also Idelson’s paper “Volter i Nyuton,” in *Volar 1694–1778. Stati i materialy* (Moscow-Leningrad, 1948), 215–241; and A. D. Lyublinskaya’s paper on the discussions between the Newtonians and the Cartesians, “K voprosu o vlianii Nyutona na frantsuzkuyu nauku” (“On the Problem of Newton’s Influence on French Science”), in *Symposium I* , 361 391. On Newton’s physics, see V. G. Fridman, “Ob uchenii Nyutona o masse” (”New ton’s Doctrine of Mass”), in *Uspekhi fizicheskikh nauk*, **61** , no. 3 (1957), 451–460.

On Newton’s optics, apart from the fundamental studies of Krylov and Vavilov, see G. G. Slyusarev, “Raboty Nyutona po geometricheskoy optike” (“Newton’s Works in Geometrical Optics”), in *Symposium I*, 127–141; 1. A. Khvosiikov, “Nyuton i razvitie uchenia o refraktsii sveta v zemnoy atmosfere” (“Newton and the Development of Studies of the Refraction of Light in the Earth’s Atmosphere”), *ibid..* 142–160; and L. I. Mandelshtam, “Qpticheskie raboty Nyutona” (“Newton’s Works in Optics”), in *Uspekhi fizivlwskikh nauk***28** , no. 1 (1946), 103–129.

P. S. Kudriavtsev treated Newtonian mechanics and physics in his *Istoria fiziki* (“History of Physics”), 2nd ed. (Moscow, 1956), I, 200–258; and also published a biography, *Isaak Nyuton* (Moscow, 1943; 2nd ed., 1955). The basic ideas of Newton’s mechanics are described in A. T. Grigorian and I. B. Pogrebyssky, eds., *Istoria mekhaniki s drevneyshikh vremen do kontsa 18 veka*(“The History of Mechanics from Antiquity to the End of the 18th Century”; Moscow, 1971).

Many works on Newton as mathematician were devoted to an analysis of his views on the foundations of infinitesimal calculus and, in particular, of his conceptions of the limiting process and of moment. S. Gouriev dealt with this question in “Kratkoe izlozhenie razlichnykh sposobov izyasnyat differentsialnoe ischislenie” (“A Brief Account of Various Methods of Explaining the Differential Calculus”), in *Umozritelnye issledovanie SPb. Akademii nauk*, **4** (1815), 159212. Gouriev’s conception was subsequently reinterpreted— occasionally with disagreement—in the commentaries of Krylov and Mordukhay-Boltovskoy (see above); and in the papers of S. A. Yanovskaya related to the publication of the mathematical MSS of Karl Marx, “O matematicheskikh rukopisyakh Marksa” (“On Marx’s Mathematical Manuscripts”), in *Marksism i estestvoznanie* (Moscow, 1933), 136–180. See also K. Marx, *Matematicheskie rukopisi* (”Mathematical Manuscripts”; Moscow, 1968), 573–576; S. A. Bogomolov, *Aktualnaya inskoiwchnost*(“Actual Infinity”; Leningrad-Moscow, 1934); N. N. Luzin, “Nyutonova teoria predelov (“Newton’s Theory of Limits”), in *Symposium I*, 53–74; S. Y. Lurie, “Predshestvenniki Nyutona v filosofii besko-nechno malykh” (“Newton’s Predecessors in the Philosophy of Infinitesimal Calculus”), *ibid.*, 75–98; A. N. Kolmogorov, “Nyuton i sovremennoe matematicheskoe myshlenie” (“Newton and Modern Mathematical Thought”), *ibid.* II, 27–42; and F. D. Kramar, “Vopross obosnovania analisa v trudakh Vallisa i Nyutona” (“The Problems of the Foundation of the Calculus in the Works of Wallis and Newton”), in *Istoriko-matematicheskie issledovaniya*, **3** (1950), 486–508.

K. A. Rybnikov studied the role of infinite series as a universal algorithm in Newton’s method of fluxions in “O roli aigoritmov v istorii obosnovania matematicheskogo analisa” (“On the Role of Algorithms in the History of the Origin of the Calculus”), in *Trudy Institute istorii estestvoznaniya i tekhmki. Akademiya nauk SSSR*, **17** (1957), 267–299. The history of Newton’s parallelogram and its applications was discussed in N. G. Chebotaryov, “Mnogougolnik Nyutona i ego rol v sovremennom razvitii matematiki” (“Newton’s Polygon and his Role in the Modern Development of Mathematics”), in *Symposium* I, 99–126. I. G. Bashmakova examined the research of Newton and Waring on the problem of reducibility of algebraic equations in “Ob odnom voprose teorii algebraicheskikh uravneny v trudakh I. Nyutona i E. Varinga” (“On a Problem of the Theory of Algebraic Equations in the Works of I. Newton and E. Waring”), in *Istoriko-matematicheskie issledovaniya,*, **12** (1959), 431–456. Newton’s use of asymptotic series was discussed in M. V. Chirikov, “Iz istorii asimptoticheskikh ryadov” (“On the History of Asymptotic Scries”), *ibid.*, **13** (I960), 441 472. On Newton’s calculations equivalent to the use of multiple integrals, see V. I. Antropova, “O geometricheskom metode ‘Matcmaticheskikh nachal naturalnoy filosofii’ I. Nyutona” (“On the Geometrical Method in Newton’s *Philosophiae naturalis mathematica principia*“), ibid., 17 (1966), 208–228; and “O roli Isaaka Nyutona v razvitii teorii pOtentSttla” (“On Isaac Newton’s Role in the Development of Potential Theory”), in *Uchenye zapiski Tulskogo gosudarstvennogo pedagogicheskogo institute* Mat. kafedr, **3** (1970), 3 56. N. I. Glagolev described Newton’s geometrical ideas in “Nyuton kak geometr” (“Newton as Geometer”), in *Symposium***II** , 71–80; and his mathematical discoveries were summarized in vols. II and III of A. P. Youschkevitch, ed., *Istoria matematiki s drevneyshikh vremen do nachala XIX stoletia* (“A History of Mathematics From Antiquity to the Beginning of the Nineteenth Century”; Moscow, 1970–1972).

See also two papers on Newton as historian of antiquity: S. Y. Lurie, “Nyuton—istorik drevnosti” (“Newton-Historian of Antiquity“), in *Symposium* I, 271–311; and E. C Skrzhinskaya, “Kembridgsky universitet i Nyuton” (“Cambridge University and Newton”), *ibid..* 392–421.

On Soviet studies of Newton, see T. P. Kravels. “Nyuton i izuchenie ego trudov v Rossii” (“Newton and the Study of His Works in Russia”), 312–328; A. P. Youschkevitch, ‘Sovetskaya yubileynaya literatura o Nyutone” (“Soviet Jubilee Literature on Newton”), in *Trudy Instituta istorii estestvoznaniya. Akadcndya nauk* SSSR, **1,** 440–455; and *Istoria estestvoznaniya. Bibliografichesky ukazatel, Literatura, opublikovannaya v SSSR (1917–1948)* (“History of Natural Science. Bibliography Literature Published in the U.S.S.R. 1917 1948”; Moscow-Leningrad, 1949).

A. P. Youschkevitch

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**Soviet Literature on Newton**