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NEWTON, ISAAC (b. Woolsthorpe, England,
25 December 1642; d. London, England, 20 March
1727), mathematics, dynamics, celestial mechanics,
astronomy, optics, natural philosophy.
NOTES
quantities. In the eighteenth century, many English
mathematicians, according to Boyer, “began to associate
fluxions with the infinitely small differentials of Leibniz.”
53. University Library, Cambridge, MS Add. 3960, fol. 177.
Newton, however, was not the first mathematician to
anticipate the Taylor series.
54. Introduction to De quadratura, in John Stewart, trans.,
Two Treatises of the Quadrature of Curves, and Analysis by
Equations of an Infinite Number of Terms . . . (London,
1745), p. 4.
55. Philosophical Transactions, no. 342 (1715), 206.
56. Attributed to Newton, May 1708, in W. G. Hiscock, ed.,
David Gregory, Isaac Newton and Their Circle (Oxford,
1937), p. 42.
57. Henry Pemberton recorded, in his preface to his View of . . .
Newton's Philosophy (London, 1728), that “I have often
heard him censure the handling [of] geometrical subjects by
algebraic calculations; and his book of Algebra he called
by the name of Universal Arithmetic, in opposition to the
injudicious title of Geometry, which Des Cartes had given
to the treatise wherein he shews, how the geometer may
assist his invention by such kind of computations.”
58. There were five Latin eds. between 1707 and 1761, of which
one was supervised by Newton, and three English eds.
between 1720 and 1769.
59. For details, see Turnbull, The Mathematical Discoveries
of Newton, pp. 49-50.
60. See C. B. Boyer, History of Mathematics, p. 450.
61. Arithmetica universalis, English ed. (London, 1728),
p. 247; see Whiteside, Mathematical Papers, V, 428-429,
470-471.
62. Arithmetica universalis, in Whiteside's translation,
Mathematical
Papers, V, 477.
63. Published by Whiteside, Mathematical Papers, I, pp. 145
ff.
64. See especially ibid., pp. 298 ff., pt. 2, sec. 5, “The
Calculus
Becomes an Algorithm.”
65. Ibid., III, pp. 120 ff.
66. Ibid.
67. In “Newton as an Originator of Polar Coördinates,”
in
American Mathematical Monthly, 56 (1949), 73-78.
68. Made available in English translation (perhaps supervised
by Newton himself) in John Harris, Lexicon technicum,
vol. II (London, 1710); reprinted in facsimile (New
York, 1966). The essay entitled “Curves” is reprinted in
Whiteside, Mathematical Papers, II.
69. C. R. M. Talbot, ed. and trans., Enumeration of Lines
of the Third Order (London, 1860), p. 72.
70. On other aspects of Newton's mathematics see Whiteside,
Mathematical Papers, specifically III, 50-52, on the
development of infinite series; II, 218-232, on an iterative
procedure for finding approximate solutions to equations;
and I, 519, and V, 360, on “Newton's identities” for
finding the sums of the powers of the roots in any polynomial
equation. See, additionally, for Newton's contributions
in porisms, solid loci, number theory, trigonometry,
and interpolation, among other topics, Whiteside,
Mathematical Papers, passim, and Turnbull, Mathematical
Discoveries.
71. See Whiteside, Mathematical Works, I, XV, and Boyer,
History of Mathematics, p. 448. Drafts of the “Liber
geometria” are University Library, Cambridge, MS
Add. 3963 passim and MS Add. 4004, fols. 129-159.
Gregory's comprehensive statement of Newton's plans
as of summer 1694 is in Edinburgh University Library,
David Gregory MS C42; an English version in Newton's
Correspondence, III, 384-386, is not entirely satisfactory.
72. Newton's laconic statement of his solution, published
anonymously in Philosophical Transactions, no. 224
(1697), p. 384, elicited from Bernoulli the reply “Ex ungue,
Leonem” (the claw was sufficient to reveal the lion); see
Histoire des ouvrages des savans (1697), 454-455.
73. See I. B. Cohen, “Isaac Newton, John Craig, and the
Design of Ships,” in Boston Studies for the Philosophy of
Science (in press).
74. Even the variants in the eds. of the Opticks have never
been fully documented in print (although Horsley's ed.
gives such information for the Queries), nor have the
differences between the Latin and English versions been
fully analyzed. Zev Bechler is in the process of publishing
four studies based on a perceptive and extensive examination
of Newton's optical MSS. Henry Guerlac is presently
engaged in preparing a new ed. of the Opticks itself.
75. The expression “experimentum crucis” is often attributed
to Bacon, but Newton in fact encountered it in Hooke's
account of his optical experiments as given in Micrographia
(observation 9), where Hooke referred to an
experiment that “will prove such a one as our thrice
excellent Verulam [that is, Francis Bacon] calls Experimentum
crucis.” While many investigators before Newton—Dietrich
von Freiberg, Marci, Descartes, and Grimaldi
among them—had observed the oval dispersion of a
circular beam of light passing through a prism, they all
tended to assign the cause of the phenomenon to the
consideration that the light source was not a point, but a
physical object, so that light from opposite limbs of the
sun would differ in angle of inclination by as much as
half a degree. Newton's measurements led him from this
initial supposition to the conclusion that the effect—a
spectrum some five times longer than its width—was too
great for the given cause, and therefore the prism must
refract some rays to a considerable degree more than
others.
76. This account of the experiment is greatly simplified, as
was Newton's own account, presented in his letter to
Oldenburg and published in Philosophical Transactions.
See J. A. Lohne, “Experimentum Crucis,” in Notes and
Records. Royal Society of London, 23 (1968), 169-199;
Lohne has traced the variations introduced into both the
later diagrams and descriptions of the experiment.
Newton's doctrine of the separation of white light into
its component colors, each corresponding to a unique and
fixed index of refraction, had been anticipated by Johannes
Marcus Marci de Kronland in his Thaumantias, liber de
arcu coelesti (Prague, 1648). An important analysis of
Newton's experiment is in A. I. Sabra, Theories of Light.
77. See R. S. Westfall, “The Development of Newton's
Theory of Color,” in Isis, 53 (1962), 339-358; and A. R.
Hall, “Newton's Notebook,” pp. 245-250.
78. Dated 13 April 1672, in Philosophical Transactions, no.
84.
79. See R. S. Westfall, “Newton's Reply to Hooke and the
Theory of Colors,” in Isis, 54 (1963), 82-96; an edited
text
of the “Hypothesis” is in Correspondence, I,
362-386.
80. Published in Birch's History of the Royal Society and in
I. B. Cohen, ed., Newton's Papers and Letters.
81. R. S. Westfall has further sketched Newton's changing
views in relation to corpuscles and the ether, and, in “Isaac
Newton's Coloured Circles Twixt Two Contiguous
Glasses,” in Archive for History of Exact Sciences, 2
(1965),
190, has concluded that “When Newton composed the
Opticks, he had ceased to believe in an aether; the pulses
of earlier years became ‘fits of easy reflection and
transmission,’
offered as observed phenomena without explanation.”
Westfall discusses Newton's abandonment of the
ether in “Uneasily Fitful Reflections on Fits of Easy
Transmission [and of Easy Reflection],” in Robert
Palter, ed., The Annus Mirabilis of Sir Isaac Newton
1666-1966, pp. 88-104; he emphasizes the pendulum
experiment that Newton reported from memory in the
Principia (bk. II, scholium at the end of sec. 7, in the first
ed., or of sec. 6, in the 2nd and 3rd eds.). Henry Guerlac
has discussed Newton's return to a modified concept of
the ether in a series of studies (see Bibliography, sec. 8).
82. Birch, History of the Royal Society, III, 299; the early
text of the “Discourse” is III, 247-305, but Newton had
