Newton–Cotesn.

Brit.

/ˌnjuːtnˈkəʊts/, U.S.

/ˈn(j)utnˈkoʊts/

Origin: From proper names. Etymons: proper names Newton, Cotes.

Etymology: < the names of Sir Isaac Newton (see Newtonian adj. and n.) and Roger Cotes (1682–1716), English mathematician: see quot. 1981.

Mathematics.

attributive. Designating or relating to (any of) a class of formulae based on Newton's method which are used to find approximate integrals for functions over a finite range (e.g. Simpson's rule, the three-eighths rule); esp. in Newton–Cotes formula. See Newton n. 1.

ΚΠ

1922 Amer. Math. Monthly 29 184 Expressions are obtained for the errors in the Newton-Cotes method.

1924 E. T. Whittaker & G. Robinson Calculus Observ. vii. 153 Among formulae of the type discussed in the last section, the oldest and best known are the Newton–Cotes formulae.

1957 L. Fox Numerical Solution Two-point Boundary Probl. ii. 31 Other Lagrangian quadrature formula [sic] are those of the Newton–Cotes type, whose most familiar member is that known as Simpson's rule.

1981 Conc. Dict. Sci. Biogr. 172/1 [Roger Cotes'] essay on Newton's differential method describes how, given n points at equidistant abscissae, the area under the curve of the nth degree joining these points may be evaluated. A modernized form of his result is known as the Newton–Cotes formula.

This is a new entry (OED Third Edition, September 2003; most recently modified version published online March 2022).

单词	newton–cotes
释义	Newton–Cotesn. Brit. /ˌnjuːtnˈkəʊts/, U.S. /ˈn(j)utnˈkoʊts/ Origin: From proper names. Etymons: proper names Newton, Cotes. Etymology: < the names of Sir Isaac Newton (see Newtonian adj. and n.) and Roger Cotes (1682–1716), English mathematician: see quot. 1981. Mathematics. attributive. Designating or relating to (any of) a class of formulae based on Newton's method which are used to find approximate integrals for functions over a finite range (e.g. Simpson's rule, the three-eighths rule); esp. in Newton–Cotes formula. See Newton n. 1. ΚΠ 1922 Amer. Math. Monthly 29 184 Expressions are obtained for the errors in the Newton-Cotes method. 1924 E. T. Whittaker & G. Robinson Calculus Observ. vii. 153 Among formulae of the type discussed in the last section, the oldest and best known are the Newton–Cotes formulae. 1957 L. Fox Numerical Solution Two-point Boundary Probl. ii. 31 Other Lagrangian quadrature formula [sic] are those of the Newton–Cotes type, whose most familiar member is that known as Simpson's rule. 1981 Conc. Dict. Sci. Biogr. 172/1 [Roger Cotes'] essay on Newton's differential method describes how, given n points at equidistant abscissae, the area under the curve of the nth degree joining these points may be evaluated. A modernized form of his result is known as the Newton–Cotes formula. This is a new entry (OED Third Edition, September 2003; most recently modified version published online March 2022). < n.1922
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