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单词 leibniz
释义

Leibnizn.

Brit. /ˈlʌɪbnɪts/, /ˈliːbnɪts/, U.S. /ˈlaɪbˌnɪts/
Forms: Also Leibniz.
Etymology: < the name of Gottfried Wilhelm Leibniz, German philosopher and mathematician: see Leibnizian adj. and n.
Philosophy.
Leibniz law n. (also Leibniz's law) the principle of the identity of indiscernibles (see indiscernible adj. 2).
ΘΚΠ
the mind > mental capacity > philosophy > metaphysics > ontology > [noun] > monism > monadism > elements of
monad1692
entelechy1877
Leibniz law1941
1941 O. Helmer tr. A. Tarski Introd. Logic §17. 55 x = y if, and only if, x has every property which y has, and y has every property which x has... [This] was first stated by Leibniz..and hence may be called Leibniz's law.
1965 Philos. Rev. 74 341 Physicalism violates Leibniz' law, which requires that if two things are identical they have all their non-intensional and nonmodal properties in common.
1968 Aristotelian Soc. Suppl. Vol. XLII. 99 Let us consider Leibniz's law firstly as a principle about the identity of individuals.

Draft additions 1997

Leibniz theorem n. Mathematics the theorem that the nth derivative of a product of two functions may be expressed as a sum of products of the derivatives of the individual functions, the coefficients being the same as those occurring in the binomial theorem.
ΘΚΠ
the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem > relating to functions
Taylor's theorem1816
Maclaurin's theorem1820
Leibniz theorem1852
Green's theorem1857
Laurent's theorem1893
factor theorem1894
factor law1901
1852 B. Price Treat. Infinitesimal Calculus I. iii. 85 The following theorem, due to Leibnitz, and commonly called Leibnitz's Theorem, may be conveniently employed to find the general (the rth) derived-function of a product of two functions of x.
1965 Math. Gaz. 49 49 The derivation involved a generalized form of Leibniz's theorem.
1967 Math. Rev. 33 675/1 The Leibniz theorem referred to in the title is Wilson's theorem in the form (p − 2)!  1 (mod p).
This entry has not yet been fully updated (first published 1976; most recently modified version published online March 2022).
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n.1852
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