英语词汇“prime ratio”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

prime ratio n. [after post-classical Latin prima ratio (1704 in the passage translated in quot. 1710); compare ultimate ratio at ultimate adj. 3c] Mathematics (now historical) (in Newton's theory of fluxions) the ratio of the infinitesimal increments of two variable quantities as they recede from particular values; the rate of change of one variable with respect to another (cf. ultimate ratio at ultimate adj. 3c); method of prime and ultimate ratios = doctrine (also method) of limits n. at limit n. Phrases 2.

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1710 J. Harris tr. I. Newton Introd. Quadrature Curves in Lexicon Technicum II. at Quadrature Fluxions are very nearly as the Augments of the Fluents, generated in equal, but infinitely small parts of Time; and to speak exactly, are in the Prime Ratio [L. prima ratione] of the nascent Augments.

1728 H. Pemberton View Sir I. Newton's Philos. iii. 129 A method of reasoning, which Sir Isaac Newton makes great use of, and which he introduced into geometry, thereby greatly inriching that science..[etc.]. (Note viz. His doctrine of prime and ultimate ratios.)

1745 J. Stewart tr. I. Newton Treat. Quadrature Curves in Two Treat. Quadrature & Anal. Equations Explained 4 By like ways of reasoning, the Fluxions of Lines, whether right or curve in all Cases, as likewise the Fluxions of Superficies's, Angles and other Quantities, may be collected by the Method of prime and ultimate Ratios.

1842 W. T. Brande Dict. Sci., Lit. & Art 974/2 They are called prime ratios, or ultimate ratios, according as the ratios of the variables are considered as receding from, or approaching to, the ratios of the limits.

1972 M. Kline Math. Thought xvii. 364 The rate of change of y with respect to x is nxⁿ¹. This is the prime ratio of the nascent increments.

单词	prime ratio
释义	> as lemmas prime ratio prime ratio n. [after post-classical Latin prima ratio (1704 in the passage translated in quot. 1710); compare ultimate ratio at ultimate adj. 3c] Mathematics (now historical) (in Newton's theory of fluxions) the ratio of the infinitesimal increments of two variable quantities as they recede from particular values; the rate of change of one variable with respect to another (cf. ultimate ratio at ultimate adj. 3c); method of prime and ultimate ratios = doctrine (also method) of limits n. at limit n. Phrases 2. ΚΠ 1710 J. Harris tr. I. Newton Introd. Quadrature Curves in Lexicon Technicum II. at Quadrature Fluxions are very nearly as the Augments of the Fluents, generated in equal, but infinitely small parts of Time; and to speak exactly, are in the Prime Ratio [L. prima ratione] of the nascent Augments. 1728 H. Pemberton View Sir I. Newton's Philos. iii. 129 A method of reasoning, which Sir Isaac Newton makes great use of, and which he introduced into geometry, thereby greatly inriching that science..[etc.]. (Note viz. His doctrine of prime and ultimate ratios.) 1745 J. Stewart tr. I. Newton Treat. Quadrature Curves in Two Treat. Quadrature & Anal. Equations Explained 4 By like ways of reasoning, the Fluxions of Lines, whether right or curve in all Cases, as likewise the Fluxions of Superficies's, Angles and other Quantities, may be collected by the Method of prime and ultimate Ratios. 1842 W. T. Brande Dict. Sci., Lit. & Art 974/2 They are called prime ratios, or ultimate ratios, according as the ratios of the variables are considered as receding from, or approaching to, the ratios of the limits. 1972 M. Kline Math. Thought xvii. 364 The rate of change of y with respect to x is nxⁿ¹. This is the prime ratio of the nascent increments. extracted from primeadj.int.adv. < as lemmas
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