first-orderadj.

Brit.

/ˌfəːs(t)ˈɔːdə/, U.S.

/ˌfərs(t)ˈɔrdər/

Origin: Formed within English, by compounding. Etymons: first adj., order n.

Etymology: < first adj. + order n.

1. Designating a Fresnel lens in the first of a series of orders based on their focal length and size; (of a lighthouse) employing such a lens.Fresnel used four orders in his classification; more were added later. A first-order lens originally corresponded to the largest focal length, 92 cm (approx. 36 inches).

ΘΚΠ

the world > physical sensation > sight and vision > optical instruments > lens > [adjective] > types of lenses

convex?a1560

planoconvex1665

concavo-convex1677

convexo-concave1693

strong1732

aplanatic1799

periscopic1803

omphaloptic1819

polyzonal1823

shallow1837

first-order1846

periscopical1846

orthoscopic1853

rectilinear1874

overcorrected1875

sphero-cylindrical1881

wide-aperture1882

afocal1887

apochromatic1887

anastigmatic1890

telecentric1892

photovisual1899

aspherical1922

aspheric1923

multifocal1928

plano1944

demagnifying1959

1846 Rep. Secretary of Treasury Improvem. Light-house Syst. in Public Documents U.S. Senate (29th Congress 1st Sess.) IX. No. 488. 73 A first order dioptric light has been seen fifty miles very often, and one of the fourth order as far as 16 miles.

1852 M. Faraday Let. 9 Nov. in Corr. (1996) IV. 441 Your note seems to me to imply that you think that one first order lens sends forward as much light as ten lamps & reflectors.

1912 L. J. Vance Destroying Angel xvi A light-house—probably a first-order light—with its characteristic flash, not duplicated anywhere along this section of the Atlantic coast.

2004 World Archaeol. 36 581 As of 1896..France had electrified about one-third of its first-order lighthouses—these were the brightest lights, spaced widely along the coast at prominent locations.

2. Surveying. Designating the set of largest triangles in a triangulation network; defining or based on such triangles.

ΘΚΠ

the world > the earth > earth sciences > geography > map-making > surveying > [adjective] > specific orders of triangulation

principal1790

secondary1790

tertiary1851

first-order1863

primary1920

1863 in Rep. Superintendent Coast Surv. (U.S. House of Representatives 38th Congress 1st Session) (1864) 20 The secondary work was kept in connexion with the primary triangulation by taking in the first order stations Howard, Trescott Rock, and Chamcook.

1927 Sixth Ann. Rep. Bureau of Budget (U.S.) 138 A new theodolite for first order triangulation has been designed and constructed.

1991 Land Subsidence (Proc. 4th Internat. Symp. Land Subsidence) iv. 254 Horizontal wing points are located on the ground and field tied by first-order triangulation.

2000 D. R. Headrick When Information came of Age iv. 101 Surveyors had to fill in the first-order triangles with second- and third-order ones and then add paths, rivers, buildings, hills, and myriad other details.

3. Mathematics and Science. Having a numerical order of one; spec. designating mathematical equations involving only the first power of the independent variable or only the first derivative of a function.

ΚΠ

1897 R. H. Smith Calculus for Engineers & Physicists i. x. 130 This again is a first- order equation between X and x.

1904 London, Edinb., & Dublin Philos. Mag. 6th Ser. 7 460 The first-order spectrum of a Rowland's grating.

1936 S. Glasstone Recent Adv. Gen. Chem. vii. 271 When the equation k = Ze^−E/RT is applied to first-order reactions, it is found that the observed velocity constant is invariably greater than the calculated value.

1957 L. Fox Numerical Solution Two-point Boundary Probl. v. 106 First-order equations are generally amenable only to step-by-step methods.

1970 Nature 12 Dec. 1031/2 The reaction follows first-order kinetics.

1998 C. Suryanarayana & M. G. Norton X-Ray Diffraction i. i. 52 A first-order reflection occurs when n = 1 and the scattered and incident waves have a path difference of one wavelength.

2010 M. M. Domach Introd. Biomed. Engin. (ed. 2) xiii. 260 Equations that correspond to the general form are called first-order linear differential equations.

a. Logic and Philosophy. Of a proposition, statement, etc.: belonging to a basic level or type in so far as it is itself the object of higher-level investigation or discourse; (hence) referring directly to the world rather than to the propositions, concepts, etc., which refer to the world.

ΚΠ

1908 B. Russell in Amer. Jrnl. Math. 30 238 Elementary propositions together with such as contain only individuals as apparent variables we will call first-order propositions... We can thus form new propositions in which first-order propositions occur as apparent variables. These we will call second-order propositions... Thus, e.g., if Epimenides asserts ‘all first-order propositions affirmed by me are false’, he asserts a second-order proposition.

1936 Mind 45 171 The difference between a first-order proposition and a second-order proposition (or proposition of second intention)..is that the former says something about the realm of facts, while the latter says something about ‘propositions’.

1971 Sci. Amer. Aug. 98/1 All the axioms of a complete ordered field are first-order sentences except for the completion axiom.., which talks about a property of all subsets.

1993 R. Nozick Nature of Rationality v. 142 An addict who desires not to desire heroin may know that he cannot feasibly obliterate his first-order desire for heroin, and thus know that the only way to resolve the conflict of preferences is to drop his second-order desire not to have that first-order desire.

2003 N. Everitt Non-existence of God iii. 54 To say ‘The woman in the corner is wise’ is a first order statement, since it attributes a property (wisdom) to an object (the woman in the corner). But to say ‘There is a woman in the corner’ is a second order statement since it is not about an object (a woman) but about a concept. It says ‘The concept woman in the corner has at least one instance’.

b. In extended use.

ΚΠ

1941 J. S. Huxley Uniqueness of Man xi. 245 Cells are first-order individuals, bodies second-order ones, and human societies (like hydroid colonies or beehives) third-order ones.

1991 N.Y. Rev. Bks. 14 Feb. 49/1 It is teaching about teaching rather than teaching about first-order subject matter.

1993 C. Tilley Interpretative Archaeol. 13 A lived first-order narrative readily translates into the second-order discursive narrative.

2011 D. W. Surry et al. Technol. Integration in Higher Educ. i. i. 3 The most basic first order question that colleges and universities should ask is what technology options are available.

This entry has been updated (OED Third Edition, September 2014; most recently modified version published online March 2022).

单词	first-order
释义	first-orderadj. Brit. /ˌfəːs(t)ˈɔːdə/, U.S. /ˌfərs(t)ˈɔrdər/ Origin: Formed within English, by compounding. Etymons: first adj., order n. Etymology: < first adj. + order n. 1. Designating a Fresnel lens in the first of a series of orders based on their focal length and size; (of a lighthouse) employing such a lens.Fresnel used four orders in his classification; more were added later. A first-order lens originally corresponded to the largest focal length, 92 cm (approx. 36 inches). ΘΚΠ the world > physical sensation > sight and vision > optical instruments > lens > [adjective] > types of lenses convex?a1560 planoconvex1665 concavo-convex1677 convexo-concave1693 strong1732 aplanatic1799 periscopic1803 omphaloptic1819 polyzonal1823 shallow1837 first-order1846 periscopical1846 orthoscopic1853 rectilinear1874 overcorrected1875 sphero-cylindrical1881 wide-aperture1882 afocal1887 apochromatic1887 anastigmatic1890 telecentric1892 photovisual1899 aspherical1922 aspheric1923 multifocal1928 plano1944 demagnifying1959 1846 Rep. Secretary of Treasury Improvem. Light-house Syst. in Public Documents U.S. Senate (29th Congress 1st Sess.) IX. No. 488. 73 A first order dioptric light has been seen fifty miles very often, and one of the fourth order as far as 16 miles. 1852 M. Faraday Let. 9 Nov. in Corr. (1996) IV. 441 Your note seems to me to imply that you think that one first order lens sends forward as much light as ten lamps & reflectors. 1912 L. J. Vance Destroying Angel xvi A light-house—probably a first-order light—with its characteristic flash, not duplicated anywhere along this section of the Atlantic coast. 2004 World Archaeol. 36 581 As of 1896..France had electrified about one-third of its first-order lighthouses—these were the brightest lights, spaced widely along the coast at prominent locations. 2. Surveying. Designating the set of largest triangles in a triangulation network; defining or based on such triangles. ΘΚΠ the world > the earth > earth sciences > geography > map-making > surveying > [adjective] > specific orders of triangulation principal1790 secondary1790 tertiary1851 first-order1863 primary1920 1863 in Rep. Superintendent Coast Surv. (U.S. House of Representatives 38th Congress 1st Session) (1864) 20 The secondary work was kept in connexion with the primary triangulation by taking in the first order stations Howard, Trescott Rock, and Chamcook. 1927 Sixth Ann. Rep. Bureau of Budget (U.S.) 138 A new theodolite for first order triangulation has been designed and constructed. 1991 Land Subsidence (Proc. 4th Internat. Symp. Land Subsidence) iv. 254 Horizontal wing points are located on the ground and field tied by first-order triangulation. 2000 D. R. Headrick When Information came of Age iv. 101 Surveyors had to fill in the first-order triangles with second- and third-order ones and then add paths, rivers, buildings, hills, and myriad other details. 3. Mathematics and Science. Having a numerical order of one; spec. designating mathematical equations involving only the first power of the independent variable or only the first derivative of a function. ΚΠ 1897 R. H. Smith Calculus for Engineers & Physicists i. x. 130 This again is a first- order equation between X and x. 1904 London, Edinb., & Dublin Philos. Mag. 6th Ser. 7 460 The first-order spectrum of a Rowland's grating. 1936 S. Glasstone Recent Adv. Gen. Chem. vii. 271 When the equation k = Ze^−E/RT is applied to first-order reactions, it is found that the observed velocity constant is invariably greater than the calculated value. 1957 L. Fox Numerical Solution Two-point Boundary Probl. v. 106 First-order equations are generally amenable only to step-by-step methods. 1970 Nature 12 Dec. 1031/2 The reaction follows first-order kinetics. 1998 C. Suryanarayana & M. G. Norton X-Ray Diffraction i. i. 52 A first-order reflection occurs when n = 1 and the scattered and incident waves have a path difference of one wavelength. 2010 M. M. Domach Introd. Biomed. Engin. (ed. 2) xiii. 260 Equations that correspond to the general form are called first-order linear differential equations. 4. a. Logic and Philosophy. Of a proposition, statement, etc.: belonging to a basic level or type in so far as it is itself the object of higher-level investigation or discourse; (hence) referring directly to the world rather than to the propositions, concepts, etc., which refer to the world. ΚΠ 1908 B. Russell in Amer. Jrnl. Math. 30 238 Elementary propositions together with such as contain only individuals as apparent variables we will call first-order propositions... We can thus form new propositions in which first-order propositions occur as apparent variables. These we will call second-order propositions... Thus, e.g., if Epimenides asserts ‘all first-order propositions affirmed by me are false’, he asserts a second-order proposition. 1936 Mind 45 171 The difference between a first-order proposition and a second-order proposition (or proposition of second intention)..is that the former says something about the realm of facts, while the latter says something about ‘propositions’. 1971 Sci. Amer. Aug. 98/1 All the axioms of a complete ordered field are first-order sentences except for the completion axiom.., which talks about a property of all subsets. 1993 R. Nozick Nature of Rationality v. 142 An addict who desires not to desire heroin may know that he cannot feasibly obliterate his first-order desire for heroin, and thus know that the only way to resolve the conflict of preferences is to drop his second-order desire not to have that first-order desire. 2003 N. Everitt Non-existence of God iii. 54 To say ‘The woman in the corner is wise’ is a first order statement, since it attributes a property (wisdom) to an object (the woman in the corner). But to say ‘There is a woman in the corner’ is a second order statement since it is not about an object (a woman) but about a concept. It says ‘The concept woman in the corner has at least one instance’. b. In extended use. ΚΠ 1941 J. S. Huxley Uniqueness of Man xi. 245 Cells are first-order individuals, bodies second-order ones, and human societies (like hydroid colonies or beehives) third-order ones. 1991 N.Y. Rev. Bks. 14 Feb. 49/1 It is teaching about teaching rather than teaching about first-order subject matter. 1993 C. Tilley Interpretative Archaeol. 13 A lived first-order narrative readily translates into the second-order discursive narrative. 2011 D. W. Surry et al. Technol. Integration in Higher Educ. i. i. 3 The most basic first order question that colleges and universities should ask is what technology options are available. This entry has been updated (OED Third Edition, September 2014; most recently modified version published online March 2022). < adj.1846
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