parabolan.

Brit.

/pəˈrabələ/,

/pəˈrabl̩ə/, U.S.

/pəˈræbələ/

Origin: A borrowing from Latin. Etymon: Latin parabola.

Etymology: < post-classical Latin parabola (16th cent. (see below); also parabole ) < ancient Greek παραβολή juxtaposition, application, specifically in Geometry, the ‘application’ of a given area to a given straight line, hence also, the curve described below, specific application of παραβολή parable n. With the rhetorical sense compare use of classical Latin parabola and ancient Greek παραβολή in sense ‘comparison, illustration’ in a rhetorical context in Quintilian and Aristotle respectively. Compare Middle French, French parabole (1555 in geometry; 1727 designating a curving trajectory; compare sense 1c), Italian parabola (1556 as parabole ), Spanish parábola (1567 in geometry), German Parabel (1525 or earlier). Compare earlier parabolic adj.To the earlier Greek geometers, including Archimedes (c287–212 b.c.), who investigated only sections perpendicular to the surface of the cone, the parabola was known as ὀρθογωνίου κώνου τομή (sectio rectanguli coni) ‘the [perpendicular] section of a right-angled cone’. The use of παραβολή, ‘application’, in this sense is due to Apollonius of Perga, c210 b.c., and with him referred to the fact that a rectangle bounded by the abscissa and the latus rectum has an area equal to that of a square on the ordinate, without either excess (as in the hyperbola) or deficiency (as in the ellipse) (see C. Taylor Introd. Anc. & Mod. Geom. Conics (1881) pp. xliii, 82; T. L. Heath Apollonius of Perga's Treat. Conic Sections (1896) p. lxxx). But an alternative explanation of the name, from the much more obvious property of the parallelism of the section to a side of the cone, is given by Eutokius of Ascalon c a.d. 550, and is frequent in later writers. Compare:1544 Archimedis Opera 142 (heading) Archimedis qvadratvra parabolæ, id est portionis contentæ a linea recta & sectione rectanguli coni.1558 F. Commandino tr. Archimedes Opera f. 18^v, (heading) Archimedis qvadratvra paraboles.

a. Mathematics. A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side; the curve traced by a point whose distance from a given point (the focus) is equal to its distance from a given straight line (the directrix); a curve that is the graph of an equation of the type y² = 2px, or y = ax², where p and a are constants. Also more fully (now historical) Apollonian parabola (see Apollonian adj. 2).All three definitions are equivalent. The path of a projectile under the influence of gravity follows a curve of approximately this shape. The parabola is one of the conic sections, along with the circle, ellipse, and hyperbola.biquadratic, helicoid parabola: see the first element.

ΘΚΠ

the world > relative properties > number > geometry > curve > [noun] > conic section > parabola

parabola1559

parabolic1657

parabole1676

1559 P. Morwyng tr. C. Gesner Treasure of Euonymus 71 A parabolæ is a deuision of a Geometrical figure, called conus [L. parabola conifectio].

1579 L. Digges & T. Digges Stratioticos 188 I demaunde whether then this Eleipsis shal not make an Angle with the Parabola Section equal to the distaunce betweene the grade of Randon proponed, and the grade of vttermost Randon.

1656 T. Hobbes Six Lessons Ep. Ded. in Elements Philos. I have exhibited and demonstrated the proportion of the Parabola and Parabolasters to the Parallelograms of the same height and base.

1696 W. Whiston New Theory of Earth i. 13 The Orbits describ'd will be one of the other Conick Sections, either Parabola's or Hyperbola's.

1704 J. Harris Lexicon Technicum I Helicoid Parabola, or the Parabolick Spiral, is a Curve which arises from the Supposition of the Axis of the common Apollonian Parabola's being bent round into the Periphery of a Circle.

1706 W. Jones Synopsis Palmariorum Matheseos 246 'Tis evident the Parabola has but one Focus.

1760 L. Sterne Life Tristram Shandy II. iii. 22 He found the precise path to be a Parabola,—or else an Hyperbola.

1828 O. Gregory Hutton's Course Math. (ed. 9) II. 136 The Area or Space of a Parabola, is equal to Two-Thirds of its Circumscribing Parallelogram.

1868 J. N. Lockyer Elem. Lessons Astron. (1870) xxiii. 124 The orbit of a comet is generally best represented by what is called a parabola; that is, an infinitely long ellipse.

1935 C. J. Smith Intermediate Physics (ed. 2) v. xlvi. 769 For most pure metals the curve showing the variation of resistance with temperature measured on the gas scale is almost a perfect parabola.

1993 Math. Rev. 93 M. 6499/2 The turning rule and moving curve procedure which Descartes applies to the Apollonian parabola to obtain his ‘Cartesian parabola’.

b. Mathematics. More widely: a plane curve resembling a parabola in having branches which do not tend towards asymptotes, and represented by an equation analogous to that of the common parabola. Chiefly with distinguishing word.cubical parabola: see cubical adj.

ΘΚΠ

the world > relative properties > number > geometry > curve > [noun] > conic section > parabola > resembling

parabolaster1656

paraboloid1656

parabola1664

1664 Philos. Trans. (Royal Soc.) 1 15 A Method for the Quadrature of Parabola's of all degrees.

1728 E. Chambers Cycl. (at cited word) Parabola's of the higher Kinds are Algebraic Curves, defin'd by a^{m − 1}x = y^m... Some call these Paraboloides.

1765 T. H. Croker et al. Compl. Dict. Arts & Sci. II. (at cited word) Cartesian Parabola.

1795 C. Hutton Math. & Philos. Dict. II. 192 A bell-form Parabola, with a conjugate point.

1836 Philos. Trans. (Royal Soc.) 126 202 A new and interesting property of the cubic parabola.

1873 B. Williamson Elem. Treat. Differential Calculus (ed. 2) xviii. §252 The curve y² = x² (x−a)..is a cubical parabola having a conjugate point.

1921 Amer. Math. Monthly 28 253 We refer the cubical parabola to an equilateral triangle of reference.

1959 G. James & R. C. James Math. Dict. (ed. 2) 279/1 The cubical and semicubical parabolas are not parabolas.

1991 C. B. Boyer & U. C. Merzbach Hist. Math. (ed. 2) xviii. 378 Of all Fermat's discoveries in mathematics it was only the rectification of the semicubical parabola, usually known as Neil's parabola, that was published by him.

c. In extended use and figurative. Any similar (actual or notional) curve, esp. one described by something moving through time or space; a curving trajectory, an arc.

ΚΠ

1841 R. W. Emerson Ess. 1st Ser. (Boston ed.) xi. 281 Year after year our tables get no completeness, and at last we discover that our curve is a parabola, whose arcs will never meet.

1874 T. Hardy Far from Madding Crowd II. xvi. 193 The base of the liquid parabola [sc. of rainwater] has come forward from the wall, has advanced over the plinth mouldings..into the midst of Fanny Robin's grave.

1922 D. H. Lawrence in Eng. Rev. Nov. 381 A circle swoop, and a quick parabola under the bridge arches.

1967 J. A. Barker Peregrine iii. 144 He..skimmed over the boundary poplars, curved down in a tremendous wing-lit parabola.

1974 Times Lit. Suppl. 8 Feb. 138/5 Its publication is valuable in adding to the repertoire of African drama and in completing the parabola of Soyinka's development over fifteen astonishing years.

1993 Classic CD June 57/1 Just listen to the galactic phrasing in the Song of the Priestess of Apollo—especially the graceful parabola on the word ‘Säulenhalle’.

2. Rhetoric. A figure of speech expressing a comparison drawn between two things or facts, a simile; metaphorical speech. Now rare.

ΘΚΠ

society > leisure > the arts > literature > style of language or writing > figure of speech > figures of meaning > [noun] > simile

ylikenessOE

likenessc1175

comparisona1382

similec1400

similitudec1400

resemblancec1405

analogya1536

likening1573

parabola1577

icon1589

parabole1828

1577 H. Peacham Garden of Eloquence sig. Uii Parabola, is a similitude taken of those thinges which are done, or of those which are ioyned to thinges by nature or hap.

1589 G. Puttenham Arte Eng. Poesie iii. xix. 205 The Greekes call it Parabola, which terme is also by custome accepted of vs: neuerthelesse we may call him in English the resemblance misticall.

1678 E. Phillips New World of Words (new ed.) Parabola, a Similitude of a thing: In Rhetorick it is a similitudinary speech whereby one thing is uttered and another signified; as in this Example; ‘As Cedars beaten with continual storms, so great men flourish’.

1996 Representations 53 88 The German metaphor for ‘the meaning is obvious’ becomes a parabola, a didactic anecdote that illuminates a truth about human nature.

This entry has been updated (OED Third Edition, June 2005; most recently modified version published online March 2022).

单词	parabola
释义	parabolan. Brit. /pəˈrabələ/, /pəˈrabl̩ə/, U.S. /pəˈræbələ/ Origin: A borrowing from Latin. Etymon: Latin parabola. Etymology: < post-classical Latin parabola (16th cent. (see below); also parabole ) < ancient Greek παραβολή juxtaposition, application, specifically in Geometry, the ‘application’ of a given area to a given straight line, hence also, the curve described below, specific application of παραβολή parable n. With the rhetorical sense compare use of classical Latin parabola and ancient Greek παραβολή in sense ‘comparison, illustration’ in a rhetorical context in Quintilian and Aristotle respectively. Compare Middle French, French parabole (1555 in geometry; 1727 designating a curving trajectory; compare sense 1c), Italian parabola (1556 as parabole ), Spanish parábola (1567 in geometry), German Parabel (1525 or earlier). Compare earlier parabolic adj.To the earlier Greek geometers, including Archimedes (c287–212 b.c.), who investigated only sections perpendicular to the surface of the cone, the parabola was known as ὀρθογωνίου κώνου τομή (sectio rectanguli coni) ‘the [perpendicular] section of a right-angled cone’. The use of παραβολή, ‘application’, in this sense is due to Apollonius of Perga, c210 b.c., and with him referred to the fact that a rectangle bounded by the abscissa and the latus rectum has an area equal to that of a square on the ordinate, without either excess (as in the hyperbola) or deficiency (as in the ellipse) (see C. Taylor Introd. Anc. & Mod. Geom. Conics (1881) pp. xliii, 82; T. L. Heath Apollonius of Perga's Treat. Conic Sections (1896) p. lxxx). But an alternative explanation of the name, from the much more obvious property of the parallelism of the section to a side of the cone, is given by Eutokius of Ascalon c a.d. 550, and is frequent in later writers. Compare:1544 Archimedis Opera 142 (heading) Archimedis qvadratvra parabolæ, id est portionis contentæ a linea recta & sectione rectanguli coni.1558 F. Commandino tr. Archimedes Opera f. 18^v, (heading) Archimedis qvadratvra paraboles. 1. a. Mathematics. A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side; the curve traced by a point whose distance from a given point (the focus) is equal to its distance from a given straight line (the directrix); a curve that is the graph of an equation of the type y² = 2px, or y = ax², where p and a are constants. Also more fully (now historical) Apollonian parabola (see Apollonian adj. 2).All three definitions are equivalent. The path of a projectile under the influence of gravity follows a curve of approximately this shape. The parabola is one of the conic sections, along with the circle, ellipse, and hyperbola.biquadratic, helicoid parabola: see the first element. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > conic section > parabola parabola1559 parabolic1657 parabole1676 1559 P. Morwyng tr. C. Gesner Treasure of Euonymus 71 A parabolæ is a deuision of a Geometrical figure, called conus [L. parabola conifectio]. 1579 L. Digges & T. Digges Stratioticos 188 I demaunde whether then this Eleipsis shal not make an Angle with the Parabola Section equal to the distaunce betweene the grade of Randon proponed, and the grade of vttermost Randon. 1656 T. Hobbes Six Lessons Ep. Ded. in Elements Philos. I have exhibited and demonstrated the proportion of the Parabola and Parabolasters to the Parallelograms of the same height and base. 1696 W. Whiston New Theory of Earth i. 13 The Orbits describ'd will be one of the other Conick Sections, either Parabola's or Hyperbola's. 1704 J. Harris Lexicon Technicum I Helicoid Parabola, or the Parabolick Spiral, is a Curve which arises from the Supposition of the Axis of the common Apollonian Parabola's being bent round into the Periphery of a Circle. 1706 W. Jones Synopsis Palmariorum Matheseos 246 'Tis evident the Parabola has but one Focus. 1760 L. Sterne Life Tristram Shandy II. iii. 22 He found the precise path to be a Parabola,—or else an Hyperbola. 1828 O. Gregory Hutton's Course Math. (ed. 9) II. 136 The Area or Space of a Parabola, is equal to Two-Thirds of its Circumscribing Parallelogram. 1868 J. N. Lockyer Elem. Lessons Astron. (1870) xxiii. 124 The orbit of a comet is generally best represented by what is called a parabola; that is, an infinitely long ellipse. 1935 C. J. Smith Intermediate Physics (ed. 2) v. xlvi. 769 For most pure metals the curve showing the variation of resistance with temperature measured on the gas scale is almost a perfect parabola. 1993 Math. Rev. 93 M. 6499/2 The turning rule and moving curve procedure which Descartes applies to the Apollonian parabola to obtain his ‘Cartesian parabola’. b. Mathematics. More widely: a plane curve resembling a parabola in having branches which do not tend towards asymptotes, and represented by an equation analogous to that of the common parabola. Chiefly with distinguishing word.cubical parabola: see cubical adj. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > conic section > parabola > resembling parabolaster1656 paraboloid1656 parabola1664 1664 Philos. Trans. (Royal Soc.) 1 15 A Method for the Quadrature of Parabola's of all degrees. 1728 E. Chambers Cycl. (at cited word) Parabola's of the higher Kinds are Algebraic Curves, defin'd by a^{m − 1}x = y^m... Some call these Paraboloides. 1765 T. H. Croker et al. Compl. Dict. Arts & Sci. II. (at cited word) Cartesian Parabola. 1795 C. Hutton Math. & Philos. Dict. II. 192 A bell-form Parabola, with a conjugate point. 1836 Philos. Trans. (Royal Soc.) 126 202 A new and interesting property of the cubic parabola. 1873 B. Williamson Elem. Treat. Differential Calculus (ed. 2) xviii. §252 The curve y² = x² (x−a)..is a cubical parabola having a conjugate point. 1921 Amer. Math. Monthly 28 253 We refer the cubical parabola to an equilateral triangle of reference. 1959 G. James & R. C. James Math. Dict. (ed. 2) 279/1 The cubical and semicubical parabolas are not parabolas. 1991 C. B. Boyer & U. C. Merzbach Hist. Math. (ed. 2) xviii. 378 Of all Fermat's discoveries in mathematics it was only the rectification of the semicubical parabola, usually known as Neil's parabola, that was published by him. c. In extended use and figurative. Any similar (actual or notional) curve, esp. one described by something moving through time or space; a curving trajectory, an arc. ΚΠ 1841 R. W. Emerson Ess. 1st Ser. (Boston ed.) xi. 281 Year after year our tables get no completeness, and at last we discover that our curve is a parabola, whose arcs will never meet. 1874 T. Hardy Far from Madding Crowd II. xvi. 193 The base of the liquid parabola [sc. of rainwater] has come forward from the wall, has advanced over the plinth mouldings..into the midst of Fanny Robin's grave. 1922 D. H. Lawrence in Eng. Rev. Nov. 381 A circle swoop, and a quick parabola under the bridge arches. 1967 J. A. Barker Peregrine iii. 144 He..skimmed over the boundary poplars, curved down in a tremendous wing-lit parabola. 1974 Times Lit. Suppl. 8 Feb. 138/5 Its publication is valuable in adding to the repertoire of African drama and in completing the parabola of Soyinka's development over fifteen astonishing years. 1993 Classic CD June 57/1 Just listen to the galactic phrasing in the Song of the Priestess of Apollo—especially the graceful parabola on the word ‘Säulenhalle’. 2. Rhetoric. A figure of speech expressing a comparison drawn between two things or facts, a simile; metaphorical speech. Now rare. ΘΚΠ society > leisure > the arts > literature > style of language or writing > figure of speech > figures of meaning > [noun] > simile ylikenessOE likenessc1175 comparisona1382 similec1400 similitudec1400 resemblancec1405 analogya1536 likening1573 parabola1577 icon1589 parabole1828 1577 H. Peacham Garden of Eloquence sig. Uii Parabola, is a similitude taken of those thinges which are done, or of those which are ioyned to thinges by nature or hap. 1589 G. Puttenham Arte Eng. Poesie iii. xix. 205 The Greekes call it Parabola, which terme is also by custome accepted of vs: neuerthelesse we may call him in English the resemblance misticall. 1678 E. Phillips New World of Words (new ed.) Parabola, a Similitude of a thing: In Rhetorick it is a similitudinary speech whereby one thing is uttered and another signified; as in this Example; ‘As Cedars beaten with continual storms, so great men flourish’. 1996 Representations 53 88 The German metaphor for ‘the meaning is obvious’ becomes a parabola, a didactic anecdote that illuminates a truth about human nature. This entry has been updated (OED Third Edition, June 2005; most recently modified version published online March 2022). < n.1559
随便看	the genies the gentle art the gentle craft the gentle sex the gentlelady from the gentleman from the gentleman in black the gentleman in black velvet the gentleman in brown velvet the gentleman in velvet the gentleman who pays the rent the gentlemen's the gentler sex the gentlewoman from the genuine article the genuine quill the genus homo the geography the geography of the house the ghats the ghost of a chance the ghost of a person's former self the ghost of a person'thing's former self the ghost of —— past the ghost of —— present