hyperbolicadj.

/hʌɪpəˈbɒlɪk/

Etymology: < Greek ὑπερβολικός extravagant, < ὑπερβολή hyperbole n.; in sense 2 used as the adjective of hyperbola n. So French hyperbolique in both senses.

1. Rhetoric. = hyperbolical adj. 1.

ΘΚΠ

the mind > mental capacity > knowledge > conformity with what is known, truth > exaggeration, hyperbole > [adjective]

hyperbolical?a1475

overchargeda1542

magnificate1568

amplified1580

superlative1586

fulsome1602

hyperthetical?1611

hyperbolous1638

hyperbolic1646

bloata1657

exaggerated1725

overshot1774

overstuffed1808

overdrawn1841

fine-drawn1888

steep1895

larger-than-life1937

blown-up1961

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

hyperbolical?a1475

hyperbolous1638

hyperbolic1646

hypertrophic1874

1646 King Charles I Let. to A. Henderson (1649) 56 There are alwaies some flattering Fooles that can commend nothing but with hyperbolick expressions.

1747 S. Richardson Clarissa II. xxviii. 167 Eternal gratitude, is his word, among others still more hyperbolic.

1835 I. Taylor Spiritual Despotism ii. 55 The claims of God's ministers will be asserted in a hyperbolic yet insidious style.

a. Geometry. Of, belonging to, or of the form or nature of a hyperbola. hyperbolic branch (of a curve): an infinite branch which, like the hyperbola, continually approaches an asymptote (opposed to parabolic). hyperbolic conoid: a conoid of hyperbolic section, a hyperboloid of revolution. †hyperbolic cylindroid: name given by Wren to the hyperboloid of revolution of one sheet. hyperbolic paraboloid: a paraboloid having hyperbolic cross-sections, being concave in one direction and convex in another (like a saddle).

ΘΚΠ

the world > relative properties > number > geometry > curve > [adjective] > of conic section > hyperbolical

hyperbolical1571

hyperbolic1676

hyperboliform1728

1676 E. Halley Let. in S. P. Rigaud & S. J. Rigaud Corr. Sci. Men 17th Cent. (1841) (modernized text) I. 240 Foci and diameter describe that hyperbolic line, whose vertex is nearest to A.

1797 Encycl. Brit. VII. 687/2 When the vessel is a portion of a cone or hyperbolic conoid, the content by this method is found less than the truth.

1827 G. Higgins Celtic Druids 104 Their doctrine that comets were planets, which moved in hyperbolic curves.

1842 Penny Cycl. XXIII. 304/2 Let two parabolas have a common vertex, and let their planes be at right angles to one another, being turned contrary ways. Let the one parabola then move over the other, always continuing parallel to its first position, and having its vertex constantly on the other: its arc will then trace out an hyperbolic paraboloid.

1873 G. Salmon Treat. Higher Plane Curves (ed. 2) v. 169 Cubics having three hyperbolic branches are called by Newton redundant hyperbolas.

1988 Proc. Royal Soc. A. 418 427 Another layout that will be considered consists of four triangulated hyperbolic paraboloids of type 1 with common inner boundaries.

b. Applied to functions, operations, etc., having some relation to the hyperbola. hyperbolic curvature: the curvature of a surface whose indicatrix is a hyperbola; the same as anticlastic adj. curvature. hyperbolic function: a function having a relation to a rectangular hyperbola similar to that of the ordinary trigonometrical functions to a circle; as the hyperbolic sine, hyperbolic cosine, hyperbolic tangent, etc. (abbreviated sinh, cosh, tanh, etc.). hyperbolic geometry: the geometry of hyperbolic space. hyperbolic involution: an involution of points (or lines) whose double points (or lines) are real (opposed to elliptic involution, where they are imaginary). hyperbolic logarithm: a logarithm to the base e (2·71828..), a natural or Napierian logarithm; so called because proportional to a segment of the area between a hyperbola and its asymptote. hyperbolic navigation: navigation that utilizes the difference in the times of arrival or the phases of signals transmitted in synchronism by two radio stations to determine a hyperbola on which the receiver must lie, two intersecting hyperbolas from two pairs of stations determining its position; so hyperbolic system, etc. hyperbolic space: (a) the space between a hyperbola and its asymptote or an ordinate; (b) name given by Klein to a space, of any number of dimensions, whose curvature is uniform and negative (see quot. 1872-3²). hyperbolic spiral: a spiral in which the radius vector varies inversely as the angle turned through by it; so called from the analogy of its polar equation (rθ = constant) to the Cartesian equation of the hyperbola (xy = constant). hyperbolic substitution: term for a class of substitutions in the theory of homographic transformation.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > logarithm > [noun] > types of

hyperbolic logarithm1704

logistic logarithms1795

log log1910

lod score1977

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

hyperbole1579

hyperbola1668

hyperbolic space1704

hyperboloid1728

the world > relative properties > number > geometry > curve > [adjective] > of conic section > hyperbolical > of or relating to

hyperbolic1704

right-angled1749

society > travel > travel by water > directing or managing a ship > [noun] > types of navigation

great circle sailing1595

loxodromics1704

oblique sailing1704

orthodromics1704

right sailing1704

parallel sailing1705

orthodromy1706

plane sailing1749

composite sailing1850

loxodromy1855

radio navigation1926

hyperbolic navigation1945

satnav1970

hyperbolic system1972

1704 J. Harris Lexicon Technicum I Hyperbolick-Space, is the Area or Space contained between the Curve of an Hyperbola, and the whole Ordinate.

1743 W. Emerson Doctr. Fluxions 97 The Fluxion of any Quantity divided by that Quantity is the Fluxion of the Hyperbolic Logarithm of that Quantity.

1743 W. Emerson Doctr. Fluxions 97 The hyperbolic Space between the Assymptotes.

1816 tr. S. F. Lacroix Elem. Treat. Differential & Integral Calculus 129 An equation which belongs to the hyperbolic spiral.

1872–3 W. K. Clifford Math. Papers (1882) 189 That geometry of three-dimensional space which assumes the Euclidian postulates has been called by Dr. Klein the parabolic geometry of space, to distinguish it from two other varieties which assume uniform positive and negative curvature respectively, and which he calls the elliptic and hyperbolic geometry of space.

1872–3 W. K. Clifford Math. Papers (1882) 236 (note) According to Dr. Klein's nomenclature, a space, every point of which can be uniquely represented by a set of values of n variables, is called elliptic, parabolic, or hyperbolic, when its curvature is uniform and positive, zero, or negative.

1880 Chrystal Non-Euclidean Geom. 19 In hyperbolic space a straight line has two distinct real points at infinity.

1893 A. R. Forsyth Theory Functions Complex Variable 517 If the multiplier be a real positive quantity, the substitution is called hyperbolic.

1894 Charlotte Scott Mod. Anal. Geom. 162 A hyperbolic involution is non-overlapping.

1945 Electronics Nov. 94/1 Loran..is one of a family of systems known as ‘hyperbolic navigation systems’, which measure the relative time of arrival of two or more radio signals sent synchronously from known points.

1959 Observer 8 Feb. 4/5 A..flying aid invented in America and developed here—the ‘Decca Navigator’; its technical description is a ‘high accuracy hyperbolic navigation system’. This replaces the traditional string of radio beacons by a fine grid of radio signals sent out from four transmitters linked to make a Decca ‘chain’.

1972 Jrnl. Inst. Navigation 25 308 The navigator has three main aids—d.f. using the world-wide chain of shore-based transmitter beacons, the short-range hyperbolic systems, mainly Decca, and his own radar.

This entry has not yet been fully updated (first published 1899; most recently modified version published online June 2018).

单词	hyperbolic
释义	hyperbolicadj. /hʌɪpəˈbɒlɪk/ Etymology: < Greek ὑπερβολικός extravagant, < ὑπερβολή hyperbole n.; in sense 2 used as the adjective of hyperbola n. So French hyperbolique in both senses. 1. Rhetoric. = hyperbolical adj. 1. ΘΚΠ the mind > mental capacity > knowledge > conformity with what is known, truth > exaggeration, hyperbole > [adjective] hyperbolical?a1475 overchargeda1542 magnificate1568 amplified1580 superlative1586 fulsome1602 hyperthetical?1611 hyperbolous1638 hyperbolic1646 bloata1657 exaggerated1725 overshot1774 overstuffed1808 overdrawn1841 fine-drawn1888 steep1895 larger-than-life1937 blown-up1961 society > leisure > the arts > literature > style of language or writing > figure of speech > figures of meaning > [adjective] > hyperbolical hyperbolical?a1475 hyperbolous1638 hyperbolic1646 hypertrophic1874 1646 King Charles I Let. to A. Henderson (1649) 56 There are alwaies some flattering Fooles that can commend nothing but with hyperbolick expressions. 1747 S. Richardson Clarissa II. xxviii. 167 Eternal gratitude, is his word, among others still more hyperbolic. 1835 I. Taylor Spiritual Despotism ii. 55 The claims of God's ministers will be asserted in a hyperbolic yet insidious style. 2. a. Geometry. Of, belonging to, or of the form or nature of a hyperbola. hyperbolic branch (of a curve): an infinite branch which, like the hyperbola, continually approaches an asymptote (opposed to parabolic). hyperbolic conoid: a conoid of hyperbolic section, a hyperboloid of revolution. †hyperbolic cylindroid: name given by Wren to the hyperboloid of revolution of one sheet. hyperbolic paraboloid: a paraboloid having hyperbolic cross-sections, being concave in one direction and convex in another (like a saddle). ΘΚΠ the world > relative properties > number > geometry > curve > [adjective] > of conic section > hyperbolical hyperbolical1571 hyperbolic1676 hyperboliform1728 1676 E. Halley Let. in S. P. Rigaud & S. J. Rigaud Corr. Sci. Men 17th Cent. (1841) (modernized text) I. 240 Foci and diameter describe that hyperbolic line, whose vertex is nearest to A. 1797 Encycl. Brit. VII. 687/2 When the vessel is a portion of a cone or hyperbolic conoid, the content by this method is found less than the truth. 1827 G. Higgins Celtic Druids 104 Their doctrine that comets were planets, which moved in hyperbolic curves. 1842 Penny Cycl. XXIII. 304/2 Let two parabolas have a common vertex, and let their planes be at right angles to one another, being turned contrary ways. Let the one parabola then move over the other, always continuing parallel to its first position, and having its vertex constantly on the other: its arc will then trace out an hyperbolic paraboloid. 1873 G. Salmon Treat. Higher Plane Curves (ed. 2) v. 169 Cubics having three hyperbolic branches are called by Newton redundant hyperbolas. 1988 Proc. Royal Soc. A. 418 427 Another layout that will be considered consists of four triangulated hyperbolic paraboloids of type 1 with common inner boundaries. b. Applied to functions, operations, etc., having some relation to the hyperbola. hyperbolic curvature: the curvature of a surface whose indicatrix is a hyperbola; the same as anticlastic adj. curvature. hyperbolic function: a function having a relation to a rectangular hyperbola similar to that of the ordinary trigonometrical functions to a circle; as the hyperbolic sine, hyperbolic cosine, hyperbolic tangent, etc. (abbreviated sinh, cosh, tanh, etc.). hyperbolic geometry: the geometry of hyperbolic space. hyperbolic involution: an involution of points (or lines) whose double points (or lines) are real (opposed to elliptic involution, where they are imaginary). hyperbolic logarithm: a logarithm to the base e (2·71828..), a natural or Napierian logarithm; so called because proportional to a segment of the area between a hyperbola and its asymptote. hyperbolic navigation: navigation that utilizes the difference in the times of arrival or the phases of signals transmitted in synchronism by two radio stations to determine a hyperbola on which the receiver must lie, two intersecting hyperbolas from two pairs of stations determining its position; so hyperbolic system, etc. hyperbolic space: (a) the space between a hyperbola and its asymptote or an ordinate; (b) name given by Klein to a space, of any number of dimensions, whose curvature is uniform and negative (see quot. 1872-3²). hyperbolic spiral: a spiral in which the radius vector varies inversely as the angle turned through by it; so called from the analogy of its polar equation (rθ = constant) to the Cartesian equation of the hyperbola (xy = constant). hyperbolic substitution: term for a class of substitutions in the theory of homographic transformation. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > logarithm > [noun] > types of hyperbolic logarithm1704 logistic logarithms1795 log log1910 lod score1977 the world > relative properties > number > geometry > curve > [noun] > conic section > hyperbola hyperbole1579 hyperbola1668 hyperbolic space1704 hyperboloid1728 the world > relative properties > number > geometry > curve > [adjective] > of conic section > hyperbolical > of or relating to hyperbolic1704 right-angled1749 society > travel > travel by water > directing or managing a ship > [noun] > types of navigation great circle sailing1595 loxodromics1704 oblique sailing1704 orthodromics1704 right sailing1704 parallel sailing1705 orthodromy1706 plane sailing1749 composite sailing1850 loxodromy1855 radio navigation1926 hyperbolic navigation1945 satnav1970 hyperbolic system1972 1704 J. Harris Lexicon Technicum I Hyperbolick-Space, is the Area or Space contained between the Curve of an Hyperbola, and the whole Ordinate. 1743 W. Emerson Doctr. Fluxions 97 The Fluxion of any Quantity divided by that Quantity is the Fluxion of the Hyperbolic Logarithm of that Quantity. 1743 W. Emerson Doctr. Fluxions 97 The hyperbolic Space between the Assymptotes. 1816 tr. S. F. Lacroix Elem. Treat. Differential & Integral Calculus 129 An equation which belongs to the hyperbolic spiral. 1872–3 W. K. Clifford Math. Papers (1882) 189 That geometry of three-dimensional space which assumes the Euclidian postulates has been called by Dr. Klein the parabolic geometry of space, to distinguish it from two other varieties which assume uniform positive and negative curvature respectively, and which he calls the elliptic and hyperbolic geometry of space. 1872–3 W. K. Clifford Math. Papers (1882) 236 (note) According to Dr. Klein's nomenclature, a space, every point of which can be uniquely represented by a set of values of n variables, is called elliptic, parabolic, or hyperbolic, when its curvature is uniform and positive, zero, or negative. 1880 Chrystal Non-Euclidean Geom. 19 In hyperbolic space a straight line has two distinct real points at infinity. 1893 A. R. Forsyth Theory Functions Complex Variable 517 If the multiplier be a real positive quantity, the substitution is called hyperbolic. 1894 Charlotte Scott Mod. Anal. Geom. 162 A hyperbolic involution is non-overlapping. 1945 Electronics Nov. 94/1 Loran..is one of a family of systems known as ‘hyperbolic navigation systems’, which measure the relative time of arrival of two or more radio signals sent synchronously from known points. 1959 Observer 8 Feb. 4/5 A..flying aid invented in America and developed here—the ‘Decca Navigator’; its technical description is a ‘high accuracy hyperbolic navigation system’. This replaces the traditional string of radio beacons by a fine grid of radio signals sent out from four transmitters linked to make a Decca ‘chain’. 1972 Jrnl. Inst. Navigation 25 308 The navigator has three main aids—d.f. using the world-wide chain of shore-based transmitter beacons, the short-range hyperbolic systems, mainly Decca, and his own radar. This entry has not yet been fully updated (first published 1899; most recently modified version published online June 2018). < adj.1646
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