hyperbolan.

Brit.

/hʌɪˈpəːbələ/,

/hʌɪˈpəːbl̩ə/, U.S.

/haɪˈpərbələ/

Etymology: < modern Latin hyperbola, < Greek ὑπερβολή the name of the curve, lit. excess (compare hyperbole n.), < ὑπερβάλλειν to exceed (ὑπέρ over + βάλλειν to throw). In French hyperbole. The hyperbola was so named either because the inclination of its plane to the base of the cone exceeds that of the side of the cone (see ellipse n.), or because the side of the rectangle on the abscissa equal to the square of the ordinate is longer than the latus rectum.

Geometry.

a. One of the conic sections; a plane curve consisting of two separate, equal and similar, infinite branches, formed by the intersection of a plane with both branches of a double cone (i.e. two similar cones on opposite sides of the same vertex). It may also be defined as a curve in which the focal distance of any point bears to its distance from the directrix a constant ratio greater than unity. It has two foci, one for each branch, and two asymptotes, which intersect in the centre of the curve, midway between the vertices of its two branches. (Often applied to one branch of the curve.)

ΘΚΠ

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

hyperbole1579

hyperbola1668

hyperbolic space1704

hyperboloid1728

1668 Philos. Trans. (Royal Soc.) 3 643 The Area of one Hyperbola being computed, the Area of all others may be thence argued.

1693 R. Bentley Boyle Lect. viii. 12 They would not have..moved in Hyperbola's..or in Ellipses very Eccentric.

1706 W. Jones Synopsis Palmariorum Matheseos 256 The Sections of the opposite Cones will be equal Hyperbolas.

1728 H. Pemberton View Sir I. Newton's Philos. 232 With a velocity still greater the body will move in an hyperbola.

1828 O. Gregory Hutton's Course Math. (ed. 9) II. 102 The section is an hyperbola, when the cutting plane makes a greater angle with the base than the side of the cone makes.

1885 G. L. Goodale in A. Gray & G. L. Goodale Bot. Text-bk. (ed. 6) II. ii. xii. 381 If the outline of the growing point is a hyperbola, the periclinals will be confocal hyperbolas, with the same axis but different parameter.

b. Extended (after Newton) to algebraic curves of higher degrees denoted by equations analogous to that of the common hyperbola.

ΘΚΠ

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

hyperbola1728

hyperbolism1861

1728 E. Chambers Cycl. (at cited word) Infinite Hyperbola's, or Hyperbola's of the higher Kinds, are those defin[e]d by the Equation ay^{m + n} = bz^m(a + x)ⁿ.

1728 E. Chambers Cycl. (at cited word) As the Hyperbola of the first Kind or Order has two Asymptotes, that of the second Kind or Order has three, that of the third, four, &c.

1753 Chambers's Cycl. Suppl. Hyperbolas of all degrees may be expressed by the equation x^myⁿ = a^{m + n}.

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

This entry has not yet been fully updated (first published 1899; most recently modified version published online March 2022).

单词	hyperbola
释义	hyperbolan. Brit. /hʌɪˈpəːbələ/, /hʌɪˈpəːbl̩ə/, U.S. /haɪˈpərbələ/ Etymology: < modern Latin hyperbola, < Greek ὑπερβολή the name of the curve, lit. excess (compare hyperbole n.), < ὑπερβάλλειν to exceed (ὑπέρ over + βάλλειν to throw). In French hyperbole. The hyperbola was so named either because the inclination of its plane to the base of the cone exceeds that of the side of the cone (see ellipse n.), or because the side of the rectangle on the abscissa equal to the square of the ordinate is longer than the latus rectum. Geometry. a. One of the conic sections; a plane curve consisting of two separate, equal and similar, infinite branches, formed by the intersection of a plane with both branches of a double cone (i.e. two similar cones on opposite sides of the same vertex). It may also be defined as a curve in which the focal distance of any point bears to its distance from the directrix a constant ratio greater than unity. It has two foci, one for each branch, and two asymptotes, which intersect in the centre of the curve, midway between the vertices of its two branches. (Often applied to one branch of the curve.) ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > conic section > hyperbola hyperbole1579 hyperbola1668 hyperbolic space1704 hyperboloid1728 1668 Philos. Trans. (Royal Soc.) 3 643 The Area of one Hyperbola being computed, the Area of all others may be thence argued. 1693 R. Bentley Boyle Lect. viii. 12 They would not have..moved in Hyperbola's..or in Ellipses very Eccentric. 1706 W. Jones Synopsis Palmariorum Matheseos 256 The Sections of the opposite Cones will be equal Hyperbolas. 1728 H. Pemberton View Sir I. Newton's Philos. 232 With a velocity still greater the body will move in an hyperbola. 1828 O. Gregory Hutton's Course Math. (ed. 9) II. 102 The section is an hyperbola, when the cutting plane makes a greater angle with the base than the side of the cone makes. 1885 G. L. Goodale in A. Gray & G. L. Goodale Bot. Text-bk. (ed. 6) II. ii. xii. 381 If the outline of the growing point is a hyperbola, the periclinals will be confocal hyperbolas, with the same axis but different parameter. b. Extended (after Newton) to algebraic curves of higher degrees denoted by equations analogous to that of the common hyperbola. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > conic section > hyperbola > analogous to hyperbola1728 hyperbolism1861 1728 E. Chambers Cycl. (at cited word) Infinite Hyperbola's, or Hyperbola's of the higher Kinds, are those defin[e]d by the Equation ay^{m + n} = bz^m(a + x)ⁿ. 1728 E. Chambers Cycl. (at cited word) As the Hyperbola of the first Kind or Order has two Asymptotes, that of the second Kind or Order has three, that of the third, four, &c. 1753 Chambers's Cycl. Suppl. Hyperbolas of all degrees may be expressed by the equation x^myⁿ = a^{m + n}. 1873 G. Salmon Treat. Higher Plane Curves (ed. 2) v. 169 Cubics having three hyperbolic branches are called by Newton redundant hyperbolas. This entry has not yet been fully updated (first published 1899; most recently modified version published online March 2022). < n.1668
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