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Conjugate axis of a hyperbolaConjugate Con"ju*gate, a. [L. conjugatus, p. p. or conjugare
to unite; con- + jugare to join, yoke, marry, jugum yoke;
akin to jungere to join. See Join.]
1. United in pairs; yoked together; coupled.
2. (Bot.) In single pairs; coupled.
3. (Chem.) Containing two or more radicals supposed to act
the part of a single one. [R.]
4. (Gram.) Agreeing in derivation and radical signification;
-- said of words.
5. (Math.) Presenting themselves simultaneously and having
reciprocal properties; -- frequently used in pure and
applied mathematics with reference to two quantities,
points, lines, axes, curves, etc.
Conjugate axis of a hyperbola (Math.), the line through the
center of the curve, perpendicular to the line through the
two foci.
Conjugate diameters (Conic Sections), two diameters of an
ellipse or hyperbola such that each bisects all chords
drawn parallel to the other.
Conjugate focus (Opt.) See under Focus.
Conjugate mirrors (Optics), two mirrors so placed that rays
from the focus of one are received at the focus of the
other, especially two concave mirrors so placed that rays
proceeding from the principal focus of one and reflected
in a parallel beam are received upon the other and brought
to the principal focus.
Conjugate point (Geom.), an acnode. See Acnode, and
Double point.
Self-conjugate triangle (Conic Sections), a triangle each
of whose vertices is the pole of the opposite side with
reference to a conic. HyperbolaHyperbola Hy*per"bo*la, n. [Gr. ?, prop., an overshooting,
excess, i. e., of the angle which the cutting plane makes
with the base. See Hyperbole.] (Geom.)
A curve formed by a section of a cone, when the cutting plane
makes a greater angle with the base than the side of the cone
makes. It is a plane curve such that the difference of the
distances from any point of it to two fixed points, called
foci, is equal to a given distance. See Focus. If the
cutting plane be produced so as to cut the opposite cone,
another curve will be formed, which is also an hyperbola.
Both curves are regarded as branches of the same hyperbola.
See Illust. of Conic section, and Focus. HyperboleHyperbole Hy*per"bo*le, n. [L., fr. Gr?, prop., an
overshooting, excess, fr. Gr. ? to throw over or beyond;
"ype`r over + ? to throw. See Hyper-, Parable, and cf.
Hyperbola.] (Rhet.)
A figure of speech in which the expression is an evident
exaggeration of the meaning intended to be conveyed, or by
which things are represented as much greater or less, better
or worse, than they really are; a statement exaggerated
fancifully, through excitement, or for effect.
Our common forms of compliment are almost all of them
extravagant hyperboles. --Blair.
Somebody has said of the boldest figure in rhetoric,
the hyperbole, that it lies without deceiving.
--Macaulay. HyperbolicHyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector. hyperbolic cosinesHyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector. Hyperbolic functionsHyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector. Hyperbolic logarithmHyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector. hyperbolic sinesHyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector. Hyperbolic spiralHyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector. HyperbolicalHyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector. Hyperbolically
Hyperbolically Hy`per*bol"ic*al*ly, adv.
1. (Math.) In the form of an hyperbola.
2. (Rhet.) With exaggeration; in a manner to express more or
less than the truth. --Sir W. Raleigh.
Hyperboliform
Hyperboliform Hy`per*bol"i*form, a. [Hyperbola + -form.]
Having the form, or nearly the form, of an hyperbola.
Hyperbolism
Hyperbolism Hy*per"bo*lism, n. [Cf. F. hyperbolisme.]
The use of hyperbole. --Jefferson.
Hyperbolist
Hyperbolist Hy*per"bo*list, n.
One who uses hyperboles.
HyperbolizeHyperbolize Hy*per"bo*lize, v. i. [imp. & p. p.
Hyperbolized; p. pr. & vb. n. Hyperbolizing.] [Cf. F.
hyperboliser.]
To speak or write with exaggeration. --Bp. Montagu. Hyperbolize
Hyperbolize Hy*per"bo*lize, v. t.
To state or represent hyperbolically. --Fotherby.
HyperbolizedHyperbolize Hy*per"bo*lize, v. i. [imp. & p. p.
Hyperbolized; p. pr. & vb. n. Hyperbolizing.] [Cf. F.
hyperboliser.]
To speak or write with exaggeration. --Bp. Montagu. HyperbolizingHyperbolize Hy*per"bo*lize, v. i. [imp. & p. p.
Hyperbolized; p. pr. & vb. n. Hyperbolizing.] [Cf. F.
hyperboliser.]
To speak or write with exaggeration. --Bp. Montagu. HyperboloidHyperboloid Hy*per"bo*loid, n. [Hyperbola + -oid: cf. F.
hyperbolo["i]de.] (Geom.)
A surface of the second order, which is cut by certain planes
in hyperbolas; also, the solid, bounded in part by such a
surface.
Hyperboloid of revolution, an hyperboloid described by an
hyperbola revolving about one of its axes. The surface has
two separate sheets when the axis of revolution is the
transverse axis, but only one when the axis of revolution
is the conjugate axis of the hyperbola. Hyperboloid
Hyperboloid Hy*per"bo*loid, a. (Geom.)
Having some property that belongs to an hyperboloid or
hyperbola.
Hyperboloid of revolutionHyperboloid Hy*per"bo*loid, n. [Hyperbola + -oid: cf. F.
hyperbolo["i]de.] (Geom.)
A surface of the second order, which is cut by certain planes
in hyperbolas; also, the solid, bounded in part by such a
surface.
Hyperboloid of revolution, an hyperboloid described by an
hyperbola revolving about one of its axes. The surface has
two separate sheets when the axis of revolution is the
transverse axis, but only one when the axis of revolution
is the conjugate axis of the hyperbola. Nodated hyperbolaNodated No"da*ted, a. [L. nodatus, p. p. of nodare to make
knotty, fr. nodus knot. See Node.]
Knotted.
Nodated hyperbola (Geom.), a certain curve of the third
order having two branches which cross each other, forming
a node. OverboldOverbold O`ver*bold", a.
Excessively or presumptuously bold; impudent. --Shak. --
O"ver*bold"ly, adv. OverboldlyOverbold O`ver*bold", a.
Excessively or presumptuously bold; impudent. --Shak. --
O"ver*bold"ly, adv.
Meaning of ERBOL from wikipedia
