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Abstract number Number Num"ber, n. [OE. nombre, F. nombre, L. numerus; akin to
Gr. ? that which is dealt out, fr. ? to deal out, distribute.
See Numb, Nomad, and cf. Numerate, Numero,
Numerous.]
1. That which admits of being counted or reckoned; a unit, or
an aggregate of units; a numerable aggregate or collection
of individuals; an assemblage made up of distinct things
expressible by figures.
2. A collection of many individuals; a numerous assemblage; a
multitude; many.
Ladies are always of great use to the party they
espouse, and never fail to win over numbers.
--Addison.
3. A numeral; a word or character denoting a number; as, to
put a number on a door.
4. Numerousness; multitude.
Number itself importeth not much in armies where the
people are of weak courage. --Bacon.
5. The state or quality of being numerable or countable.
Of whom came nations, tribes, people, and kindreds
out of number. --2 Esdras
iii. 7.
6. Quantity, regarded as made up of an aggregate of separate
things.
7. That which is regulated by count; poetic measure, as
divisions of time or number of syllables; hence, poetry,
verse; -- chiefly used in the plural.
I lisped in numbers, for the numbers came. --Pope.
8. (Gram.) The distinction of objects, as one, or more than
one (in some languages, as one, or two, or more than two),
expressed (usually) by a difference in the form of a word;
thus, the singular number and the plural number are the
names of the forms of a word indicating the objects
denoted or referred to by the word as one, or as more than
one.
9. (Math.) The measure of the relation between quantities or
things of the same kind; that abstract species of quantity
which is capable of being expressed by figures; numerical
value.
Abstract number, Abundant number, Cardinal number, etc.
See under Abstract, Abundant, etc.
In numbers, in numbered parts; as, a book published in
numbers.
Abstract numbers Abstract Ab"stract` (#; 277), a. [L. abstractus, p. p. of
abstrahere to draw from, separate; ab, abs + trahere to draw.
See Trace.]
1. Withdraw; separate. [Obs.]
The more abstract . . . we are from the body.
--Norris.
2. Considered apart from any application to a particular
object; separated from matter; existing in the mind only;
as, abstract truth, abstract numbers. Hence: ideal;
abstruse; difficult.
3. (Logic)
(a) Expressing a particular property of an object viewed
apart from the other properties which constitute it;
-- opposed to concrete; as, honesty is an abstract
word. --J. S. Mill.
(b) Resulting from the mental faculty of abstraction;
general as opposed to particular; as, ``reptile' is
an abstract or general name. --Locke.
A concrete name is a name which stands for a
thing; an abstract name which stands for an
attribute of a thing. A practice has grown up in
more modern times, which, if not introduced by
Locke, has gained currency from his example, of
applying the expression ``abstract name' to all
names which are the result of abstraction and
generalization, and consequently to all general
names, instead of confining it to the names of
attributes. --J. S. Mill.
4. Abstracted; absent in mind. ``Abstract, as in a trance.'
--Milton.
An abstract idea (Metaph.), an idea separated from a
complex object, or from other ideas which naturally
accompany it; as the solidity of marble when contemplated
apart from its color or figure.
Abstract terms, those which express abstract ideas, as
beauty, whiteness, roundness, without regarding any object
in which they exist; or abstract terms are the names of
orders, genera or species of things, in which there is a
combination of similar qualities.
Abstract numbers (Math.), numbers used without application
to things, as 6, 8, 10; but when applied to any thing, as
6 feet, 10 men, they become concrete.
Abstract or Pure mathematics. See Mathematics.
Abundant number Number Num"ber, n. [OE. nombre, F. nombre, L. numerus; akin to
Gr. ? that which is dealt out, fr. ? to deal out, distribute.
See Numb, Nomad, and cf. Numerate, Numero,
Numerous.]
1. That which admits of being counted or reckoned; a unit, or
an aggregate of units; a numerable aggregate or collection
of individuals; an assemblage made up of distinct things
expressible by figures.
2. A collection of many individuals; a numerous assemblage; a
multitude; many.
Ladies are always of great use to the party they
espouse, and never fail to win over numbers.
--Addison.
3. A numeral; a word or character denoting a number; as, to
put a number on a door.
4. Numerousness; multitude.
Number itself importeth not much in armies where the
people are of weak courage. --Bacon.
5. The state or quality of being numerable or countable.
Of whom came nations, tribes, people, and kindreds
out of number. --2 Esdras
iii. 7.
6. Quantity, regarded as made up of an aggregate of separate
things.
7. That which is regulated by count; poetic measure, as
divisions of time or number of syllables; hence, poetry,
verse; -- chiefly used in the plural.
I lisped in numbers, for the numbers came. --Pope.
8. (Gram.) The distinction of objects, as one, or more than
one (in some languages, as one, or two, or more than two),
expressed (usually) by a difference in the form of a word;
thus, the singular number and the plural number are the
names of the forms of a word indicating the objects
denoted or referred to by the word as one, or as more than
one.
9. (Math.) The measure of the relation between quantities or
things of the same kind; that abstract species of quantity
which is capable of being expressed by figures; numerical
value.
Abstract number, Abundant number, Cardinal number, etc.
See under Abstract, Abundant, etc.
In numbers, in numbered parts; as, a book published in
numbers.
Abundant number Abundant A*bun"dant, a. [OE. (h)abundant, aboundant, F.
abondant, fr. L. abudans, p. pr. of abundare. See Abound.]
Fully sufficient; plentiful; in copious supply; -- followed
by in, rarely by with. ``Abundant in goodness and truth.'
--Exod. xxxiv. 6.
Abundant number (Math.), a number, the sum of whose aliquot
parts exceeds the number itself. Thus, 1, 2, 3, 4, 6, the
aliquot parts of 12, make the number 16. This is opposed
to a deficient number, as 14, whose aliquot parts are 1,
2, 7, the sum of which is 10; and to a perfect number,
which is equal to the sum of its aliquot parts, as 6,
whose aliquot parts are 1, 2., 3.
Syn: Ample; plentiful; copious; plenteous; exuberant;
overflowing; rich; teeming; profuse; bountiful; liberal.
See Ample.
Amicable numbers Amicable Am"i*ca*ble, a. [L. amicabilis, fr. amicus friend,
fr. amare to love. See Amiable.]
Friendly; proceeding from, or exhibiting, friendliness; after
the manner of friends; peaceable; as, an amicable
disposition, or arrangement.
That which was most remarkable in this contest was . .
. the amicable manner in which it was managed.
--Prideoux.
Amicable action (Law.), an action commenced and prosecuted
by amicable consent of the parties, for the purpose of
obtaining a decision of the court on some matter of law
involved in it. --Bouvier. --Burrill.
Amicable numbers (Math.), two numbers, each of which is
equal to the sum of all the aliquot parts of the other.
Syn: Friendly; peaceable; kind; harmonious.
Usage: Amicable, Friendly. Neither of these words denotes
any great warmth of affection, since friendly has by
no means the same strength as its noun friendship. It
does, however, imply something of real cordiality;
while amicable supposes very little more than that the
parties referred to are not disposed to quarrel.
Hence, we speak of amicable relations between two
countries, an amicable adjustment of difficulties.
``Those who entertain friendly feelings toward each
other can live amicably together.'
Antenumber Antenumber An`te*num"ber, n.
A number that precedes another. [R.] --Bacon.
Apocalyptic number Apocalyptic A*poc`a*lyp"tic, Apocalyptical
A*poc`a*lyp"tic*al, a. [Gr. ?.]
Of or pertaining to a revelation, or, specifically, to the
Revelation of St. John; containing, or of the nature of, a
prophetic revelation.
Apocalyptic number, the number 666, mentioned in --Rev.
xiii. 18. It has been variously interpreted.
Applicate number Applicate Ap"pli*cate, a. [L. applicatus, p. p. of applicare.
See Apply.]
Applied or put to some use.
Those applicate sciences which extend the power of man
over the elements. --I. Taylor.
Applicate number (Math.), one which applied to some
concrete case.
Applicate ordinate, right line applied at right angles to
the axis of any conic section, and bounded by the curve.
Artificial numbers Artificial Ar`ti*fi"cial, a. [L. artificialis, fr. artificium:
cf. F. artificiel. See Artifice.]
1. Made or contrived by art; produced or modified by human
skill and labor, in opposition to natural; as, artificial
heat or light, gems, salts, minerals, fountains, flowers.
Artificial strife Lives in these touches, livelier
than life. --Shak.
2. Feigned; fictitious; assumed; affected; not genuine.
``Artificial tears.' --Shak.
3. Artful; cunning; crafty. [Obs.] --Shak.
4. Cultivated; not indigenous; not of spontaneous growth; as,
artificial grasses. --Gibbon.
Artificial arguments (Rhet.), arguments invented by the
speaker, in distinction from laws, authorities, and the
like, which are called inartificial arguments or proofs.
--Johnson.
Artificial classification (Science), an arrangement based
on superficial characters, and not expressing the true
natural relations species; as, ``the artificial system'
in botany, which is the same as the Linn[ae]an system.
Artificial horizon. See under Horizon.
Artificial light, any light other than that which proceeds
from the heavenly bodies.
Artificial lines, lines on a sector or scale, so contrived
as to represent the logarithmic sines and tangents, which,
by the help of the line of numbers, solve, with tolerable
exactness, questions in trigonometry, navigation, etc.
Artificial numbers, logarithms.
Artificial person (Law). See under Person.
Artificial sines, tangents, etc., the same as logarithms
of the natural sines, tangents, etc. --Hutton.
Benumbed Benumb Be*numb", v. t. [imp. & p. p. Benumbed; p. pr. & vb.
n. Benumbing.] [OE. binomen, p. p. of binimen to take away,
AS. beniman; pref. be + niman to take. See Numb, a., and
cf. Benim.]
To make torpid; to deprive of sensation or sensibility; to
stupefy; as, a hand or foot benumbed by cold.
The creeping death benumbed her senses first. --Dryden.
Benumbed Benumbed Be*numbed", a.
Made torpid; numbed; stupefied; deadened; as, a benumbed body
and mind. -- Be*numbed"ness, n.
Benumbedness Benumbed Be*numbed", a.
Made torpid; numbed; stupefied; deadened; as, a benumbed body
and mind. -- Be*numbed"ness, n.
Biquadratic root of a number Biquadratic Bi`quad*rat"ic, a. [Pref. bi- + quadratic: cf. F.
biquadratique.] (Math.)
Of or pertaining to the biquadrate, or fourth power.
Biquadratic equation (Alg.), an equation of the fourth
degree, or an equation in some term of which the unknown
quantity is raised to the fourth power.
Biquadratic root of a number, the square root of the square
root of that number. Thus the square root of 81 is 9, and
the square root of 9 is 3, which is the biquadratic root
of 81. Hutton.
Cardinal number Number Num"ber, n. [OE. nombre, F. nombre, L. numerus; akin to
Gr. ? that which is dealt out, fr. ? to deal out, distribute.
See Numb, Nomad, and cf. Numerate, Numero,
Numerous.]
1. That which admits of being counted or reckoned; a unit, or
an aggregate of units; a numerable aggregate or collection
of individuals; an assemblage made up of distinct things
expressible by figures.
2. A collection of many individuals; a numerous assemblage; a
multitude; many.
Ladies are always of great use to the party they
espouse, and never fail to win over numbers.
--Addison.
3. A numeral; a word or character denoting a number; as, to
put a number on a door.
4. Numerousness; multitude.
Number itself importeth not much in armies where the
people are of weak courage. --Bacon.
5. The state or quality of being numerable or countable.
Of whom came nations, tribes, people, and kindreds
out of number. --2 Esdras
iii. 7.
6. Quantity, regarded as made up of an aggregate of separate
things.
7. That which is regulated by count; poetic measure, as
divisions of time or number of syllables; hence, poetry,
verse; -- chiefly used in the plural.
I lisped in numbers, for the numbers came. --Pope.
8. (Gram.) The distinction of objects, as one, or more than
one (in some languages, as one, or two, or more than two),
expressed (usually) by a difference in the form of a word;
thus, the singular number and the plural number are the
names of the forms of a word indicating the objects
denoted or referred to by the word as one, or as more than
one.
9. (Math.) The measure of the relation between quantities or
things of the same kind; that abstract species of quantity
which is capable of being expressed by figures; numerical
value.
Abstract number, Abundant number, Cardinal number, etc.
See under Abstract, Abundant, etc.
In numbers, in numbered parts; as, a book published in
numbers.
Cardinal numbers Cardinal Car"di*nal, a. [L. cardinalis, fr. cardo the hinge of
a door, that on which a thing turns or depends: cf. F.
cardinal.]
Of fundamental importance; pre["e]minent; superior; chief;
principal.
The cardinal intersections of the zodiac. --Sir T.
Browne.
Impudence is now a cardinal virtue. --Drayton.
But cardinal sins, and hollow hearts, I fear ye.
--Shak.
Cardinal numbers, the numbers one, two, three, etc., in
distinction from first, second, third, etc., which are
called ordinal numbers.
Cardinal points
(a) (Geol.) The four principal points of the compass, or
intersections of the horizon with the meridian and the
prime vertical circle, north, south east, and west.
(b) (Astrol.) The rising and setting of the sun, the zenith
and nadir.
Cardinal signs (Astron.) Aries, Libra, Cancer, and
Capricorn.
Cardinal teeth (Zo["o]l.), the central teeth of bivalve
shell. See Bivalve.
Cardinal veins (Anat.), the veins in vertebrate embryos,
which run each side of the vertebral column and returm the
blood to the heart. They remain through life in some
fishes.
Cardinal virtues, pre["e]minent virtues; among the
ancients, prudence, justice, temperance, and fortitude.
Cardinal winds, winds which blow from the cardinal points
due north, south, east, or west.
Circular numbers Circular Cir"cu*lar, a. [L. circularis, fr. circulus circle:
cf. F. circulaire. See Circle.]
1. In the form of, or bounded by, a circle; round.
2. repeating itself; ending in itself; reverting to the point
of beginning; hence, illogical; inconclusive; as, circular
reasoning.
3. Adhering to a fixed circle of legends; cyclic; hence,
mean; inferior. See Cyclic poets, under Cyclic.
Had Virgil been a circular poet, and closely adhered
to history, how could the Romans have had Dido?
--Dennis.
4. Addressed to a circle, or to a number of persons having a
common interest; circulated, or intended for circulation;
as, a circular letter.
A proclamation of Henry III., . . . doubtless
circular throughout England. --Hallam.
5. Perfect; complete. [Obs.]
A man so absolute and circular In all those
wished-for rarities that may take A virgin captive.
--Massinger.
Circular are, any portion of the circumference of a circle.
Circular cubics (Math.), curves of the third order which
are imagined to pass through the two circular points at
infinity.
Circular functions. (Math.) See under Function.
Circular instruments, mathematical instruments employed for
measuring angles, in which the graduation extends round
the whole circumference of a circle, or 360[deg].
Circular lines, straight lines pertaining to the circle, as
sines, tangents, secants, etc.
Circularnote or letter.
(a) (Com.) See under Credit.
(b) (Diplomacy) A letter addressed in identical terms to a
number of persons.
Circular numbers (Arith.), those whose powers terminate in
the same digits as the roots themselves; as 5 and 6, whose
squares are 25 and 36. --Bailey. --Barlow.
Circular points at infinity (Geom.), two imaginary points
at infinite distance through which every circle in the
plane is, in the theory of curves, imagined to pass.
Circular polarization. (Min.) See under Polarization.
Circular or Globularsailing (Naut.), the method of
sailing by the arc of a great circle.
Circular saw. See under Saw.
Commensurable numbers Commensurable Com*men"su*ra*ble, a. [L. commensurabilis; pref.
com- + mensurable. See Commensurate, and cf.
Commeasurable.]
Having a common measure; capable of being exactly measured by
the same number, quantity, or measure. --
Com*men"su*ra*ble*ness, n.
Commensurable numbers or quantities (Math.), those that
can be exactly expressed by some common unit; thus a foot
and yard are commensurable, since both can be expressed in
terms of an inch, one being 12 inches, the other 36
inches.
Numbers, or Quantities, commensurable in power, those
whose squares are commensurable.
Complex number Complex Com"plex, a. [L. complexus, p. p. of complecti to
entwine around, comprise; com- + plectere to twist, akin to
plicare to fold. See Plait, n.]
1. Composed of two or more parts; composite; not simple; as,
a complex being; a complex idea.
Ideas thus made up of several simple ones put
together, I call complex; such as beauty, gratitude,
a man, an army, the universe. --Locke.
2. Involving many parts; complicated; intricate.
When the actual motions of the heavens are
calculated in the best possible way, the process is
difficult and complex. --Whewell.
Complex fraction. See Fraction.
Complex number (Math.), in the theory of numbers, an
expression of the form a + b[root]-1, when a and b are
ordinary integers.
Syn: See Intricate.
Composite number 3. (Bot.) Belonging to the order Composit[ae]; bearing
involucrate heads of many small florets, as the daisy,
thistle, and dandelion.
Composite carriage, a railroad car having compartments of
different classes. [Eng.]
Composite number (Math.), one which can be divided exactly
by a number exceeding unity, as 6 by 2 or 3.
Compound number Compound Com"pound, a. [OE. compouned, p. p. of compounen. See
Compound, v. t.]
Composed of two or more elements, ingredients, parts;
produced by the union of several ingredients, parts, or
things; composite; as, a compound word.
Compound substances are made up of two or more simple
substances. --I. Watts.
Compound addition, subtraction, multiplication,
division (Arith.), the addition, subtraction, etc., of
compound numbers.
Compound crystal (Crystallog.), a twin crystal, or one
seeming to be made up of two or more crystals combined
according to regular laws of composition.
Compound engine (Mech.), a form of steam engine in which
the steam that has been used in a high-pressure cylinder
is made to do further service in a larger low-pressure
cylinder, sometimes in several larger cylinders,
successively.
Compound ether. (Chem.) See under Ether.
Compound flower (Bot.), a flower head resembling a single
flower, but really composed of several florets inclosed in
a common calyxlike involucre, as the sunflower or
dandelion.
Compound fraction. (Math.) See Fraction.
Compound fracture. See Fracture.
Compound householder, a householder who compounds or
arranges with his landlord that his rates shall be
included in his rents. [Eng.]
Compound interest. See Interest.
Compound larceny. (Law) See Larceny.
Compound leaf (Bot.), a leaf having two or more separate
blades or leaflets on a common leafstalk.
Compound microscope. See Microscope.
Compound motion. See Motion.
Compound number (Math.), one constructed according to a
varying scale of denomination; as, 3 cwt., 1 qr., 5 lb.;
-- called also denominate number.
Compound pier (Arch.), a clustered column.
Compound quantity (Alg.), a quantity composed of two or
more simple quantities or terms, connected by the sign +
(plus) or - (minus). Thus, a + b - c, and bb - b, are
compound quantities.
Compound radical. (Chem.) See Radical.
Compound ratio (Math.), the product of two or more ratios;
thus ab:cd is a ratio compounded of the simple ratios a:c
and b:d.
Compound rest (Mech.), the tool carriage of an engine
lathe.
Compound screw (Mech.), a screw having on the same axis two
or more screws with different pitch (a differential
screw), or running in different directions (a right and
left screw).
Compound time (Mus.), that in which two or more simple
measures are combined in one; as, 6-8 time is the joining
of two measures of 3-8 time.
Compound word, a word composed of two or more words;
specifically, two or more words joined together by a
hyphen.
Concrete number Concrete Con"crete (? or ?), a. [L. concretus, p. p. of
concrescere to grow together; con- + crescere to grow; cf. F.
concret. See Crescent.]
1. United in growth; hence, formed by coalition of separate
particles into one mass; united in a solid form.
The first concrete state, or consistent surface, of
the chaos must be of the same figure as the last
liquid state. --Bp. Burnet.
2. (Logic)
(a) Standing for an object as it exists in nature,
invested with all its qualities, as distinguished from
standing for an attribute of an object; -- opposed to
abstract. Hence:
(b) Applied to a specific object; special; particular; --
opposed to general. See Abstract, 3.
Concrete is opposed to abstract. The names of
individuals are concrete, those of classes
abstract. --J. S. Mill.
Concrete terms, while they express the quality,
do also express, or imply, or refer to, some
subject to which it belongs. --I. Watts.
Concrete number, a number associated with, or applied to, a
particular object, as three men, five days, etc., as
distinguished from an abstract number, or one used without
reference to a particular object.
Concrete quantity, a physical object or a collection of
such objects. --Davies & Peck.
Concrete science, a physical science, one having as its
subject of knowledge concrete things instead of abstract
laws.
Concrete sound or movement of the voice, one which slides
continuously up or down, as distinguished from a
discrete movement, in which the voice leaps at once from
one line of pitch to another. --Rush.
Cubic number Cubic Cu"bic (k?"b?k), Cubical Cu"bic*al (-b?-kal), a. [L.
cubicus, Gr. ?????: cf. F. cubique. See Cube.]
1. Having the form or properties of a cube; contained, or
capable of being contained, in a cube.
2. (Crystallog.) Isometric or monometric; as, cubic cleavage.
See Crystallization.
Cubic equation, an equation in which the highest power of
the unknown quantity is a cube.
Cubic foot, a volume equivalent to a cubical solid which
measures a foot in each of its dimensions.
Cubic number, a number produced by multiplying a number
into itself, and that product again by the same number.
See Cube.
Cubical parabola (Geom.), two curves of the third degree,
one plane, and one on space of three dimensions.
Deficient number Deficient De*fi"cient, a. [L. deficiens, -entis, p. pr. of
deficere to be wanting. See Defect.]
Wanting, to make up completeness; wanting, as regards a
requirement; not sufficient; inadequate; defective;
imperfect; incomplete; lacking; as, deficient parts;
deficient estate; deficient strength; deficient in judgment.
The style was indeed deficient in ease and variety.
--Macaulay.
Deficient number. (Arith.) See under Abundant. --
De*fi"cient-ly, adv.
denominate number Compound Com"pound, a. [OE. compouned, p. p. of compounen. See
Compound, v. t.]
Composed of two or more elements, ingredients, parts;
produced by the union of several ingredients, parts, or
things; composite; as, a compound word.
Compound substances are made up of two or more simple
substances. --I. Watts.
Compound addition, subtraction, multiplication,
division (Arith.), the addition, subtraction, etc., of
compound numbers.
Compound crystal (Crystallog.), a twin crystal, or one
seeming to be made up of two or more crystals combined
according to regular laws of composition.
Compound engine (Mech.), a form of steam engine in which
the steam that has been used in a high-pressure cylinder
is made to do further service in a larger low-pressure
cylinder, sometimes in several larger cylinders,
successively.
Compound ether. (Chem.) See under Ether.
Compound flower (Bot.), a flower head resembling a single
flower, but really composed of several florets inclosed in
a common calyxlike involucre, as the sunflower or
dandelion.
Compound fraction. (Math.) See Fraction.
Compound fracture. See Fracture.
Compound householder, a householder who compounds or
arranges with his landlord that his rates shall be
included in his rents. [Eng.]
Compound interest. See Interest.
Compound larceny. (Law) See Larceny.
Compound leaf (Bot.), a leaf having two or more separate
blades or leaflets on a common leafstalk.
Compound microscope. See Microscope.
Compound motion. See Motion.
Compound number (Math.), one constructed according to a
varying scale of denomination; as, 3 cwt., 1 qr., 5 lb.;
-- called also denominate number.
Compound pier (Arch.), a clustered column.
Compound quantity (Alg.), a quantity composed of two or
more simple quantities or terms, connected by the sign +
(plus) or - (minus). Thus, a + b - c, and bb - b, are
compound quantities.
Compound radical. (Chem.) See Radical.
Compound ratio (Math.), the product of two or more ratios;
thus ab:cd is a ratio compounded of the simple ratios a:c
and b:d.
Compound rest (Mech.), the tool carriage of an engine
lathe.
Compound screw (Mech.), a screw having on the same axis two
or more screws with different pitch (a differential
screw), or running in different directions (a right and
left screw).
Compound time (Mus.), that in which two or more simple
measures are combined in one; as, 6-8 time is the joining
of two measures of 3-8 time.
Compound word, a word composed of two or more words;
specifically, two or more words joined together by a
hyphen.
Figural numbers Figural Fig"ur*al, a. [From Figure.]
1. Represented by figure or delineation; consisting of
figures; as, figural ornaments. --Sir T. Browne.
2. (Mus.) Figurate. See Figurate.
Figural numbers. See Figurate numbers, under Figurate.
Figurate numbers Figurate Fig"ur*ate, a. [L. figuratus, p. p. of figurare. See
Figure.]
1. Of a definite form or figure.
Plants are all figurate and determinate, which
inanimate bodies are not. --Bacon.
2. Figurative; metaphorical. [Obs.] --Bale.
3. (Mus.) Florid; figurative; involving passing discords by
the freer melodic movement of one or more parts or voices
in the harmony; as, figurate counterpoint or descant.
Figurate counterpoint or descant (Mus.), that which is
not simple, or in which the parts do not move together
tone for tone, but in which freer movement of one or more
parts mingles passing discords with the harmony; -- called
also figural, figurative, and figured counterpoint
or descant (although the term figured is more commonly
applied to a bass with numerals written above or below to
indicate the other notes of the harmony).
Figurate numbers (Math.), numbers, or series of numbers,
formed from any arithmetical progression in which the
first term is a unit, and the difference a whole number,
by taking the first term, and the sums of the first two,
first three, first four, etc., as the successive terms of
a new series, from which another may be formed in the same
manner, and so on, the numbers in the resulting series
being such that points representing them are capable of
symmetrical arrangement in different geometrical figures,
as triangles, squares, pentagons, etc.
Note: In the following example, the two lower lines are
composed of figurate numbers, those in the second line
being triangular, and represented thus: -- . 1, 2, 3,
4, etc. . . . 1, 3, 6, 10, etc. . . . . . . . etc. 1,
4, 10, 20, etc . . . . . . . . . . . .
Heptagonal numbers Heptagonal Hep*tag"o*nal, a. [Cf. F. heptagonal.]
Having seven angles or sides.
Heptagonal numbers (Arith.), the numbers of the series 1,
7, 18, 34, 55, etc., being figurate numbers formed by
adding successively the terms of the arithmetical series
1, 6, 11, 16, 21, etc.
In numbers Number Num"ber, n. [OE. nombre, F. nombre, L. numerus; akin to
Gr. ? that which is dealt out, fr. ? to deal out, distribute.
See Numb, Nomad, and cf. Numerate, Numero,
Numerous.]
1. That which admits of being counted or reckoned; a unit, or
an aggregate of units; a numerable aggregate or collection
of individuals; an assemblage made up of distinct things
expressible by figures.
2. A collection of many individuals; a numerous assemblage; a
multitude; many.
Ladies are always of great use to the party they
espouse, and never fail to win over numbers.
--Addison.
3. A numeral; a word or character denoting a number; as, to
put a number on a door.
4. Numerousness; multitude.
Number itself importeth not much in armies where the
people are of weak courage. --Bacon.
5. The state or quality of being numerable or countable.
Of whom came nations, tribes, people, and kindreds
out of number. --2 Esdras
iii. 7.
6. Quantity, regarded as made up of an aggregate of separate
things.
7. That which is regulated by count; poetic measure, as
divisions of time or number of syllables; hence, poetry,
verse; -- chiefly used in the plural.
I lisped in numbers, for the numbers came. --Pope.
8. (Gram.) The distinction of objects, as one, or more than
one (in some languages, as one, or two, or more than two),
expressed (usually) by a difference in the form of a word;
thus, the singular number and the plural number are the
names of the forms of a word indicating the objects
denoted or referred to by the word as one, or as more than
one.
9. (Math.) The measure of the relation between quantities or
things of the same kind; that abstract species of quantity
which is capable of being expressed by figures; numerical
value.
Abstract number, Abundant number, Cardinal number, etc.
See under Abstract, Abundant, etc.
In numbers, in numbered parts; as, a book published in
numbers.
Incongruous numbers Incongruous In*con"gru*ous, a. [L. incongruus. See In- not,
and Congruous.]
Not congruous; reciprocally disagreeing; not capable of
harmonizing or readily assimilating; inharmonious;
inappropriate; unsuitable; not fitting; inconsistent;
improper; as, an incongruous remark; incongruous behavior,
action, dress, etc. ``Incongruous mixtures of opinions.'
--I. Taylor. ``Made up of incongruous parts.' --Macaulay.
Incongruous denotes that kind of absence of harmony or
suitableness of which the taste and experience of men
takes cognizance. --C. J. Smith.
Incongruous numbers (Arith.), two numbers, which, with
respect to a third, are such that their difference can not
be divided by it without a remainder, the two numbers
being said to be incongruous with respect to the third;
as, twenty-five are incongruous with respect to four.
Syn: Inconsistent; unsuitable; inharmonious; disagreeing;
absurd; inappropriate; unfit; improper. See
Inconsistent. -- In*con"gru*ous*ly, adv. --
In*con"gru*ous*ness, n.
