Definition of Equation. Meaning of Equation. Synonyms of Equation
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Definition of Equation
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Adequation Adequation Ad`e*qua"tion, n. [L. adaequatio.]
The act of equalizing; act or result of making adequate; an
equivalent. [Obs.] --Bp. Barlow.
an equation Discussion Dis*cus"sion, n. [L. discussio a shaking,
examination, discussion: cf. F. discussion.]
1. The act or process of discussing by breaking up, or
dispersing, as a tumor, or the like.
2. The act of discussing or exchanging reasons; examination
by argument; debate; disputation; agitation.
The liberty of discussion is the great safeguard of
all other liberties. --Macaulay.
Discussion of a problem or an equation (Math.), the
operation of assigning different reasonable values to the
arbitrary quantities and interpreting the result. --Math.
Dict.
Biquadratic equation 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.
Construction of an equation Construction Con*struc"tion, n. [L. constructio: cf. F.
construction.]
1. The process or art of constructing; the act of building;
erection; the act of devising and forming; fabrication;
composition.
2. The form or manner of building or putting together the
parts of anything; structure; arrangement.
An astrolabe of peculiar construction. --Whewell.
3. (Gram.) The arrangement and connection of words in a
sentence; syntactical arrangement.
Some particles . . . in certain constructions have
the sense of a whole sentence contained in them.
--Locke.
4. The method of construing, interpreting, or explaining a
declaration or fact; an attributed sense or meaning;
understanding; explanation; interpretation; sense.
Any person . . . might, by the sort of construction
that would be put on this act, become liable to the
penalties of treason. --Hallam.
Strictly, the term [construction] signifies
determining the meaning and proper effect of
language by a consideration of the subject matter
and attendant circumstances in connection with the
words employed. --Abbott.
Interpretation properly precedes construction, but
it does not go beyond the written text. --Parsons.
Construction of an equation (Math.), the drawing of such
lines and figures as will represent geometrically the
quantities in the equation, and their relations to each
other.
Construction train (Railroad), a train for transporting men
and materials for construction or repairs.
Cubic equation 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.
Determinate equations Determinate De*ter"mi*nate, a. [L. determinatus, p. p. of
determinare. See Determine.]
1. Having defined limits; not uncertain or arbitrary; fixed;
established; definite.
Quantity of words and a determinate number of feet.
--Dryden.
2. Conclusive; decisive; positive.
The determinate counsel and foreknowledge of God.
--Acts ii. 23.
3. Determined or resolved upon. [Obs.]
My determinate voyage. --Shak.
4. Of determined purpose; resolute. [Obs.]
More determinate to do than skillful how to do.
--Sir P.
Sidney.
Determinate inflorescence (Bot.), that in which the
flowering commences with the terminal bud of a stem, which
puts a limit to its growth; -- also called centrifugal
inflorescence.
Determinate problem (Math.), a problem which admits of a
limited number of solutions.
Determinate quantities, Determinate equations (Math.),
those that are finite in the number of values or
solutions, that is, in which the conditions of the problem
or equation determine the number.
Exponential equation Exponential Ex`po*nen"tial, a. [Cf. F. exponentiel.]
Pertaining to exponents; involving variable exponents; as, an
exponential expression; exponential calculus; an exponential
function.
Exponential curve, a curve whose nature is defined by means
of an exponential equation.
Exponential equation, an equation which contains an
exponential quantity, or in which the unknown quantity
enters as an exponent.
Exponential quantity (Math.), a quantity whose exponent is
unknown or variable, as a^x.
Exponential series, a series derived from the development
of exponential equations or quantities.
Identical equation Identical I*den"tic*al, a. [Cf. F. identique. See Identity.]
1. The same; the selfsame; the very same; not different; as,
the identical person or thing.
I can not remember a thing that happened a year ago,
without a conviction . . . that I, the same
identical person who now remember that event, did
then exist. --Reid.
2. Uttering sameness or the same truth; expressing in the
predicate what is given, or obviously implied, in the
subject; tautological.
When you say body is solid, I say that you make an
identical proposition, because it is impossible to
have the idea of body without that of solidity.
--Fleming.
Identical equation (Alg.), an equation which is true for
all values of the algebraic symbols which enter into it.
Inadequation Inadequation In*ad`e*qua"tion, n.
Want of exact correspondence. [Obs.] --Puller.
Incomplete equation Incomplete In`com*plete", a. [L. incompletus: cf. F.
incomplet. See In- not, and Complete.]
1. Not complete; not filled up; not finished; not having all
its parts, or not having them all adjusted; imperfect;
defective.
A most imperfect and incomplete divine. --Milton.
2. (Bot.) Wanting any of the usual floral organs; -- said of
a flower.
Incomplete equation (Alg.), an equation some of whose terms
are wanting; or one in which the coefficient of some one
or more of the powers of the unknown quantity is equal to
0.
Indeterminate equation Indeterminate In`de*ter"mi*nate, a. [L. indeterminatus.]
Not determinate; not certain or fixed; indefinite; not
precise; as, an indeterminate number of years. --Paley.
Indeterminate analysis (Math.), that branch of analysis
which has for its object the solution of indeterminate
problems.
Indeterminate coefficients (Math.), coefficients
arbitrarily assumed for convenience of calculation, or to
facilitate some artifice of analysis. Their values are
subsequently determined.
Indeterminate equation (Math.), an equation in which the
unknown quantities admit of an infinite number of values,
or sets of values. A group of equations is indeterminate
when it contains more unknown quantities than there are
equations.
Indeterminate inflorescence (Bot.), a mode of inflorescence
in which the flowers all arise from axillary buds, the
terminal bud going on to grow and sometimes continuing the
stem indefinitely; -- called also acropetal, botryose,
centripetal, & indefinite inflorescence. --Gray.
Indeterminate problem (Math.), a problem which admits of an
infinite number of solutions, or one in which there are
fewer imposed conditions than there are unknown or
required results.
Indeterminate quantity (Math.), a quantity which has no
fixed value, but which may be varied in accordance with
any proposed condition.
Indeterminate series (Math.), a series whose terms proceed
by the powers of an indeterminate quantity, sometimes also
with indeterminate exponents, or indeterminate
coefficients. -- In`de*ter"mi*nate*ly adv. --
In`de*ter"mi*nate*ness, n.
Inequation Inequation In`e*qua"tion, n. (Math.)
An inequality.
Intrinsic equation of a curve Intrinsic In*trin"sic ([i^]n*tr[i^]n"s[i^]k), a. [L.
intrinsecus inward, on the inside; intra within + secus
otherwise, beside; akin to E. second: cf. F. intrins[`e]que.
See Inter-, Second, and cf. Extrinsic.]
1. Inward; internal; hence, true; genuine; real; essential;
inherent; not merely apparent or accidental; -- opposed to
extrinsic; as, the intrinsic value of gold or silver;
the intrinsic merit of an action; the intrinsic worth or
goodness of a person.
He was better qualified than they to estimate justly
the intrinsic value of Grecian philosophy and
refinement. --I. Taylor.
2. (Anat.) Included wholly within an organ or limb, as
certain groups of muscles; -- opposed to extrinsic.
Intrinsic energy of a body (Physics), the work it can do in
virtue of its actual condition, without any supply of
energy from without.
Intrinsic equation of a curve (Geom.), the equation which
expresses the relation which the length of a curve,
measured from a given point of it, to a movable point, has
to the angle which the tangent to the curve at the movable
point makes with a fixed line.
Intrinsic value. See the Note under Value, n.
Syn: Inherent; innate; natural; real; genuine.
Personal equation Personal Per"son*al, a. [L. personalis: cf. F. personnel.]
1. Pertaining to human beings as distinct from things.
Every man so termed by way of personal difference.
--Hooker.
2. Of or pertaining to a particular person; relating to, or
affecting, an individual, or each of many individuals;
peculiar or proper to private concerns; not public or
general; as, personal comfort; personal desire.
The words are conditional, -- If thou doest well, --
and so personal to Cain. --Locke.
3. Pertaining to the external or bodily appearance;
corporeal; as, personal charms. --Addison.
4. Done in person; without the intervention of another.
``Personal communication.' --Fabyan.
The immediate and personal speaking of God. --White.
5. Relating to an individual, his character, conduct,
motives, or private affairs, in an invidious and offensive
manner; as, personal reflections or remarks.
6. (Gram.) Denoting person; as, a personal pronoun.
Personal action (Law), a suit or action by which a man
claims a debt or personal duty, or damages in lieu of it;
or wherein he claims satisfaction in damages for an injury
to his person or property, or the specific recovery of
goods or chattels; -- opposed to real action.
Personal equation. (Astron.) See under Equation.
Personal estate or property (Law), movables; chattels; --
opposed to real estate or property. It usually consists of
things temporary and movable, including all subjects of
property not of a freehold nature.
Personal identity (Metaph.), the persistent and continuous
unity of the individual person, which is attested by
consciousness.
Personal pronoun (Gram.), one of the pronouns I, thou,
he, she, it, and their plurals.
Personal representatives (Law), the executors or
administrators of a person deceased.
Personal rights, rights appertaining to the person; as, the
rights of a personal security, personal liberty, and
private property.
Personal tithes. See under Tithe.
Personal verb (Gram.), a verb which is modified or
inflected to correspond with the three persons.
Reciprocal equation Reciprocal Re*cip"ro*cal, a. [L. reciprocus; of unknown
origin.]
1. Recurring in vicissitude; alternate.
2. Done by each to the other; interchanging or interchanged;
given and received; due from each to each; mutual; as,
reciprocal love; reciprocal duties.
Let our reciprocal vows be remembered. --Shak.
3. Mutually interchangeable.
These two rules will render a definition reciprocal
with the thing defined. --I. Watts.
4. (Gram.) Reflexive; -- applied to pronouns and verbs, but
sometimes limited to such pronouns as express mutual
action.
5. (Math.) Used to denote different kinds of mutual relation;
often with reference to the substitution of reciprocals
for given quantities. See the Phrases below.
Reciprocal equation (Math.), one which remains unchanged in
form when the reciprocal of the unknown quantity is
substituted for that quantity.
Reciprocal figures (Geom.), two figures of the same kind
(as triangles, parallelograms, prisms, etc.), so related
that two sides of the one form the extremes of a
proportion of which the means are the two corresponding
sides of the other; in general, two figures so related
that the first corresponds in some special way to the
second, and the second corresponds in the same way to the
first.
Reciprocal proportion (Math.), a proportion such that, of
four terms taken in order, the first has to the second the
same ratio which the fourth has to the third, or the first
has to the second the same ratio which the reciprocal of
the third has to the reciprocal of the fourth. Thus, 2:5:
:20:8 form a reciprocal proportion, because 2:5:
:1/20:1/8.
Reciprocal quantities (Math.), any two quantities which
produce unity when multiplied together.
Reciprocal ratio (Math.), the ratio between the reciprocals
of two quantities; as, the reciprocal ratio of 4 to 9 is
that of 3/4 to 1/9.
Reciprocal terms (Logic), those terms which have the same
signification, and, consequently, are convertible, and may
be used for each other.
Syn: Mutual; alternate.
Usage: Reciprocal, Mutual. The distinctive idea of mutual
is, that the parties unite by interchange in the same
act; as, a mutual covenant; mutual affection, etc. The
distinctive idea of reciprocal is, that one party acts
by way of return or response to something previously
done by the other party; as, a reciprocal kindness;
reciprocal reproaches, etc. Love is reciprocal when
the previous affection of one party has drawn forth
the attachment of the other. To make it mutual in the
strictest sense, the two parties should have fallen in
love at the same time; but as the result is the same,
the two words are here used interchangeably. The
ebbing and flowing of the tide is a case where the
action is reciprocal, but not mutual.
Root of an equation 2. An edible or esculent root, especially of such plants as
produce a single root, as the beet, carrot, etc.; as, the
root crop.
3. That which resembles a root in position or function, esp.
as a source of nourishment or support; that from which
anything proceeds as if by growth or development; as, the
root of a tooth, a nail, a cancer, and the like.
Specifically:
(a) An ancestor or progenitor; and hence, an early race; a
stem.
They were the roots out of which sprang two
distinct people. --Locke.
(b) A primitive form of speech; one of the earliest terms
employed in language; a word from which other words
are formed; a radix, or radical.
(c) The cause or occasion by which anything is brought
about; the source. ``She herself . . . is root of
bounty.' --Chaucer.
The love of money is a root of all kinds of
evil. --1 Tim. vi.
10 (rev. Ver.)
(d) (Math.) That factor of a quantity which when
multiplied into itself will produce that quantity;
thus, 3 is a root of 9, because 3 multiplied into
itself produces 9; 3 is the cube root of 27.
(e) (Mus.) The fundamental tone of any chord; the tone
from whose harmonics, or overtones, a chord is
composed. --Busby.
(f) The lowest place, position, or part. ``Deep to the
roots of hell.' --Milton. ``The roots of the
mountains.' --Southey.
4. (Astrol.) The time which to reckon in making calculations.
When a root is of a birth yknowe [known]. --Chaucer.
A["e]rial roots. (Bot.)
(a) Small roots emitted from the stem of a plant in the
open air, which, attaching themselves to the bark of
trees, etc., serve to support the plant.
(b) Large roots growing from the stem, etc., which descend
and establish themselves in the soil. See Illust. of
Mangrove.
Multiple primary root (Bot.), a name given to the numerous
roots emitted from the radicle in many plants, as the
squash.
Primary root (Bot.), the central, first-formed, main root,
from which the rootlets are given off.
Root and branch, every part; wholly; completely; as, to
destroy an error root and branch.
Root-and-branch men, radical reformers; -- a designation
applied to the English Independents (1641). See Citation
under Radical, n., 2.
Root barnacle (Zo["o]l.), one of the Rhizocephala.
Root hair (Bot.), one of the slender, hairlike fibers found
on the surface of fresh roots. They are prolongations of
the superficial cells of the root into minute tubes.
--Gray.
Root leaf (Bot.), a radical leaf. See Radical, a., 3
(b) .
Root louse (Zo["o]l.), any plant louse, or aphid, which
lives on the roots of plants, as the Phylloxera of the
grapevine. See Phylloxera.
Root of an equation (Alg.), that value which, substituted
for the unknown quantity in an equation, satisfies the
equation.
Root of a nail
(Anat.), the part of a nail which is covered by the skin.
Root of a tooth (Anat.), the part of a tooth contained in
the socket and consisting of one or more fangs.
Secondary roots (Bot.), roots emitted from any part of the
plant above the radicle.
To strike root, To take root, to send forth roots; to
become fixed in the earth, etc., by a root; hence, in
general, to become planted, fixed, or established; to
increase and spread; as, an opinion takes root. ``The
bended twigs take root.' --Milton.
Simple equation 12. (Min.) Homogenous.
13. (Zo["o]l.) Consisting of a single individual or zooid;
as, a simple ascidian; -- opposed to compound.
Simple contract (Law), any contract, whether verbal or
written, which is not of record or under seal. --J. W.
Smith. --Chitty.
Simple equation (Alg.), an eqyation containing but one
unknown quantity, and that quantity only in the first
degree.
Simple eye (Zo["o]l.), an eye having a single lens; --
opposed to compound eye.
Simple interest. See under Interest.
Simple larceny. (Law) See under Larceny.
Simple obligation (Rom. Law), an obligation which does not
depend for its execution upon any event provided for by
the parties, or is not to become void on the happening of
any such event. --Burrill.
Syn: Single; uncompounded; unmingled; unmixed; mere;
uncombined; elementary; plain; artless; sincere;
harmless; undesigning; frank; open; unaffected;
inartificial; unadorned; credulous; silly; foolish;
shallow; unwise.
Usage: Simple, Silly. One who is simple is sincere,
unaffected, and inexperienced in duplicity, -- hence
liable to be duped. A silly person is one who is
ignorant or weak and also self-confident; hence, one
who shows in speech and act a lack of good sense.
Simplicity is incompatible with duplicity, artfulness,
or vanity, while silliness is consistent with all
three. Simplicity denotes lack of knowledge or of
guile; silliness denotes want of judgment or right
purpose, a defect of character as well as of
education.
I am a simple woman, much too weak To oppose
your cunning. --Shak.
He is the companion of the silliest people in
their most silly pleasure; he is ready for every
impertinent entertainment and diversion. --Law.
Simultaneous equations Simultaneous Si`mul*ta"ne*ous, a. [LL. simultim at the same
time, fr. L. simul. See Simulate.]
Existing, happening, or done, at the same time; as,
simultaneous events. -- Si`mul*ta"ne*ous*ly, adv. --
Si`mul*ta"ne*ous*ness, n.
Simultaneous equations (Alg.), two or more equations in
which the values of the unknown quantities entering them
are the same at the same time in both or in all.
To reduce an equation 4. To bring to a certain state or condition by grinding,
pounding, kneading, rubbing, etc.; as, to reduce a
substance to powder, or to a pasty mass; to reduce fruit,
wood, or paper rags, to pulp.
It were but right And equal to reduce me to my dust.
--Milton.
5. To bring into a certain order, arrangement,
classification, etc.; to bring under rules or within
certain limits of descriptions and terms adapted to use in
computation; as, to reduce animals or vegetables to a
class or classes; to reduce a series of observations in
astronomy; to reduce language to rules.
6. (Arith.)
(a) To change, as numbers, from one denomination into
another without altering their value, or from one
denomination into others of the same value; as, to
reduce pounds, shillings, and pence to pence, or to
reduce pence to pounds; to reduce days and hours to
minutes, or minutes to days and hours.
(b) To change the form of a quantity or expression without
altering its value; as, to reduce fractions to their
lowest terms, to a common denominator, etc.
7. (Chem.) To bring to the metallic state by separating from
impurities; hence, in general, to remove oxygen from; to
deoxidize; to combine with, or to subject to the action
of, hydrogen; as, ferric iron is reduced to ferrous iron;
or metals are reduced from their ores; -- opposed to
oxidize.
8. (Med.) To restore to its proper place or condition, as a
displaced organ or part; as, to reduce a dislocation, a
fracture, or a hernia.
Reduced iron (Chem.), metallic iron obtained through
deoxidation of an oxide of iron by exposure to a current
of hydrogen or other reducing agent. When hydrogen is used
the product is called also iron by hydrogen.
To reduce an equation (Alg.), to bring the unknown quantity
by itself on one side, and all the known quantities on the
other side, without destroying the equation.
To reduce an expression (Alg.), to obtain an equivalent
expression of simpler form.
To reduce a square (Mil.), to reform the line or column
from the square.
Syn: To diminish; lessen; decrease; abate; shorten; curtail;
impair; lower; subject; subdue; subjugate; conquer.
Transcendental equation Trancscendental Tranc`scen*den"tal, a. [Cf. F. transcendantal,
G. transcendental.]
1. Supereminent; surpassing others; as, transcendental being
or qualities.
2. (Philos.) In the Kantian system, of or pertaining to that
which can be determined a priori in regard to the
fundamental principles of all human knowledge. What is
transcendental, therefore, transcends empiricism; but is
does not transcend all human knowledge, or become
transcendent. It simply signifies the a priori or
necessary conditions of experience which, though affording
the conditions of experience, transcend the sphere of that
contingent knowledge which is acquired by experience.
3. Vaguely and ambitiously extravagant in speculation,
imagery, or diction.
Note: In mathematics, a quantity is said to be transcendental
relative to another quantity when it is expressed as a
transcendental function of the latter; thus, a^x,
10^2x, log x, sin x, tan x, etc., are transcendental
relative to x.
Transcendental curve (Math.), a curve in which one ordinate
is a transcendental function of the other.
Transcendental equation (Math.), an equation into which a
transcendental function of one of the unknown or variable
quantities enters.
Transcendental function. (Math.) See under Function.
Syn: Transcendental, Empirical.
Usage: These terms, with the corresponding nouns,
transcendentalism and empiricism, are of comparatively
recent origin. Empirical refers to knowledge which is
gained by the experience of actual phenomena, without
reference to the principles or laws to which they are
to be referred, or by which they are to be explained.
Transcendental has reference to those beliefs or
principles which are not derived from experience, and
yet are absolutely necessary to make experience
possible or useful. Such, in the better sense of the
term, is the transcendental philosophy, or
transcendentalism. Each of these words is also used in
a bad sense, empiricism applying to that one-sided
view of knowledge which neglects or loses sight of the
truths or principles referred to above, and trusts to
experience alone; transcendentalism, to the opposite
extreme, which, in its deprecation of experience,
loses sight of the relations which facts and phenomena
sustain to principles, and hence to a kind of
philosophy, or a use of language, which is vague,
obscure, fantastic, or extravagant.
Zonal equation Zonal on"al, a. [L. zonalis.]
Of or pertaining to a zone; having the form of a zone or
zones.
Zonal equation (Crystallog.), the mathematical relation
which belongs to all the planes of a zone, and expresses
their common position with reference to the axes.
Zonal structure (Crystallog.), a structure characterized by
the arrangements of color, inclusions, etc., of a crystal
in parallel or concentric layers, which usually follow the
outline of the crystal, and mark the changes that have
taken place during its growth.
Zonal symmetry. (Biol.) See the Note under Symmetry.
