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slovo definícia equation (encz) equation,rovnice n: [mat.] Equation (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] equation (wn) equation n 1: a mathematical statement that two expressions are equal 2: a state of being essentially equal or equivalent; equally balanced; "on a par with the best" [syn: equality, equivalence, equation, par] 3: the act of regarding as equal [syn: equation, equating]

podobné slovo definícia algebraic equation (encz) algebraic equation,algebraická rovnice n: [mat.] difference equation (encz) difference equation,diferenční rovnice n: [mat.] differential equation (encz) differential equation,diferenciální rovnice n: [mat.] equation of exchange (encz) equation of exchange,rovnice směny [eko.] RNDr. Pavel Piskač equations (encz) equations,rovnice pl. Zdeněk Brož exponential equation (encz) exponential equation, n: inequation (encz) inequation,nerovnice n: [mat.] linear equation (encz) linear equation, n: ordinary differential equation (encz) ordinary differential equation,obyčejná diferenciální rovnice [mat.] partial differential equation (encz) partial differential equation,parciální diferenciální rovnice [mat.] personal equation (encz) personal equation, n: quadratic equation (encz) quadratic equation,kvadratická rovnice n: [mat.] Milan Svoboda reduced form equation (encz) reduced form equation, regression equation (encz) regression equation, n: simultaneous equations (encz) simultaneous equations,soustava rovnic Vít Profant structural equation (encz) structural equation, wave equation (encz) wave equation, n: Absolute equation (gcide) Absolute \Ab"so*lute\, a. [L. absolutus, p. p. of absolvere: cf. F. absolu. See Absolve.] 1. Loosed from any limitation or condition; uncontrolled; unrestricted; unconditional; as, absolute authority, monarchy, sovereignty, an absolute promise or command; absolute power; an absolute monarch. [1913 Webster] 2. Complete in itself; perfect; consummate; faultless; as, absolute perfection; absolute beauty. [1913 Webster] So absolute she seems, And in herself complete. --Milton. [1913 Webster] 3. Viewed apart from modifying influences or without comparison with other objects; actual; real; -- opposed to relative and comparative; as, absolute motion; absolute time or space. [1913 Webster] Note: Absolute rights and duties are such as pertain to man in a state of nature as contradistinguished from relative rights and duties, or such as pertain to him in his social relations. [1913 Webster] 4. Loosed from, or unconnected by, dependence on any other being; self-existent; self-sufficing. [1913 Webster] Note: In this sense God is called the Absolute by the Theist. The term is also applied by the Pantheist to the universe, or the total of all existence, as only capable of relations in its parts to each other and to the whole, and as dependent for its existence and its phenomena on its mutually depending forces and their laws. [1913 Webster] 5. Capable of being thought or conceived by itself alone; unconditioned; non-relative. [1913 Webster] Note: It is in dispute among philosopher whether the term, in this sense, is not applied to a mere logical fiction or abstraction, or whether the absolute, as thus defined, can be known, as a reality, by the human intellect. [1913 Webster] To Cusa we can indeed articulately trace, word and thing, the recent philosophy of the absolute. --Sir W. Hamilton. [1913 Webster] 6. Positive; clear; certain; not doubtful. [R.] [1913 Webster] I am absolute 't was very Cloten. --Shak. [1913 Webster] 7. Authoritative; peremptory. [R.] [1913 Webster] The peddler stopped, and tapped her on the head, With absolute forefinger, brown and ringed. --Mrs. Browning. [1913 Webster] 8. (Chem.) Pure; unmixed; as, absolute alcohol. [1913 Webster] 9. (Gram.) Not immediately dependent on the other parts of the sentence in government; as, the case absolute. See Ablative absolute, under Ablative. [1913 Webster] Absolute curvature (Geom.), that curvature of a curve of double curvature, which is measured in the osculating plane of the curve. Absolute equation (Astron.), the sum of the optic and eccentric equations. Absolute space (Physics), space considered without relation to material limits or objects. Absolute terms. (Alg.), such as are known, or which do not contain the unknown quantity. --Davies & Peck. Absolute temperature (Physics), the temperature as measured on a scale determined by certain general thermo-dynamic principles, and reckoned from the absolute zero. Absolute zero (Physics), the be ginning, or zero point, in the scale of absolute temperature. It is equivalent to -273[deg] centigrade or -459.4[deg] Fahrenheit. [1913 Webster] Syn: Positive; peremptory; certain; unconditional; unlimited; unrestricted; unqualified; arbitrary; despotic; autocratic. [1913 Webster]Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Adequation (gcide) Adequation \Ad`e*qua"tion\, n. [L. adaequatio.] The act of equalizing; act or result of making adequate; an equivalent. [Obs.] --Bp. Barlow. [1913 Webster] Biquadratic equation (gcide) Biquadratic \Bi`quad*rat"ic\, a. [Pref. bi- + quadratic: cf. F. biquadratique.] (Math.) Of or pertaining to the biquadrate, or fourth power. [1913 Webster] 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. [1913 Webster] Construction of an equation (gcide) 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. [1913 Webster] 2. The form or manner of building or putting together the parts of anything; structure; arrangement. [1913 Webster] An astrolabe of peculiar construction. --Whewell. [1913 Webster] 3. (Gram.) The arrangement and connection of words in a sentence; syntactical arrangement. [1913 Webster] Some particles . . . in certain constructions have the sense of a whole sentence contained in them. --Locke. [1913 Webster] 4. The method of construing, interpreting, or explaining a declaration or fact; an attributed sense or meaning; understanding; explanation; interpretation; sense. [1913 Webster] Any person . . . might, by the sort of construction that would be put on this act, become liable to the penalties of treason. --Hallam. [1913 Webster] 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. [1913 Webster] Interpretation properly precedes construction, but it does not go beyond the written text. --Parsons. [1913 Webster] 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. [1913 Webster] Cubic equation (gcide) 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. [1913 Webster] 2. (Crystallog.) Isometric or monometric; as, cubic cleavage. See Crystallization. [1913 Webster] 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. [1913 Webster] Determinate equations (gcide) 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. [1913 Webster] Quantity of words and a determinate number of feet. --Dryden. [1913 Webster] 2. Conclusive; decisive; positive. [1913 Webster] The determinate counsel and foreknowledge of God. --Acts ii. 23. [1913 Webster] 3. Determined or resolved upon. [Obs.] [1913 Webster] My determinate voyage. --Shak. [1913 Webster] 4. Of determined purpose; resolute. [Obs.] [1913 Webster] More determinate to do than skillful how to do. --Sir P. Sidney. [1913 Webster] 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. [1913 Webster] Discussion of an equation (gcide) 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. [archaic] [1913 Webster] 2. The act of discussing or exchanging reasons; examination by argument; debate; disputation; agitation. [1913 Webster] The liberty of discussion is the great safeguard of all other liberties. --Macaulay. [1913 Webster] Discussion of a problem or Discussion of an equation (Math.), the operation of assigning different reasonable values to the arbitrary quantities and interpreting the result. --Math. Dict. [1913 Webster] Equation (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equation box (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equation clock (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equation of a curve (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equation of condition (gcide) Condition \Con*di"tion\, n. [F., fr. L. conditio (better condicio) agreement, compact, condition; con- + a root signifying to show, point out, akin to dicere to say, dicare to proclaim, dedicate. See Teach, Token.] 1. Mode or state of being; state or situation with regard to external circumstances or influences, or to physical or mental integrity, health, strength, etc.; predicament; rank; position, estate. [1913 Webster] I am in my condition A prince, Miranda; I do think, a king. --Shak. [1913 Webster] And O, what man's condition can be worse Than his whom plenty starves and blessings curse? --Cowley. [1913 Webster] The new conditions of life. --Darwin. [1913 Webster] 2. Essential quality; property; attribute. [1913 Webster] It seemed to us a condition and property of divine powers and beings to be hidden and unseen to others. --Bacon. [1913 Webster] 3. Temperament; disposition; character. [Obs.] [1913 Webster] The condition of a saint and the complexion of a devil. --Shak. [1913 Webster] 4. That which must exist as the occasion or concomitant of something else; that which is requisite in order that something else should take effect; an essential qualification; stipulation; terms specified. [1913 Webster] I had as lief take her dowry with this condition, to be whipped at the high cross every morning. --Shak. [1913 Webster] Many are apt to believe remission of sins, but they believe it without the condition of repentance. --Jer. Taylor. [1913 Webster] 5. (Law) A clause in a contract, or agreement, which has for its object to suspend, to defeat, or in some way to modify, the principal obligation; or, in case of a will, to suspend, revoke, or modify a devise or bequest. It is also the case of a future uncertain event, which may or may not happen, and on the occurrence or non-occurrence of which, the accomplishment, recission, or modification of an obligation or testamentary disposition is made to depend. --Blount. Tomlins. Bouvier. Wharton. [1913 Webster] Equation of condition. (Math.) See under Equation. On condition or Upon condition (that), used for if in introducing conditional sentences. "Upon condition thou wilt swear to pay him tribute . . . thou shalt be placed as viceroy under him." --Shak. Conditions of sale, the terms on which it is proposed to sell property by auction; also, the instrument containing or expressing these terms. Syn: State; situation; circumstances; station; case; mode; plight; predicament; stipulation; qualification; requisite; article; provision; arrangement. See State. [1913 Webster] Equation of equinoxes (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equation of payments (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equation of the center (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equation of time (gcide) Time \Time\, n.; pl. Times. [OE. time, AS. t[imac]ma, akin to t[imac]d time, and to Icel. t[imac]mi, Dan. time an hour, Sw. timme. [root]58. See Tide, n.] 1. Duration, considered independently of any system of measurement or any employment of terms which designate limited portions thereof. [1913 Webster] The time wasteth [i. e. passes away] night and day. --Chaucer. [1913 Webster] I know of no ideas . . . that have a better claim to be accounted simple and original than those of space and time. --Reid. [1913 Webster] 2. A particular period or part of duration, whether past, present, or future; a point or portion of duration; as, the time was, or has been; the time is, or will be. [1913 Webster] God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets. --Heb. i. 1. [1913 Webster] 3. The period at which any definite event occurred, or person lived; age; period; era; as, the Spanish Armada was destroyed in the time of Queen Elizabeth; -- often in the plural; as, ancient times; modern times. [1913 Webster] 4. The duration of one's life; the hours and days which a person has at his disposal. [1913 Webster] Believe me, your time is not your own; it belongs to God, to religion, to mankind. --Buckminster. [1913 Webster] 5. A proper time; a season; an opportunity. [1913 Webster] There is . . . a time to every purpose. --Eccl. iii. 1. [1913 Webster] The time of figs was not yet. --Mark xi. 13. [1913 Webster] 6. Hour of travail, delivery, or parturition. [1913 Webster] She was within one month of her time. --Clarendon. [1913 Webster] 7. Performance or occurrence of an action or event, considered with reference to repetition; addition of a number to itself; repetition; as, to double cloth four times; four times four, or sixteen. [1913 Webster] Summers three times eight save one. --Milton. [1913 Webster] 8. The present life; existence in this world as contrasted with immortal life; definite, as contrasted with infinite, duration. [1913 Webster] Till time and sin together cease. --Keble. [1913 Webster] 9. (Gram.) Tense. [1913 Webster] 10. (Mus.) The measured duration of sounds; measure; tempo; rate of movement; rhythmical division; as, common or triple time; the musician keeps good time. [1913 Webster] Some few lines set unto a solemn time. --Beau. & Fl. [1913 Webster] Note: Time is often used in the formation of compounds, mostly self-explaining; as, time-battered, time-beguiling, time-consecrated, time-consuming, time-enduring, time-killing, time-sanctioned, time-scorner, time-wasting, time-worn, etc. [1913 Webster] Absolute time, time irrespective of local standards or epochs; as, all spectators see a lunar eclipse at the same instant of absolute time. Apparent time, the time of day reckoned by the sun, or so that 12 o'clock at the place is the instant of the transit of the sun's center over the meridian. Astronomical time, mean solar time reckoned by counting the hours continuously up to twenty-four from one noon to the next. At times, at distinct intervals of duration; now and then; as, at times he reads, at other times he rides. Civil time, time as reckoned for the purposes of common life in distinct periods, as years, months, days, hours, etc., the latter, among most modern nations, being divided into two series of twelve each, and reckoned, the first series from midnight to noon, the second, from noon to midnight. Common time (Mil.), the ordinary time of marching, in which ninety steps, each twenty-eight inches in length, are taken in one minute. Equation of time. See under Equation, n. In time. (a) In good season; sufficiently early; as, he arrived in time to see the exhibition. (b) After a considerable space of duration; eventually; finally; as, you will in time recover your health and strength. Mean time. See under 4th Mean. Quick time (Mil.), time of marching, in which one hundred and twenty steps, each thirty inches in length, are taken in one minute. Sidereal time. See under Sidereal. Standard time, the civil time that has been established by law or by general usage over a region or country. In England the standard time is Greenwich mean solar time. In the United States and Canada four kinds of standard time have been adopted by the railroads and accepted by the people, viz., Eastern, Central, Mountain, and Pacific time, corresponding severally to the mean local times of the 75th, 90th, 105th, and 120th meridians west from Greenwich, and being therefore five, six, seven, and eight hours slower than Greenwich time. Time ball, a ball arranged to drop from the summit of a pole, to indicate true midday time, as at Greenwich Observatory, England. --Nichol. Time bargain (Com.), a contract made for the sale or purchase of merchandise, or of stock in the public funds, at a certain time in the future. Time bill. Same as Time-table. [Eng.] Time book, a book in which is kept a record of the time persons have worked. Time detector, a timepiece provided with a device for registering and indicating the exact time when a watchman visits certain stations in his beat. Time enough, in season; early enough. "Stanly at Bosworth field, . . . came time enough to save his life." --Bacon. Time fuse, a fuse, as for an explosive projectile, which can be so arranged as to ignite the charge at a certain definite interval after being itself ignited. Time immemorial, or Time out of mind. (Eng. Law) See under Immemorial. Time lock, a lock having clockwork attached, which, when wound up, prevents the bolt from being withdrawn when locked, until a certain interval of time has elapsed. Time of day, salutation appropriate to the times of the day, as "good morning," "good evening," and the like; greeting. To kill time. See under Kill, v. t. To make time. (a) To gain time. (b) To occupy or use (a certain) time in doing something; as, the trotting horse made fast time. To move against time, To run against time, or {To go against time}, to move, run, or go a given distance without a competitor, in the quickest possible time; or, to accomplish the greatest distance which can be passed over in a given time; as, the horse is to run against time. True time. (a) Mean time as kept by a clock going uniformly. (b) (Astron.) Apparent time as reckoned from the transit of the sun's center over the meridian. [1913 Webster] [1913 Webster]Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equation watch (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equational box (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Equations of condition (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Exponential equation (gcide) Exponential \Ex`po*nen"tial\, a. [Cf. F. exponentiel.] 1. Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function. [1913 Webster] 2. changing over time in an exponential manner, i. e. increasing or decreasing by a fixed ratio for each unit of time; as, exponential growth; exponential decay. [PJC] Note: Exponential growth is characteristic of bacteria and other living populations in circumstances where the conditions of growth are favorable, and all required nutrients are plentiful. For example, the bacterium Escherichia coli in rich media may double in number every 20 minutes until one of the nutrients becomes exhausted or waste products begin to inhibit growth. Many fascinating thought experiments are proposed on the theme of exponential growth. One may calculate, for example how long it would take the progeny of one Escherichia coli to equal the mass of the known universe if it multiplied unimpeded at such a rate. The answer, assuming the equivalent of 10^80 hydrogen atoms in the universe, is less than three days. Exponential increases in a quantity can be surprising, and this principle is often used by banks to make investment at a certain rate of interest seem to be very profitable over time. Exponential decay is exhibited by decay of radioactive materials and some chemical reactions (first order reactions), in which one-half of the initial quantity of radioactive element (or chemical substance) is lost for each lapse of a characteristic time called the half-life. [PJC] 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. [1913 Webster] Identical equation (gcide) 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. [1913 Webster] 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. [1913 Webster] 2. Uttering sameness or the same truth; expressing in the predicate what is given, or obviously implied, in the subject; tautological. [1913 Webster] 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. [1913 Webster] Identical equation (Alg.), an equation which is true for all values of the algebraic symbols which enter into it. [1913 Webster] Identic Inadequation (gcide) Inadequation \In*ad`e*qua"tion\, n. Lack of exact correspondence. [Obs.] --Puller. [1913 Webster] Incomplete equation (gcide) Incomplete \In`com*plete"\, a. [L. incompletus: cf. F. incomplet. See In- not, and Complete.] [1913 Webster] 1. Not complete; not filled up; not finished; not having all its parts, or not having them all adjusted; imperfect; defective. [1913 Webster] A most imperfect and incomplete divine. --Milton. [1913 Webster] 2. (Bot.) Wanting any of the usual floral organs; -- said of a flower. [1913 Webster] 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. [1913 Webster] Indeterminate equation (gcide) 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. [1913 Webster] 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 inflorescence}, botryose inflorescence, {centripetal inflorescence}, and 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. [1913 Webster] Inequation (gcide) Inequation \In`e*qua"tion\, n. (Math.) An inequality. [1913 Webster] Intrinsic equation of a curve (gcide) 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.] [1913 Webster] 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. [1913 Webster] He was better qualified than they to estimate justly the intrinsic value of Grecian philosophy and refinement. --I. Taylor. [1913 Webster] 2. (Anat.) Included wholly within an organ or limb, as certain groups of muscles; -- opposed to extrinsic. [1913 Webster] 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. [1913 Webster] Lateral equation (gcide) Lateral \Lat"er*al\, a. [L. lateralis, fr. latus, lateris, side: cf. F. lat['e]ral.] 1. Of or pertaining to the sides; as, the lateral walls of a house; the lateral branches of a tree. [1913 Webster] 2. (Anat.) Lying at, or extending toward, the side; away from the mesial plane; external; -- opposed to mesial. [1913 Webster] 3. Directed to the side; as, a lateral view of a thing. [1913 Webster] Lateral cleavage (Crystallog.), cleavage parallel to the lateral planes. Lateral equation (Math.), an equation of the first degree. [Obs.] Lateral line (Anat.), in fishes, a line of sensory organs along either side of the body, often marked by a distinct line of color. Lateral pressure or stress (Mech.), a pressure or stress at right angles to the length, as of a beam or bridge; -- distinguished from longitudinal pressure or stress. Lateral strength (Mech.), strength which resists a tendency to fracture arising from lateral pressure. Lateral system (Bridge Building), the system of horizontal braces (as between two vertical trusses) by which lateral stiffness is secured. [1913 Webster] lateral Linear differential equation (gcide) Linear \Lin"e*ar\ (l[i^]n"[-e]*[~e]r), a. [L. linearis, linearius, fr. linea line: cf. F. lin['e]aire. See 3d Line.] 1. Of or pertaining to a line; consisting of lines; in a straight direction; lineal. [1913 Webster] 2. (Bot.) Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf. [1913 Webster] 3. Thinking in a step-by-step analytical and logical fashion; contrasted with holistic, i.e. thinking in terms of complex interrelated patterns; as, linear thinkers. [PJC] Linear thinkers concluded that by taking the world apart, the actions of people were more predictable and controllable. --David Morris (Conference presentation, Fairfield University, October 31, 1997) Linear differential equation (Math.), an equation which is of the first degree, when the expression which is equated to zero is regarded as a function of the dependent variable and its differential coefficients. Linear equation (Math.), an equation of the first degree between two variables; -- so called because every such equation may be considered as representing a right line. Linear measure, the measurement of length. Linear numbers (Math.), such numbers as have relation to length only: such is a number which represents one side of a plane figure. If the plane figure is square, the linear figure is called a root. Linear problem (Geom.), a problem which may be solved geometrically by the use of right lines alone. Linear transformation (Alg.), a change of variables where each variable is replaced by a function of the first degree in the new variable. [1913 Webster] Linear equation (gcide) Linear \Lin"e*ar\ (l[i^]n"[-e]*[~e]r), a. [L. linearis, linearius, fr. linea line: cf. F. lin['e]aire. See 3d Line.] 1. Of or pertaining to a line; consisting of lines; in a straight direction; lineal. [1913 Webster] 2. (Bot.) Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf. [1913 Webster] 3. Thinking in a step-by-step analytical and logical fashion; contrasted with holistic, i.e. thinking in terms of complex interrelated patterns; as, linear thinkers. [PJC] Linear thinkers concluded that by taking the world apart, the actions of people were more predictable and controllable. --David Morris (Conference presentation, Fairfield University, October 31, 1997) Linear differential equation (Math.), an equation which is of the first degree, when the expression which is equated to zero is regarded as a function of the dependent variable and its differential coefficients. Linear equation (Math.), an equation of the first degree between two variables; -- so called because every such equation may be considered as representing a right line. Linear measure, the measurement of length. Linear numbers (Math.), such numbers as have relation to length only: such is a number which represents one side of a plane figure. If the plane figure is square, the linear figure is called a root. Linear problem (Geom.), a problem which may be solved geometrically by the use of right lines alone. Linear transformation (Alg.), a change of variables where each variable is replaced by a function of the first degree in the new variable. [1913 Webster] Literal equation (gcide) Literal \Lit"er*al\ (l[i^]t"[~e]r*al), a. [F. lit['e]ral, litt['e]ral, L. litteralis, literalis, fr. littera, litera, a letter. See Letter.] 1. According to the letter or verbal expression; real; not figurative or metaphorical; as, the literal meaning of a phrase. [1913 Webster] It hath but one simple literal sense whose light the owls can not abide. --Tyndale. [1913 Webster] 2. Following the letter or exact words; not free. [1913 Webster] A middle course between the rigor of literal translations and the liberty of paraphrasts. --Hooker. [1913 Webster] 3. Consisting of, or expressed by, letters. [1913 Webster] The literal notation of numbers was known to Europeans before the ciphers. --Johnson. [1913 Webster] 4. Giving a strict or literal construction; unimaginative; matter-of-fact; -- applied to persons. [1913 Webster] Literal contract (Law), a contract of which the whole evidence is given in writing. --Bouvier. Literal equation (Math.), an equation in which known quantities are expressed either wholly or in part by means of letters; -- distinguished from a numerical equation. [1913 Webster] Normal equation (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Normal equations (gcide) Normal \Nor"mal\ (n[^o]r"mal), a. [L. normalis, fr. norma rule, pattern, carpenter's square; prob. akin to noscere to know; cf. Gr. gnw`rimos well known, gnw`mwn gnomon, also, carpenter's square: cf. F. normal. See Known, and cf. Abnormal, Enormous.] [1913 Webster] 1. According to an established norm, rule, or principle; conformed to a type, standard, or regular form; performing the proper functions; not abnormal; regular; natural; analogical. [1913 Webster] Deviations from the normal type. --Hallam. [1913 Webster] 2. (Geom.) According to a square or rule; perpendicular; forming a right angle; as, a line normal to the base. Specifically: Of or pertaining to a normal. [1913 Webster] 3. (Chem.) Standard; original; exact; typical. Specifically: (a) (Quantitative Analysis) Denoting a solution of such strength that every cubic centimeter contains the same number of milligrams of the element in question as the number of its molecular weight. (b) (Chem.) Denoting certain hypothetical compounds, as acids from which the real acids are obtained by dehydration; thus, normal sulphuric acid and normal nitric acid are respectively S(OH)6, and N(OH)5. (c) (Organ. Chem.) Denoting that series of hydrocarbons in which no carbon atom is bound to more than two other carbon atoms; as, normal pentane, hexane, etc. Cf. Iso-. [1913 Webster] Normal equations (Method of Least Squares), a set of equations of the first degree equal in number to the number of unknown quantities, and derived from the observations by a specified process. The solution of the normal equations gives the most probable values of the unknown quantities. Normal group (Geol.), a group of rocks taken as a standard. --Lyell. Normal place (of a planet or comet) (Astron.), the apparent place in the heavens of a planet or comet at a specified time, the place having been determined by a considerable number of observations, extending perhaps over many days, and so combined that the accidental errors of observation have largely balanced each other. Normal school, a school whose methods of instruction are to serve as a model for imitation; an institution for the training of teachers. [1913 Webster] Syn: Normal, Regular, Ordinary. Usage: Regular and ordinary are popular terms of well-known signification; normal has now a more specific sense, arising out of its use in science. A thing is normal, or in its normal state, when strictly conformed to those principles of its constitution which mark its species or to the standard of a healthy and natural condition. It is abnormal when it departs from those principles. [1913 Webster] Numerical equation (gcide) Numeric \Nu*mer"ic\, Numerical \Nu*mer"ic*al\, a. [Cf. F. num['e]rique. See Number, n.] [1913 Webster] 1. Belonging to number; denoting number; consisting in numbers; expressed by numbers, and not letters; as, numerical characters; a numerical equation; a numerical statement. [1913 Webster] Note: Numerical, as opposed to algebraical, is used to denote a value irrespective of its sign; thus, -5 is numerically greater than -3, though algebraically less. [1913 Webster] 2. The same in number; hence, identically the same; identical; as, the same numerical body. [Obs.] --South. [1913 Webster] Would to God that all my fellow brethren, which with me bemoan the loss of their books, . . . might rejoice for the recovery thereof, though not the same numerical volumes. --Fuller. [1913 Webster] 3. relating to or having ability to think in or work with numbers; as, tests for rating numerical aptitude. Contrasted with verbal. Syn: mathematical. [WordNet 1.5] Numerical equation (Alg.), an equation which has all the quantities except the unknown expressed in numbers; -- distinguished from literal equation. Numerical value of an equation or expression, that deduced by substituting numbers for the letters, and reducing. [1913 Webster] Order of a differential equation (gcide) Order \Or"der\, n. [OE. ordre, F. ordre, fr. L. ordo, ordinis. Cf. Ordain, Ordinal.] [1913 Webster] 1. Regular arrangement; any methodical or established succession or harmonious relation; method; system; as: (a) Of material things, like the books in a library. (b) Of intellectual notions or ideas, like the topics of a discource. (c) Of periods of time or occurrences, and the like. [1913 Webster] The side chambers were . . . thirty in order. --Ezek. xli. 6. [1913 Webster] Bright-harnessed angels sit in order serviceable. --Milton. [1913 Webster] Good order is the foundation of all good things. --Burke. [1913 Webster] 2. Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order. --Locke. [1913 Webster] 3. The customary mode of procedure; established system, as in the conduct of debates or the transaction of business; usage; custom; fashion. --Dantiel. [1913 Webster] And, pregnant with his grander thought, Brought the old order into doubt. --Emerson. [1913 Webster] 4. Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet; as, to preserve order in a community or an assembly. [1913 Webster] 5. That which prescribes a method of procedure; a rule or regulation made by competent authority; as, the rules and orders of the senate. [1913 Webster] The church hath authority to establish that for an order at one time which at another time it may abolish. --Hooker. [1913 Webster] 6. A command; a mandate; a precept; a direction. [1913 Webster] Upon this new fright, an order was made by both houses for disarming all the papists in England. --Clarendon. [1913 Webster] 7. Hence: A commission to purchase, sell, or supply goods; a direction, in writing, to pay money, to furnish supplies, to admit to a building, a place of entertainment, or the like; as, orders for blankets are large. [1913 Webster] In those days were pit orders -- beshrew the uncomfortable manager who abolished them. --Lamb. [1913 Webster] 8. A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a group or division of men in the same social or other position; also, a distinct character, kind, or sort; as, the higher or lower orders of society; talent of a high order. [1913 Webster] They are in equal order to their several ends. --Jer. Taylor. [1913 Webster] Various orders various ensigns bear. --Granville. [1913 Webster] Which, to his order of mind, must have seemed little short of crime. --Hawthorne. [1913 Webster] 9. A body of persons having some common honorary distinction or rule of obligation; esp., a body of religious persons or aggregate of convents living under a common rule; as, the Order of the Bath; the Franciscan order. [1913 Webster] Find a barefoot brother out, One of our order, to associate me. --Shak. [1913 Webster] The venerable order of the Knights Templars. --Sir W. Scott. [1913 Webster] 10. An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry; -- often used in the plural; as, to take orders, or to take holy orders, that is, to enter some grade of the ministry. [1913 Webster] 11. (Arch.) The disposition of a column and its component parts, and of the entablature resting upon it, in classical architecture; hence (as the column and entablature are the characteristic features of classical architecture) a style or manner of architectural designing. [1913 Webster] Note: The Greeks used three different orders, easy to distinguish, Doric, Ionic, and Corinthian. The Romans added the Tuscan, and changed the Doric so that it is hardly recognizable, and also used a modified Corinthian called Composite. The Renaissance writers on architecture recognized five orders as orthodox or classical, -- Doric (the Roman sort), Ionic, Tuscan, Corinthian, and Composite. See Illust. of Capital. [1913 Webster] 12. (Nat. Hist.) An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia. [1913 Webster] Note: The Linnaean artificial orders of plants rested mainly on identity in the numer of pistils, or agreement in some one character. Natural orders are groups of genera agreeing in the fundamental plan of their flowers and fruit. A natural order is usually (in botany) equivalent to a family, and may include several tribes. [1913 Webster] 13. (Rhet.) The placing of words and members in a sentence in such a manner as to contribute to force and beauty or clearness of expression. [1913 Webster] 14. (Math.) Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation. [1913 Webster] Artificial order or Artificial system. See {Artificial classification}, under Artificial, and Note to def. 12 above. Close order (Mil.), the arrangement of the ranks with a distance of about half a pace between them; with a distance of about three yards the ranks are in {open order}. The four Orders, The Orders four, the four orders of mendicant friars. See Friar. --Chaucer. General orders (Mil.), orders issued which concern the whole command, or the troops generally, in distinction from special orders. Holy orders. (a) (Eccl.) The different grades of the Christian ministry; ordination to the ministry. See def. 10 above. (b) (R. C. Ch.) A sacrament for the purpose of conferring a special grace on those ordained. In order to, for the purpose of; to the end; as means to. The best knowledge is that which is of greatest use in order to our eternal happiness. --Tillotson. Minor orders (R. C. Ch.), orders beneath the diaconate in sacramental dignity, as acolyte, exorcist, reader, doorkeeper. Money order. See under Money. Natural order. (Bot.) See def. 12, Note. Order book. (a) A merchant's book in which orders are entered. (b) (Mil.) A book kept at headquarters, in which all orders are recorded for the information of officers and men. (c) A book in the House of Commons in which proposed orders must be entered. [Eng.] Order in Council, a royal order issued with and by the advice of the Privy Council. [Great Britain] Order of battle (Mil.), the particular disposition given to the troops of an army on the field of battle. Order of the day, in legislative bodies, the special business appointed for a specified day. Order of a differential equation (Math.), the greatest index of differentiation in the equation. Sailing orders (Naut.), the final instructions given to the commander of a ship of war before a cruise. Sealed orders, orders sealed, and not to be opened until a certain time, or arrival at a certain place, as after a ship is at sea. Standing order. (a) A continuing regulation for the conduct of parliamentary business. (b) (Mil.) An order not subject to change by an officer temporarily in command. To give order, to give command or directions. --Shak. To take order for, to take charge of; to make arrangements concerning. [1913 Webster] Whiles I take order for mine own affairs. --Shak. [1913 Webster] Syn: Arrangement; management. See Direction. [1913 Webster] Personal equation (gcide) Personal \Per"son*al\ (p[~e]r"s[u^]n*al), a. [L. personalis: cf. F. personnel.] 1. Pertaining to human beings as distinct from things. [1913 Webster] Every man so termed by way of personal difference. --Hooker. [1913 Webster] 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. [1913 Webster] The words are conditional, -- If thou doest well, -- and so personal to Cain. --Locke. [1913 Webster] 3. Pertaining to the external or bodily appearance; corporeal; as, personal charms. --Addison. [1913 Webster] 4. Done in person; without the intervention of another. "Personal communication." --Fabyan. [1913 Webster] The immediate and personal speaking of God. --White. [1913 Webster] 5. Relating to an individual, his character, conduct, motives, or private affairs, in an invidious and offensive manner; as, personal reflections or remarks. [1913 Webster] 6. (Gram.) Denoting person; as, a personal pronoun. [1913 Webster] 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 Personal property (Law), movables; chattels; -- opposed to real estate or real 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. [1913 Webster]Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] Polar equation of a line (gcide) Polar \Po"lar\, a. [Cf. F. polaire. See Pole of the earth.] 1. Of or pertaining to one of the poles of the earth, or of a sphere; situated near, or proceeding from, one of the poles; as, polar regions; polar seas; polar winds. [1913 Webster] 2. Of or pertaining to the magnetic pole, or to the point to which the magnetic needle is directed. [1913 Webster] 3. (Geom.) Pertaining to, reckoned from, or having a common radiating point; as, polar coordinates. [1913 Webster] Polar axis, that axis of an astronomical instrument, as an equatorial, which is parallel to the earths axis. Polar bear (Zool.), a large bear (Ursus maritimus syn. Thalarctos maritimus) inhabiting the arctic regions. It sometimes measures nearly nine feet in length and weighs 1,600 pounds. It is partially amphibious, very powerful, and the most carnivorous of all the bears. The fur is white, tinged with yellow. Called also White bear. See Bear. Polar body, Polar cell, or Polar globule (Biol.), a minute cell which separates by karyokinesis from the ovum during its maturation. In the maturation of ordinary ova two polar bodies are formed, but in parthogenetic ova only one. The first polar body formed is usually larger than the second one, and often divides into two after its separation from the ovum. Each of the polar bodies removes maternal chromatin from the ovum to make room for the chromatin of the fertilizing spermatozoon; but their functions are not fully understood. Polar circles (Astron. & Geog.), two circles, each at a distance from a pole of the earth equal to the obliquity of the ecliptic, or about 23[deg] 28', the northern called the arctic circle, and the southern the antarctic circle. Polar clock, a tube, containing a polarizing apparatus, turning on an axis parallel to that of the earth, and indicating the hour of the day on an hour circle, by being turned toward the plane of maximum polarization of the light of the sky, which is always 90[deg] from the sun. Polar coordinates. See under 3d Coordinate. Polar dial, a dial whose plane is parallel to a great circle passing through the poles of the earth. --Math. Dict. Polar distance, the angular distance of any point on a sphere from one of its poles, particularly of a heavenly body from the north pole of the heavens. Polar equation of a line or Polar equation of a surface, an equation which expresses the relation between the polar coordinates of every point of the line or surface. Polar forces (Physics), forces that are developed and act in pairs, with opposite tendencies or properties in the two elements, as magnetism, electricity, etc. Polar hare (Zool.), a large hare of Arctic America ({Lepus arcticus}), which turns pure white in winter. It is probably a variety of the common European hare ({Lepus timidus}). Polar lights, the aurora borealis or australis. Polar opposition, or Polaric opposition or {Polar contrast} or Polaric contrast (Logic), an opposition or contrast made by the existence of two opposite conceptions which are the extremes in a species, as white and black in colors; hence, as great an opposition or contrast as possible. Polar projection. See under Projection. Polar spherical triangle (Spherics), a spherical triangle whose three angular points are poles of the sides of a given triangle. See 4th Pole, 2. Polar whale (Zool.), the right whale, or bowhead. See Whale. [1913 Webster] Polar equation of a surface (gcide) Polar \Po"lar\, a. [Cf. F. polaire. See Pole of the earth.] 1. Of or pertaining to one of the poles of the earth, or of a sphere; situated near, or proceeding from, one of the poles; as, polar regions; polar seas; polar winds. [1913 Webster] 2. Of or pertaining to the magnetic pole, or to the point to which the magnetic needle is directed. [1913 Webster] 3. (Geom.) Pertaining to, reckoned from, or having a common radiating point; as, polar coordinates. [1913 Webster] Polar axis, that axis of an astronomical instrument, as an equatorial, which is parallel to the earths axis. Polar bear (Zool.), a large bear (Ursus maritimus syn. Thalarctos maritimus) inhabiting the arctic regions. It sometimes measures nearly nine feet in length and weighs 1,600 pounds. It is partially amphibious, very powerful, and the most carnivorous of all the bears. The fur is white, tinged with yellow. Called also White bear. See Bear. Polar body, Polar cell, or Polar globule (Biol.), a minute cell which separates by karyokinesis from the ovum during its maturation. In the maturation of ordinary ova two polar bodies are formed, but in parthogenetic ova only one. The first polar body formed is usually larger than the second one, and often divides into two after its separation from the ovum. Each of the polar bodies removes maternal chromatin from the ovum to make room for the chromatin of the fertilizing spermatozoon; but their functions are not fully understood. Polar circles (Astron. & Geog.), two circles, each at a distance from a pole of the earth equal to the obliquity of the ecliptic, or about 23[deg] 28', the northern called the arctic circle, and the southern the antarctic circle. Polar clock, a tube, containing a polarizing apparatus, turning on an axis parallel to that of the earth, and indicating the hour of the day on an hour circle, by being turned toward the plane of maximum polarization of the light of the sky, which is always 90[deg] from the sun. Polar coordinates. See under 3d Coordinate. Polar dial, a dial whose plane is parallel to a great circle passing through the poles of the earth. --Math. Dict. Polar distance, the angular distance of any point on a sphere from one of its poles, particularly of a heavenly body from the north pole of the heavens. Polar equation of a line or Polar equation of a surface, an equation which expresses the relation between the polar coordinates of every point of the line or surface. Polar forces (Physics), forces that are developed and act in pairs, with opposite tendencies or properties in the two elements, as magnetism, electricity, etc. Polar hare (Zool.), a large hare of Arctic America ({Lepus arcticus}), which turns pure white in winter. It is probably a variety of the common European hare ({Lepus timidus}). Polar lights, the aurora borealis or australis. Polar opposition, or Polaric opposition or {Polar contrast} or Polaric contrast (Logic), an opposition or contrast made by the existence of two opposite conceptions which are the extremes in a species, as white and black in colors; hence, as great an opposition or contrast as possible. Polar projection. See under Projection. Polar spherical triangle (Spherics), a spherical triangle whose three angular points are poles of the sides of a given triangle. See 4th Pole, 2. Polar whale (Zool.), the right whale, or bowhead. See Whale. [1913 Webster] Reciprocal equation (gcide) Reciprocal \Re*cip"ro*cal\ (r[-e]*s[i^]p"r[-o]*kal), a. [L. reciprocus; of unknown origin.] 1. Recurring in vicissitude; alternate. [1913 Webster] 2. Done by each to the other; interchanging or interchanged; given and received; due from each to each; mutual; as, reciprocal love; reciprocal duties. [1913 Webster] Let our reciprocal vows be remembered. --Shak. [1913 Webster] 3. Mutually interchangeable. [1913 Webster] These two rules will render a definition reciprocal with the thing defined. --I. Watts. [1913 Webster] 4. (Gram.) Reflexive; -- applied to pronouns and verbs, but sometimes limited to such pronouns as express mutual action. [1913 Webster] 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. [1913 Webster] 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 1/4 to [frac19]. Reciprocal terms (Logic), those terms which have the same signification, and, consequently, are convertible, and may be used for each other. [1913 Webster] 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. [1913 Webster] Relativistic mass equation (gcide) Relativistic mass equation \Rel`a*tiv*ist"ic mass e*qua"tion\, n. (physics) an equation expressing the mass of an object as a function of its velocity: as the velocity v of an object increases, its mass m increases from its rest mass m0 according to the equation: m = m0/root{1 - v^2/c^2} where c is the speed of light in a vacuum. If the speed of an object were to become equal to that of light, it can be seen that the mass would be infinite, from which it follows that nothing can accelerate up to or beyond the speed of light. [PJC] Note: The theoretical possibility that there are particles which always move faster than light cannot at present be disproved and is not denied by this equation; in such a case, the relativistic mass equation asserts that such particles can never decelerate to or below the speed of light. Such hypothetical particles are referred to as tachyons. [PJC] Root of an equation (gcide) Root \Root\, n. [Icel. r[=o]t (for vr[=o]t); akin to E. wort, and perhaps to root to turn up the earth. See Wort.] 1. (Bot.) (a) The underground portion of a plant, whether a true root or a tuber, a bulb or rootstock, as in the potato, the onion, or the sweet flag. (b) The descending, and commonly branching, axis of a plant, increasing in length by growth at its extremity only, not divided into joints, leafless and without buds, and having for its offices to fix the plant in the earth, to supply it with moisture and soluble matters, and sometimes to serve as a reservoir of nutriment for future growth. A true root, however, may never reach the ground, but may be attached to a wall, etc., as in the ivy, or may hang loosely in the air, as in some epiphytic orchids. [1913 Webster] 2. An edible or esculent root, especially of such plants as produce a single root, as the beet, carrot, etc.; as, the root crop. [1913 Webster] 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. [1913 Webster] They were the roots out of which sprang two distinct people. --Locke. [1913 Webster] (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. [1913 Webster] The love of money is a root of all kinds of evil. --1 Tim. vi. 10 (rev. Ver.) [1913 Webster] (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. [1913 Webster] (f) The lowest place, position, or part. "Deep to the roots of hell." --Milton. "The roots of the mountains." --Southey. [1913 Webster] 4. (Astrol.) The time which to reckon in making calculations. [1913 Webster] When a root is of a birth yknowe [known]. --Chaucer. [1913 Webster] Aerial 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 (Zool.), 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 (Zool.), 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. [1913 Webster] Secular equation (gcide) Secular \Sec"u*lar\, a. [OE. secular, seculer. L. saecularis, fr. saeculum a race, generation, age, the times, the world; perhaps akin to E. soul: cf. F. s['e]culier.] 1. Coming or observed once in an age or a century. [1913 Webster] The secular year was kept but once a century. --Addison. [1913 Webster] 2. Pertaining to an age, or the progress of ages, or to a long period of time; accomplished in a long progress of time; as, secular inequality; the secular refrigeration of the globe. [1913 Webster] 3. Of or pertaining to this present world, or to things not spiritual or holy; relating to temporal as distinguished from eternal interests; not immediately or primarily respecting the soul, but the body; worldly. [1913 Webster] New foes arise, Threatening to bind our souls with secular chains. --Milton. [1913 Webster] 4. (Eccl.) Not regular; not bound by monastic vows or rules; not confined to a monastery, or subject to the rules of a religious community; as, a secular priest. [1913 Webster] He tried to enforce a stricter discipline and greater regard for morals, both in the religious orders and the secular clergy. --Prescott. [1913 Webster] 5. Belonging to the laity; lay; not clerical. [1913 Webster] I speak of folk in secular estate. --Chaucer. [1913 Webster] Secular equation (Astron.), the algebraic or numerical expression of the magnitude of the inequalities in a planet's motion that remain after the inequalities of a short period have been allowed for. Secular games (Rom. Antiq.), games celebrated, at long but irregular intervals, for three days and nights, with sacrifices, theatrical shows, combats, sports, and the like. Secular music, any music or songs not adapted to sacred uses. Secular hymn or Secular poem, a hymn or poem composed for the secular games, or sung or rehearsed at those games. [1913 Webster] Simple equation (gcide) Simple \Sim"ple\, a. [Compar. Simpler; superl. Simplest.] [F., fr. L. simplus, or simplex, gen. simplicis. The first part of the Latin words is probably akin to E. same, and the sense, one, one and the same; cf. L. semel once, singuli one to each, single. Cg. Single, a., Same, a., and for the last part of the word cf. Double, Complex.] 1. Single; not complex; not infolded or entangled; uncombined; not compounded; not blended with something else; not complicated; as, a simple substance; a simple idea; a simple sound; a simple machine; a simple problem; simple tasks. [1913 Webster] 2. Plain; unadorned; as, simple dress. "Simple truth." --Spenser. "His simple story." --Burns. [1913 Webster] 3. Mere; not other than; being only. [1913 Webster] A medicine . . . whose simple touch Is powerful to araise King Pepin. --Shak. [1913 Webster] 4. Not given to artifice, stratagem, or duplicity; undesigning; sincere; true. [1913 Webster] Full many fine men go upon my score, as simple as I stand here, and I trust them. --Marston. [1913 Webster] Must thou trust Tradition's simple tongue? --Byron. [1913 Webster] To be simple is to be great. --Emerson. [1913 Webster] 5. Artless in manner; unaffected; unconstrained; natural; inartificial;; straightforward. [1913 Webster] In simple manners all the secret lies. --Young. [1913 Webster] 6. Direct; clear; intelligible; not abstruse or enigmatical; as, a simple statement; simple language. [1913 Webster] 7. Weak in intellect; not wise or sagacious; of but moderate understanding or attainments; hence, foolish; silly. "You have simple wits." --Shak. [1913 Webster] The simple believeth every word; but the prudent man looketh well to his going. --Prov. xiv. 15. [1913 Webster] 8. Not luxurious; without much variety; plain; as, a simple diet; a simple way of living. [1913 Webster] Thy simple fare and all thy plain delights. --Cowper. [1913 Webster] 9. Humble; lowly; undistinguished. [1913 Webster] A simple husbandman in garments gray. --Spenser. [1913 Webster] Clergy and laity, male and female, gentle and simple made the fuel of the same fire. --Fuller. [1913 Webster] 10. (BOt.) Without subdivisions; entire; as, a simple stem; a simple leaf. [1913 Webster] 11. (Chem.) Not capable of being decomposed into anything more simple or ultimate by any means at present known; elementary; thus, atoms are regarded as simple bodies. Cf. Ultimate, a. [1913 Webster] Note: A simple body is one that has not as yet been decomposed. There are indications that many of our simple elements are still compound bodies, though their actual decomposition into anything simpler may never be accomplished. [1913 Webster] 12. (Min.) Homogenous. [1913 Webster] 13. (Zool.) Consisting of a single individual or zooid; as, a simple ascidian; -- opposed to compound. [1913 Webster] 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 equation containing but one unknown quantity, and that quantity only in the first degree. Simple eye (Zool.), 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. [1913 Webster] 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. [1913 Webster] I am a simple woman, much too weak To oppose your cunning. --Shak. [1913 Webster] He is the companion of the silliest people in their most silly pleasure; he is ready for every impertinent entertainment and diversion. --Law. [1913 Webster] Simultaneous equations (gcide) 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. [1913 Webster] 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. [1913 Webster] Theory of equations (gcide) Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F. ['e]quation equation. See Equate.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night. --Rowe. [1913 Webster] 2. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc. [1913 Webster] 3. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion. [1913 Webster] Absolute equation. See under Absolute. Equation box, or Equational box, a system of differential gearing used in spinning machines for regulating the twist of the yarn. It resembles gearing used in equation clocks for showing apparent time. Equation of the center (Astron.), the difference between the place of a planet as supposed to move uniformly in a circle, and its place as moving in an ellipse. Equations of condition (Math.), equations formed for deducing the true values of certain quantities from others on which they depend, when different sets of the latter, as given by observation, would yield different values of the quantities sought, and the number of equations that may be found is greater than the number of unknown quantities. Equation of a curve (Math.), an equation which expresses the relation between the co["o]rdinates of every point in the curve. Equation of equinoxes (Astron.), the difference between the mean and apparent places of the equinox. Equation of payments (Arith.), the process of finding the mean time of payment of several sums due at different times. Equation of time (Astron.), the difference between mean and apparent time, or between the time of day indicated by the sun, and that by a perfect clock going uniformly all the year round. Equation clock or Equation watch, a timepiece made to exhibit the differences between mean solar and apparent solar time. --Knight. Normal equation. See under Normal. Personal equation (Astron.), the difference between an observed result and the true qualities or peculiarities in the observer; particularly the difference, in an average of a large number of observation, between the instant when an observer notes a phenomenon, as the transit of a star, and the assumed instant of its actual occurrence; or, relatively, the difference between these instants as noted by two observers. It is usually only a fraction of a second; -- sometimes applied loosely to differences of judgment or method occasioned by temperamental qualities of individuals. Theory of equations (Math.), the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity. [1913 Webster] To reduce an equation (gcide) Reduce \Re*duce"\ (r[-e]*d[=u]s"), v. t. [imp. & p. p. Reduced (-d[=u]st"),; p. pr. & vb. n. Reducing (-d[=u]"s[i^]ng).] [L. reducere, reductum; pref. red-. re-, re- + ducere to lead. See Duke, and cf. Redoubt, n.] 1. To bring or lead back to any former place or condition. [Obs.] [1913 Webster] And to his brother's house reduced his wife. --Chapman. [1913 Webster] The sheep must of necessity be scattered, unless the great Shephered of souls oppose, or some of his delegates reduce and direct us. --Evelyn. [1913 Webster] 2. To bring to any inferior state, with respect to rank, size, quantity, quality, value, etc.; to diminish; to lower; to degrade; to impair; as, to reduce a sergeant to the ranks; to reduce a drawing; to reduce expenses; to reduce the intensity of heat. "An ancient but reduced family." --Sir W. Scott. [1913 Webster] Nothing so excellent but a man may fasten upon something belonging to it, to reduce it. --Tillotson. [1913 Webster] Having reduced Their foe to misery beneath their fears. --Milton. [1913 Webster] Hester Prynne was shocked at the condition to which she found the clergyman reduced. --Hawthorne. [1913 Webster] 3. To bring to terms; to humble; to conquer; to subdue; to capture; as, to reduce a province or a fort. [1913 Webster] 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. [1913 Webster] It were but right And equal to reduce me to my dust. --Milton. [1913 Webster] 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. [1913 Webster] 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. [1913 Webster] 7. (Chem.) To add an electron to an atom or ion. Specifically: To remove oxygen from; to deoxidize. (Metallurgy) To bring to the metallic state by separating from combined oxygen and impurities; as, metals are reduced from their ores. (Chem.) To combine with, or to subject to the action of, hydrogen or any other reducing agent; as, ferric iron is reduced to ferrous iron; aldehydes can be reduced to alcohols by lithium hydride; -- opposed to oxidize. [1913 Webster +PJC] 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. [1913 Webster] 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. [1913 Webster] Syn: To diminish; lessen; decrease; abate; shorten; curtail; impair; lower; subject; subdue; subjugate; conquer. [1913 Webster] Transcendental equation (gcide) Transcendental \Tran`scen*den"tal\, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster] 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. [1913 Webster] 3. Vaguely and ambitiously extravagant in speculation, imagery, or diction. [1913 Webster] 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. [1913 Webster] 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. [1913 Webster] 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. [1913 Webster] Verification of an equation (gcide) Verification \Ver`i*fi*ca"tion\, n. [Cf. F. v['e]rification.] 1. The act of verifying, or the state of being verified; confirmation; authentication. [1913 Webster] 2. (Law) (a) Confirmation by evidence. (b) A formal phrase used in concluding a plea. [1913 Webster] Verification of an equation (Math.), the operation of testing the equation of a problem, to see whether it expresses truly the conditions of the problem. --Davies & Peck. (Math. Dict.) [1913 Webster] Zonal equation (gcide) Zonal \Zon"al\, a. [L. zonalis.] Of or pertaining to a zone; having the form of a zone or zones. [1913 Webster] 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. [1913 Webster] biquadratic equation (wn) biquadratic equation n 1: an equation of the fourth degree [syn: {biquadratic equation}, biquadratic] differential equation (wn) differential equation n 1: an equation containing differentials of a function exponential equation (wn) exponential equation n 1: an equation involving exponential functions of a variable linear equation (wn) linear equation n 1: a polynomial equation of the first degree