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Transcendental equation

Trancscendental Tranc`scen*den"tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. 2. (Philos.) In the Kantian system, of or pertaining to that which can be determined a priori in regard to the fundamental principles of all human knowledge. What is transcendental, therefore, transcends empiricism; but is does not transcend all human knowledge, or become transcendent. It simply signifies the a priori or necessary conditions of experience which, though affording the conditions of experience, transcend the sphere of that contingent knowledge which is acquired by experience. 3. Vaguely and ambitiously extravagant in speculation, imagery, or diction. Note: In mathematics, a quantity is said to be transcendental relative to another quantity when it is expressed as a transcendental function of the latter; thus, a^x, 10^2x, log x, sin x, tan x, etc., are transcendental relative to x. Transcendental curve (Math.), a curve in which one ordinate is a transcendental function of the other. Transcendental equation (Math.), an equation into which a transcendental function of one of the unknown or variable quantities enters. Transcendental function. (Math.) See under Function. Syn: Transcendental, Empirical. Usage: These terms, with the corresponding nouns, transcendentalism and empiricism, are of comparatively recent origin. Empirical refers to knowledge which is gained by the experience of actual phenomena, without reference to the principles or laws to which they are to be referred, or by which they are to be explained. Transcendental has reference to those beliefs or principles which are not derived from experience, and yet are absolutely necessary to make experience possible or useful. Such, in the better sense of the term, is the transcendental philosophy, or transcendentalism. Each of these words is also used in a bad sense, empiricism applying to that one-sided view of knowledge which neglects or loses sight of the truths or principles referred to above, and trusts to experience alone; transcendentalism, to the opposite extreme, which, in its deprecation of experience, loses sight of the relations which facts and phenomena sustain to principles, and hence to a kind of philosophy, or a use of language, which is vague, obscure, fantastic, or extravagant.

Trancscendental Tranc`scen*den"tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. 2. (Philos.) In the Kantian system, of or pertaining to that which can be determined a priori in regard to the fundamental principles of all human knowledge. What is transcendental, therefore, transcends empiricism; but is does not transcend all human knowledge, or become transcendent. It simply signifies the a priori or necessary conditions of experience which, though affording the conditions of experience, transcend the sphere of that contingent knowledge which is acquired by experience. 3. Vaguely and ambitiously extravagant in speculation, imagery, or diction. Note: In mathematics, a quantity is said to be transcendental relative to another quantity when it is expressed as a transcendental function of the latter; thus, a^x, 10^2x, log x, sin x, tan x, etc., are transcendental relative to x. Transcendental curve (Math.), a curve in which one ordinate is a transcendental function of the other. Transcendental equation (Math.), an equation into which a transcendental function of one of the unknown or variable quantities enters. Transcendental function. (Math.) See under Function. Syn: Transcendental, Empirical. Usage: These terms, with the corresponding nouns, transcendentalism and empiricism, are of comparatively recent origin. Empirical refers to knowledge which is gained by the experience of actual phenomena, without reference to the principles or laws to which they are to be referred, or by which they are to be explained. Transcendental has reference to those beliefs or principles which are not derived from experience, and yet are absolutely necessary to make experience possible or useful. Such, in the better sense of the term, is the transcendental philosophy, or transcendentalism. Each of these words is also used in a bad sense, empiricism applying to that one-sided view of knowledge which neglects or loses sight of the truths or principles referred to above, and trusts to experience alone; transcendentalism, to the opposite extreme, which, in its deprecation of experience, loses sight of the relations which facts and phenomena sustain to principles, and hence to a kind of philosophy, or a use of language, which is vague, obscure, fantastic, or extravagant.

- In applied mathematics, a transcendental equation is an equation over the real (or complex) numbers that is not algebraic, that is, if at least one of...

- 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2 − 2 = 0. The golden ratio (denoted φ {\displaystyle...

- In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the...

- integers A transcendental equation is an equation involving a transcendental function of its unknowns A parametric equation is an equation in which the...

- {\displaystyle b} the semi-minor axis. Kepler's equation is a transcendental equation because sine is a transcendental function, and it cannot be solved for E...

- Lambert's Transcendental Equation in 1758, which led to an article by Leonhard Euler in 1783 that discussed the special case of wew. The equation Lambert...

- are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities...

- relationship as a pair of intersecting circles". Its solution involves a transcendental equation. The problem derives from "A Country House Visit", one of Jan Struther's...

- to compute the multiplicative inverse of a power series. Many transcendental equations can be solved up to an arbitrary precision by using Newton's method...

- Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation...

- 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2 − 2 = 0. The golden ratio (denoted φ {\displaystyle...

- In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the...

- integers A transcendental equation is an equation involving a transcendental function of its unknowns A parametric equation is an equation in which the...

- {\displaystyle b} the semi-minor axis. Kepler's equation is a transcendental equation because sine is a transcendental function, and it cannot be solved for E...

- Lambert's Transcendental Equation in 1758, which led to an article by Leonhard Euler in 1783 that discussed the special case of wew. The equation Lambert...

- are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities...

- relationship as a pair of intersecting circles". Its solution involves a transcendental equation. The problem derives from "A Country House Visit", one of Jan Struther's...

- to compute the multiplicative inverse of a power series. Many transcendental equations can be solved up to an arbitrary precision by using Newton's method...

- Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation...

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