Word Finder - analytical

definition

Of or pertaining to analysis; resolving into elements or constituent parts

example

an analytical experiment

definition

Using analytic reasoning as opposed to synthetic.

example

an analytical mind

The complete analytical treatment was first given by Leonhard Euler.

He appears to have attended Dirichlet's lectures on theory of numbers, theory of definite integrals, and partial differential equations, and Jacobi's on analytical mechanics and higher algebra.

The Mecanique celeste is, even to those most conversant with analytical methods, by no means easy reading.

The germs of analytical chemistry are to be found in the writings of the pharmacists and chemists of the iatrochemical period.

In England this branch of chemistry is especially cared for by the Institute of Chemistry, which, since its foundation in 1877, has done much for the training of analytical chemists.

The essential point in his advance on Euler's mode of investigating curves of maximum or minimum consisted in his purely analytical conception of the subject.

Analytical Chemistry This branch of chemistry has for its province the determination of the constituents of a chemical compound or of a mixture of compounds.

In the preceding sketch we have given a necessarily brief account of the historical development of analytical chemistry in its main branches.

Brown's philosophy occupies an intermediate place between the earlier Scottish school and the later analytical or associational psychology.

The passing of the Food and Drug Acts (1875-1899) in England, and the existence of similar adulteration acts in other countries, have occasioned great progress in the analysis of foods, drugs, &c. For further information on this branch of analytical chemistry, see Adulteration.

It is unnecessary here to dwell on the precautions which can only be conveniently acquired by experience; a sound appreciation of analytical methods is only possible after the reactions and characters of individual substances have been studied, and we therefore refer the reader to the articles on the particular elements and compounds for more information on this subject.

The progress of analytical geometry led to a geometrical interpretation both of negative and also of imaginary quantities; and when a " meaning " or, more properly, an interpretation, had thus been found for the symbols in question, a reconsideration of the old algebraic problem became inevitable, and the true solution, now so obvious, was eventually obtained.

They are the best for analytical computation.

Secondly, I will describe our multilingual corpus, and our analytical procedure.

For the subjects under this heading see the articles CONIC SECTIONS; CIRCLE; CURVE; GEOMETRICAL CONTINUITY; GEOMETRY, Axioms of; GEOMETRY, Euclidean; GEOMETRY, Projective; GEOMETRY, Analytical; GEOMETRY, Line; KNOTS, MATHEMATICAL THEORY OF; MENSURATION; MODELS; PROJECTION; Surface; Trigonometry.

For the subjects of this general heading see the articles Mechanics; Dynamics, Analytical; Gyroscope; Harmonic Analysis; Wave; HYDROMechanics; Elasticity; Motion, Laws Of; Energy; Energetics; Astronomy (Celestial Mechanics); Tide.

The method of "generalized coordinates," as it is now called, by which he attained this result, is the most brilliant achievement of the analytical method.

Adrien Augier resumed the work, giving Lebeuf's text, though correcting the numerous typographical errors of the original edition (5 vols., 1883), and added a sixth volume containing an analytical table of contents.

Clebsch has shown, from purely analytical considerations (Crelle, lvi.); and then = Z d(?G, m), ?

The analytical treatment of such vortex rings is the same as for the electro-magnetic effect of a current circulating in each ring.

Bryan, in which the analytical equations of motion are deduced of a perforated solid in liquid, from considerations purely hydrodynamical.

The simplicity, moderate accuracy, and adaptability of this method to every class of substance which can be vaporized entitles it to rank as one of the most potent methods in analytical chemistry; its invention is indissolubly connected with the name of Victor Meyer, being termed "Meyer's method" to the exclusion of his other original methods.

He studied at Berlin University, where he obtained the degree of doctor of philosophy in 1825, his thesis being an analytical discussion of the theory of fractions.

On his return he removed to Berlin, where he lived as a royal pensioner till his death, which occurred on the 18th of February 18 His investigations in elliptic functions, the theory of which he established upon quite a new basis, and more particularly his development of the theta-function, as given in his great treatise Fundamenta nova theoriae functionum ellipticarum (Konigsberg, 1829), and in later papers in Crelle's Journal, constitute his grandest analytical discoveries.

It was in analytical development that Jacobi's peculiar power mainly lay, and he made many important contributions of this kind to other departments of mathematics, as a glance at the long list of papers that were published by him in Crelle's Journal and elsewhere from 1826 onwards will sufficiently indicate.

Beyond this point, analytical methods must be adopted, and the student passes to trigonometry and the infinitesimal calculus.

The third stage is analytical mensuration, the essential feature of which is that account is taken of the manner in which a figure is generated.

To prevent discontinuity of results at this stage, recapitulation from an analytical point of view is desirable.

The treatment of an angle as generated by rotation, the investigation of the relations between trigonometrical ratios and circular measure, the application of interpolation to trigonometrical tables, and the general use of graphical methods to represent continuous variation, all imply an analytical onlook, and must therefore be deferred to this stage.

There are certain special cases where the treatment is really analytical, but where, on account of the simplicity or importance of the figures involved, the analysis does not take a prominent part.

The process of unrolling is analytical, but the unrolled area can be measured by methods not applicable to other surfaces.

Similarly, analytical plane geometry deals with the curve described by a point moving in a particular way, while analytical plane mensuration deals with the figure generated by an ordinate moving so that its length varies in a particular manner depending on its position.

In the same way, in the case of a figure in three dimensions, analytical geometry is concerned with the form of the surface, while analytical mensuration is concerned with the figure as a whole.

In analytical geometry, the equation to the sphere takes the forms x 2 +y 2 +z 2 =a 2, and r=a, the first applying to rectangular Cartesian co-ordinates, the second to polar, the origin being in both cases at the centre of the sphere.

The analytical equations which represent the propagation of light in free aether, and also in aether modified by the presence of matter, were originally developed on the analogy of the equations of propagation of elastic effects in solid media.

If v varies with respect to locality, or if there is a velocity of convection (p,q,r) variable with respect to direction and position, and analytical expression of the relation (ii) assumes a more complex form; we thus derive the most general equations of electrodynamic propagation for matter treated as continuous, anyhow distributed and moving in any manner.

We have for the number of partitions an analytical theory depending on generating functions; thus for the partitions of a number n with the parts I, 2, 3, 4, 5, &c., without repetitions, writing down the product I +x.

We have such analytical formulae as that is, any number from I to 15 can be made with the parts I, 2, 4, 8; and similarly any can be made up, and in one way only, with A like formula is I - x 3 I - x9 I - x27 I x.

Thus in arithmetical calculations if the base is not expressed it is understood to be io, so that log m denotes log n m; but in analytical formulae it is understood to be e.

It follows from this property of the function that we cannot have for log x a series which shall be convergent for all values of x, as is the case with sin x and cos x, for such a series could only represent a uniform function, and in fact the equation log(I +x) =x -",, x2 +3x 3 -4x 4 + is true only when the analytical modulus of x is less than unity.

John Casey, professor of mathematics at the Catholic university of Dublin, has given elementary demonstrations founded on the theory of similitude and coaxal circles which are reproduced in his Sequel to Euclid; an analytical solution by Gergonne is given in Salmon's Conic Sections.

He was an admirer of Marx's learning and analytical power, but he would never submit to the tyrannical pedantry of Marx's school and stood up for an elemental awaking of revolutionary instincts.

The principle with which he starts and from which follows his well-known distinction between relations of ideas and matters of fact, a distinction which Kant appears to have thought identical with his distinction between analytical and synthetical judgments, is comparatively simple.

If taken in isolation this passage might appear sufficient justification for Kant's view that, according to Hume, geometrical judgments are analytical and therefore perfect.

The previous treatment of the motion of a rigid body had in every case been purely analytical, and so gave no aid to the formation of a mental picture of the body's motion; and the great value of this work lies in the fact that, as Poinsot himself says in the introduction, it enables us to represent to ourselves the motion of a rigid body as clearly as that of a moving point.

The general relations between the parabola, ellipse and hyperbola are treated in the articles Geometry, Analytical, and Conic Sections; and various projective properties are demonstrated in the article Geometry, Projective.

In the article Geometry, Analytical, it iS Shown that the general equation of the second degree represents a parabola when the highest terms form a perfect square.

Analytic This is the analytical expression of the projective Geometry.

See the bibliography to the articles Conic Sections; Geometry, Analytical; and Geometry, Projective.

On the 14th of August 1789 the Constituent Assembly made Camus its archivist, and in that capacity he organized the national archives, classified the papers of the different assemblies of the Revolution and drew up analytical tables of the procesverbaux.