## Analytical Sentence Examples

- The formation of spores is used as an
**analytical**method for determining whether a yeast is contaminated with another species, - for example: a sample of yeast is placed on a gypsum or porcelain block saturated with water; if in ten days at a temperature of 52° F. - The
**analytical**society thus formed in 1813 published various memoirs, and translated S. - First of all, his genetic method as applied to the mind's ideas - which laid the foundations of English
**analytical**psychology - was a step in the direction of a conception of mental life as a gradual evolution. - An exact and conscientious worker, he did much to improve and systematize the processes of
**analytical**chemistry and mineralogy, and his appreciation of the value of quantitative methods led him to become one of the earliest adherents of the Lavoisierian doctrines outside France. - The first Pitaka contains the Vinaya - that is, Rules of the Order; the second the Suttas, giving the doctrine, and the third the Abhidhamma,
**analytical**exercises in the psychological system on which the doctrine is based. - This latter work included the differential and integral calculus, the calculus of variations, the theory of attractions, and
**analytical**mechanics. - Between Roberval and Descartes there existed a feeling of ill - will, owing to the jealousy aroused in the mind of the former by the criticism which Descartes offered to some of the methods employed by him and by Pierre de Fermat; and this led him to criticize and oppose the
**analytical**methods which Descartes introduced into geometry about this time. - Most of these were simple records of patient and laborious
**analytical**operations, and it is perhaps surprising that among all the substances he analysed he only detected two new elements - beryllium (1798) in beryl and chromium (1797) in a red lead ore from Siberia. - The complete
**analytical**treatment was first given by Leonhard Euler. **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.- The germs of
**analytical**chemistry are to be found in the writings of the pharmacists and chemists of the iatrochemical period. - His fame rests upon his exposition of the principles necessary to chemistry as a secience, but of his contributions to
**analytical**inorganic chemistry little can be said. - We may, however, notice Heinrich Rose i and Friedrich WShler, 2 who, having worked up the results of their teacher Berzelius, and combined them with their own valuable observations, exerted great influence on the progress of
**analytical**chemistry by publishing works which contained admirable accounts of the then known methods of analysis. - Fresenius, the founder of the Zeitschrift fiir analytische Chemie (1862), we are particularly indebted for perfecting and systematizing the various methods of
**analytical**chemistry. - The quantitative precipitation of metals by the electric current, although known to Michael Faraday, was not applied to
**analytical**chemistry until O. - 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. - 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. - In the preceding sketch we have given a necessarily brief account of the historical development of
**analytical**chemistry in its main branches. - 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. - (I) In general
**analytical**work the standard solution contains the equivalent weight of the substance in grammes dissolved in a litre of water. - Crookes, Select Methods in
**Analytical**Chemistry). - Brown's philosophy occupies an intermediate place between the earlier Scottish school and the later
**analytical**or associational psychology. - Among the
**analytical**methods worked up by him the best known is that for the estimation of sugars by "Fehling's solution," which consists of a solution of cupric sulphate mixed with alkali and potassium-sodium tartrate (Rochelle salt). - Under the general heading "Analysis" occur the subheadings "Foundations of Analysis," with the topics theory of functions of real variables, series and other infinite processes, principles and elements of the differential and of the integral calculus, definite integrals, and calculus of variations; "Theory of Functions of Complex Variables," with the topics functions of one variable and of several variables; "Algebraic Functions and their Integrals," with the topics algebraic functions of one and of several variables, elliptic functions and single theta functions, Abelian integrals; "Other Special Functions," with the topics Euler's, Legendre's, Bessel's and automorphic functions; "Differential Equations," with the topics existence theorems, methods of solution, general theory; "Differential Forms and Differential Invariants," with the topics differential forms, including Pfaffians, transformation of differential forms, including tangential (or contact) transformations, differential invariants; "
**Analytical**Methods connected with Physical Subjects," with the topics harmonic analysis, Fourier's series, the differential equations of applied mathematics, Dirichlet's problem; "Difference Equations and Functional Equations," with the topics recurring series, solution of equations of finite differences and functional equations. - Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of
**analytical**geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces. - 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. - These headings are: "Geometry and Kinematics of Particles and Solid Bodies"; "Principles of Rational Mechanics"; "Statics of Particles, Rigid Bodies, &c."; "Kinetics of Particles, Rigid Bodies, &c."; "General
**Analytical**Mechanics"; "Statics and Dynamics of Fluids"; "Hydraulics and Fluid Resistances"; "Elasticity." - 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. - During this period logarithms were invented, trigonometry and algebra developed,
**analytical**geometry invented, dynamics put upon a sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the differential calculus by Newton and Leibnitz and the discovery of gravitation. - In addition to these departments provided for in the organic act, the university included in 1909 colleges of dentistry (three-year course), pharmacy (two-year and three-year courses), a school of mines (1891; four-year course, leading to the degree of Engineer of Mines or Metallurgical Engineer), a school of
**analytical**and applied chemistry (four-year courses, leading to the degree of Bachelor in Science in Chemistry, or in Chemical Engineering), a college of education (1906; three-year course, after two years of college work, leading to a Master's degree), a graduate school (with courses leading to the degrees of Master of Arts, of Science and of Laws, and of Doctor of Philosophy, of Science and of Civil Law), and a university summer school. - 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. - 960) roused his enthusiasm for the
**analytical**method, of which he was destined to develop the utmost capabilities. - 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. - Thus a universal science of matter and motion was derived, by an unbroken sequence of deduction, from one radical principle; and
**analytical**mechanics assumed the clear and complete form of logical perfection which it now wears. - By means of this "calculus of derived functions" Lagrange hoped to give to the solution of all
**analytical**problems the utmost "rigour of the demonstrations of the ancients"; 6 but it cannot be said that the attempt was successful. - The validity of his fundamental position was impaired by the absence of a well-constituted theory of series; the notation employed was inconvenient, and was abandoned by its inventor in the second edition of his Mecanique; while his scruples as to the admission into
**analytical**investigations of the idea of limits or vanishing ratios have long since been laid aside as idle. - The calculus of variations lay undeveloped in Euler's mode of treating isoperimetrical problems. The fruitful method, again, of the variation of elements was introduced by Euler, but adopted and perfected by Lagrange, who first recognized its supreme importance to the
**analytical**investigation of the planetary movements. - A lack of imagination and of the philosophic spirit prevented him from penetrating or drawing characters, but his
**analytical**gift, joined to persevering toil and honesty of purpose enabled him to present a faithful account of ascertained facts and a satisfactory and lucid explanation of political and economic events. - 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. - The
**analytical**tournament closed with the communication to the Academy by Laplace, 1 "Recherches sur le calcul integral," Mélanges de la Soc. Roy. - The Mecanique celeste is, even to those most conversant with
**analytical**methods, by no means easy reading. - The Exposition du Systeme du monde (Paris, 1796) has been styled by Arago "the Mecanique celeste disembarrassed of its
**analytical**paraphernalia." - By it his extraordinary
**analytical**powers became strictly subordinated to physical investigations. - The results of his many papers on this subject - characterized by him as "un des points les plus interessans du systeme du monde" - are embodied in the Mecanique celeste, and furnish one of the most remarkable proofs of his
**analytical**genius. - This reaction has taken the form of a return to the alliance between algebra and geometry (ï¿½5), on which modern
**analytical**geometry is based; the alliance, however, being concerned with the application of graphical methods to particular cases rather than to general expressions. - These applications are sometimes treated under arithmetic, sometimes under algebra; but it is more convenient to regard graphics as a separate subject, closely allied to arithmetic, algebra, mensuration and
**analytical**geometry. - Complex numbers are conveniently treated in connexion not only with the theory of equations but also with
**analytical**trigonometry, which suggests the graphic representation of a+b,l - by a line of length (a 2 +b 2)i drawn in a direction different from that of the line along which real numbers are represented. - 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. - In his famous Geometria (1637), which is really a treatise on the algebraic representation of geometric theorems, he founded the modern theory of
**analytical**geometry (see Geometry), and at the same time he rendered signal service to algebra, more especially in the theory of equations. - A general
**analytical**verification has been given by Sir G.