The complete analytical treatment was first given by Leonhard Euler.
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.
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.
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.
The quantitative precipitation of metals by the electric current, although known to Michael Faraday, was not applied to analytical chemistry until O.
In the preceding sketch we have given a necessarily brief account of the historical development of analytical chemistry in its main branches.
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.
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."
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.
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.
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 Mecanique celeste is, even to those most conversant with analytical methods, by no means easy reading.
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.
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 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.
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.
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.
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.
(I) In general analytical work the standard solution contains the equivalent weight of the substance in grammes dissolved in a litre of water.
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).
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.
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.
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.
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 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.
A general analytical verification has been given by Sir G.
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.
This latter work included the differential and integral calculus, the calculus of variations, the theory of attractions, and analytical mechanics.
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.
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.
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 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.
In analytical invention, and mastery over the calculus, the Turin mathematician was admittedly unrivalled.
Lagrange saw in the problems of nature so many occasions for analytical triumphs; Laplace regarded analytical triumphs as the means of solving the problems of nature.
Uranyl nitrate is used in photography, and also in analytical chemistry as a precipitant for phosphoric acid (as uranyl ammonium phosphate, U02 NH4 P04).
Primary, secondary and spurious bows were formed, and their radii measured; a comparison of these observations exhibited agreement with Airy's analytical values.
Such is the basis of the algebraical or modern analytical geometry.
Carrying on the same analytical method into the special department of moral philosophy, Green held that ethics applies to the peculiar conditions of social life that investigation into man's nature which metaphysics began.
It has the strength of an analytical treatise, the charm of a popular dissertation.
In the former the author sets forth the analytical process by which the laws he discovered were deduced from facts.