Analytical sentence example

analytical
  • The complete analytical treatment was first given by Leonhard Euler.
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  • 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.
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  • The Mecanique celeste is, even to those most conversant with analytical methods, by no means easy reading.
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  • 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.
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  • 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.
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  • The germs of analytical chemistry are to be found in the writings of the pharmacists and chemists of the iatrochemical period.
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  • 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.
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  • In the preceding sketch we have given a necessarily brief account of the historical development of analytical chemistry in its main branches.
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  • Brown's philosophy occupies an intermediate place between the earlier Scottish school and the later analytical or associational psychology.
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  • They are the best for analytical computation.
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  • 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.
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  • The ordinary definition of a circle is equivalent to definition as the figure generated by the rotation of a radius of constant length in a plane, and is thus essentially analytical.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • The analytical tournament closed with the communication to the Academy by Laplace, 1 "Recherches sur le calcul integral," Mélanges de la Soc. Roy.
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  • Clebsch has shown, from purely analytical considerations (Crelle, lvi.); and then = Z d(?G, m), ?
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  • The analytical treatment of such vortex rings is the same as for the electro-magnetic effect of a current circulating in each ring.
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  • Bryan, in which the analytical equations of motion are deduced of a perforated solid in liquid, from considerations purely hydrodynamical.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • Beyond this point, analytical methods must be adopted, and the student passes to trigonometry and the infinitesimal calculus.
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  • 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.
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  • To prevent discontinuity of results at this stage, recapitulation from an analytical point of view is desirable.
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  • 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.
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  • 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.
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  • The process of unrolling is analytical, but the unrolled area can be measured by methods not applicable to other surfaces.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • Analytic This is the analytical expression of the projective Geometry.
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  • See the bibliography to the articles Conic Sections; Geometry, Analytical; and Geometry, Projective.
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  • 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.
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  • Besides pamphlets on the Catholic and slavery questions, as well as several fugitive jeux d'esprit, and a number of unsigned articles in the Analytical Review, Geddes also published a free metrical version of Select Satires of Horace (1779), and a verbal rendering of the First Book of the Iliad of Homer (1792).
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  • Analytical problems, such as the isolation of certain organic radicals, attracted his attention to begin with, but he soon turned to synthetical studies, and he was only about twenty-five years of age when an investigation, doubtless suggested by the work of his master, Bunsen, on cacodyl, yielded the interesting discovery of the organo-metallic compounds.
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  • As it happened this deductive tendency helped the development of logic. The obscurer premises of analogy and induction, together with the paucity of experience and the backward state of physical science in Aristotle's time would have baffled even his analytical genius.
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  • He agrees with Jevons in calling this second syllogism analytical deduction, and with Jevons and Sigwart in calling it hypothetical deduction.
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  • Mill confused Newton's analytical deduction with hypothetical deduction; and thereupon Jevons confused induction with both.
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  • For the same reason induction cannot be reduced to analytical deduction of the second kind in the form, S-P, M-S,.
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  • Still less can induction be reduced to analytical deduction of the first kind in the form - P-M, S-P,.
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  • This analytical, Xoyos he offers as his substitute for knowledge.
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  • Propositions analytical of a combination in the sense alleged do not give knowledge.
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  • So long as the relation of the nominal to the real essence has no other background than Locke's doctrine of perception, the conclusion that what Kant afterwards calls analytical judgments a priori and synthetic judgments a posteriori exhaust the field follows inevitably, with its corollary, which Locke himself has the courage to draw, that the natural sciences are in strictness impossible.
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  • Its analytical definition will appear later.
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  • Minot (1844-1850); see also Mr Bancroft Davis's Notes upon the Treaties of the United States with other Powers, preceded by a list of the Treaties and Conventions with Foreign Powers, chronologically arranged and followed by an Analytical Index and a Synoptical Index of the Treaties (1873).
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  • The formal analytical reduction of a system of coplanar forces is as follows.
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  • The analytical treatment of small displacements is as follows.
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  • The analytical reduction of a three-dimensional system can now be conducted as follows.
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  • The analytical calculation of the work done by a system of forces in any infinitesimal displacement is as follows.
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  • In the analytical investigations of line geometry, these six quantities, supposed subject to the relation (4), are used to specify a line, and are called the six co-ordinates of the line; they are of course equivalent to only four independent quantities.
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  • The same thing follows of course from the analytical expression (2) for the virtual work.
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  • Examples will be found in textbooks of the calculus and of analytical statics.
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  • Lagranges own proof will be found under DYNAMIcs, Analytical.
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  • Whatever he touches, lies already dead on the dissecting table, and his skill is that of the analytical pathologist.
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  • He has the perspicuity and analytical penetration of a Venetian ambassador.
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  • It oxidizes carbon compounds to carbon dioxide and water, and therefore finds extensive application in analytical organic chemistry.
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  • It was apparently intended by the author as an analytical introduction to the constructive exposition of his system, which he presently essayed in the Ethics.
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  • The problem of finding a system which reproduces a given object upon a given plane with given magnification (in so far as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties are too great.
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  • The analytical approximation theory is often employed provisionally, since its accuracy does not generally suffice.
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  • The analytical expression for the motion in the latter case involves exponential terms, one of which (except in case of a particular relation between the initial displacements and velocities) increases rapidly, being equally multiplied in equal times.
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  • Strauss's mind was almost exclusively analytical and critical, without depth of religious feeling or philosophical penetration, or historical sympathy; his work was accordingly rarely constructive.
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  • Competent judges have compared him to Leonhard Euler for his range, analytical power and introduction of new and fertile theories.
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  • He continued his labours in the theory of numbers and other analytical subjects, and communicated a long series of memoirs to the Royal Society of Sciences (Königliche Gesellschaft der Wissenschaften) at Göttingen.
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  • Plucker aimed at furnishing modern geometry with suitable analytical methods so as to give it an independent analytical development.
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  • With the development of analytical and especially of pneumatic chemistry, the air was recognized not to be one homogeneous substance, as was long supposed, and different "airs," or gases, came to be distinguished.
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  • At the commencement of his new career he enriched the academical collection with many memoirs, which excited a noble emulation between him and the Bernoullis, though this did not in any way affect their friendship. It was at this time that he carried the integral calculus to a higher degree of perfection, invented the calculation of sines, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics.
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  • He soon commenced to read the Principia, and at sixteen he had mastered a great part of that work, besides some more modern works on analytical geometry and the differential calculus.
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  • Nothing could be better fitted to call forth such mathematical powers as those of Hamilton; for Laplace's great work, rich to profusion in analytical processes alike novel and powerful, demands from the most gifted student careful and often laborious study.
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  • The larger treatises here mentioned contain very full bibliographies, and a complete analytical index to the annual literature of the Echinoderma has for many years been published in the Zoological Record (London).
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  • The analytical theory by Cartesian co-ordinates was first considered by Alexis Claude Clairaut, Recherches sur les courbes et double courbure (Paris, 1731).
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  • The term "gas analysis" is given to that branch of analytical chemistry which has for its object the quantitative determination of the components of a gaseous mixture.
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  • Analytical investigations revealed the existence of series or sequences which had no limit to the number of terms, as for example the fraction 1/(1 - x) which on division gives the series.
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  • A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two fixed points at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.
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  • The first sort is analytical; mathematical and ethical knowledge represents the second; physical science forms the third; real knowledge of self, God and the world constitutes the fourth.
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  • In expounding these, he gives throughout the pure result of analytical observation of the common moral consciousness of his age.
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  • The abundant store of just and close analytical observation contained in Aristotle's account of these notions give it a permanent interest, even beyond its historical value as a delineation of the Greek ideal of " fair and good " life.
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  • Partly, again, the analytical distinctness of Aristotle's manner brings into special prominence the difficulties that attend the Socratic effort to reconcile the ideal aspirations of men with the principles on which their practical reasonings are commonly conducted.
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  • It must be admitted that any intelligent comprehension of the subject requires at least a grasp of the fundamental conceptions of analytical geometry and the infinitesimal calculus, such as only one with some training in these subjects can be expected to have.
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  • When the subject was taken up by the continental mathematicians, using the analytical method, the question naturally arose whether the motions of three bodies under their mutual attraction could not be determined with a degree of rigour approximating to that with which Newton had solved the problem of two bodies.
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  • Voltaire, Montesquieu, the Encyclopaedists and the Physiocrats (recurring to the tradition of Bayle and Fontenelle), by dissolving in their analytical crucible all consecrated beliefs and all fixed institutions, brought back into the human society of the 18th century that humanity which had been so rudely eliminated.
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  • Since a beam of common light can be resolved into plane polarized streams and these on recomposition give a stream with properties indistinguishable from those of common light, whatever their relative retardation may be, it is natural to assume that an analytical representation of common light can be obtained in which no longitudinal vector occurs.
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  • But in modern geometry, especially in the analytical and projective methods, the "principle of continuity" renders advisable the inclusion of the other forms of the section of a cone, viz.
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  • In analytical geometry the conic is represented by an algebraic equation of the second degree, and the species of conic is solely determined by means of certain relations between the coefficients.
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  • The subject of analytical geometry which he virtually created enabled him to view the conic sections as algebraic equations of the second degree, the form of the section depending solely on the coefficients.
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  • He also rendered good service to historians by the publication of his Collection des meilleures dissertations, notices et traites relatifs 4 l'histoire de France (20 vols., 1826-1840); in the absence of an index, since Leber did not give one, an analytical table of contents is to be found in Alfred Franklin's Sources de l'histoire de France (1876, pp. 342 sqq.).
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  • The methods sketched here do not yet exhaust the armoury of the analytical chemist, but it can only be pointed out in passing that the detection of hydroxylated acids enables the analyst to ascertain the presence of castor oil, just as the isolation and determination of oxidized fatty acids enables him to differentiate blown oils from other oils.
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  • This he treated synthetically, to the total exclusion of analysis, which he hated, and he is said to have considered it a disgrace to synthetical geometry if equal or higher results were obtained by analytical methods.
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  • It is true that Leibnitz himself did not work out any complete doctrine of knowledge, but in the hands of his successors the theory took definite shape in the principle that the whole work of cognition is in essence analytical.
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  • For the one adequate explanation is found in the logical axiom of analytical thinking; for the other no such explanation is to be had.
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  • Metaphysics, on the other hand, is analytical in method; in it the notions are given, and by analysis they are cleared up. It is to be observed that the description of mathematics as synthetic is not an anticipation of the critical doctrine on the same subject.
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  • In the Dissertation sense-perception had been taken as receptivity of representations of objects, and experience as the product of the treatment of such representations by the logical or analytical processes of understanding.
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  • The notion of the ego as a purely logical unity, containing in itself no element of difference, and having only analytical identity, is fundamental in the critical system, and lies at the root of all its difficulties and perplexities.
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  • The paper juxtaposed narratives and analytical passages.
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  • Enhance your skills with regard to both the analytical and visual aspects of i2 analyst 's Notebook.
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  • And yet these oppositions do not seem to be purely analytical constructions.
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  • He's very, very calm, very analytical.
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  • The approach is not analytical, but the approach of ' designing the way forward ' .
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  • So there will be an active, thoughtful, appreciative, even analytical faculty present during most of meditative practice.
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  • Papert sincerely wants to escape the one-sidedness of an overly analytical, abstract approach to learning.
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  • Essentially analytical skills are the main requirement along with the ability to understand and contextualize the business environment.
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  • The course also prepares students well for more traditional courses that may have analytical, theoretical or technology components.
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  • Each analytical batch contained at least 5 method blanks, consisting of the entire analytical procedure but omitting the sample.
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  • The award recognized Vanessa's innovative research project in analytical biochemistry.
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  • But rather than playing buffoon to Lee's philosopher, Richard is more laid back and less analytical.
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  • The challenges posed by these demands require the analytical chemist to be well versed in a diverse range of scientific areas.
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  • Secondly, I will describe our multilingual corpus, and our analytical procedure.
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  • He seems to have informed Picasso's move from analytical cubism to synthetic Cubism, for instance.
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  • F Attainment of intended learning outcomes appreciably deficient in critical respects, lacking secure basis in relevant factual and analytical dimensions.
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  • Methods The analytical methodology for determining dioxin and PCB concentrations in cows ' milk has already been reported 15.
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  • Her background is mainly in analytical geochemistry, with a bias toward ' environmental ' topics.
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  • Whatever the reason, analytical hypnotherapy is, by far, the best method used here for any of these problems.
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  • Analytical thinking requires both intuition and reason, or more correctly, both intuition and insight.
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  • The student will also develop investigative, analytical and communication skills through the writing of the report.
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  • You should have good manual dexterity, be pc literate & have some experience working with computer controlled analytical equipment.
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  • With recent advances in analytical methodology, soil components can be separated and characterized at an increasing level of detail.
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  • The Laboratory Group will provide mutual with analytical chemistry and stability services for revenue of more than $ 1.5m per annum.
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  • Enhance your skills with regard to both the analytical and visual aspects of i2 analyst's notebook.
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  • The course will adopt an analytical rather than a narrative approach to this formative period in the history of the medieval papacy.
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  • Analytical expertise also supports experimental and clinical pharmacokinetics, including support for clinical trials involving new drugs at Mount Vernon Hospital and elsewhere.
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  • In the final year, you focus on analytical science biotechnology medicinal chemistry molecular pharmacology.
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  • It will present a perspective on epistemology that overcomes the existing divides between analytical and continental philosophy.
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  • The project will combine analytical studies and numerical modeling tools for simulating wave propagation in fractured porous rock.
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  • Members of the Center staff are practicing psychoanalysts, analytical psychologists or psychoanalytic psychotherapists.
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  • It aims to provide an experience of learning from which it's graduates will qualify as competent and responsible practitioners of Jungian analytical psychotherapy.
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  • Using these analytical solutions, the effect of the velocity shear on the damping rate of the surface wave can easily be investigated.
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  • Give presentations to training courses, officers and visitors to the Force in respect of analytical techniques.
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  • The technique is particularly powerful analytical tool for obtaining compositional depth profiles.
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  • Mass spectrometry is used both as an analytical tool and for metabolic studies using stable isotope tracers.
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  • When he began his active career it was generally believed that, although some instances of the synthetical production of organic substances had been observed, on the whole organic chemistry must remain an analytical science and could not become a constructive one, because the formation of the substances with which it deals required the intervention of vital activity in some shape.
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  • Apart from his administrative duties Fresenius occupied himself almost exclusively with analytical chemistry, and the fullness and accuracy of his text-books on that subject (of which that on qualitative analysis first appeared in 1841 and that on quantitative in 1846) soon rendered them standard works.
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  • Only a reference can be made in this summary to the many fields in which analytical chemistry has been developed.
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  • His defence, at first only a pamphlet, became in its third edition a lengthy treatise entitled Inquiry into the Relation of Cause and Ef f ect, and is a fine specimen of Brown's analytical faculty.
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  • 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.
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  • 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.
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  • As notable instances may be mentioned Laplace's discoveries relating to the velocity of sound and the secular acceleration of the moon, both of which were led close up to by Lagrange's analytical demonstrations.
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  • The Exposition du Systeme du monde (Paris, 1796) has been styled by Arago "the Mecanique celeste disembarrassed of its analytical paraphernalia."
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  • 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.
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  • 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.
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  • 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.
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  • Among the principal were the London Review (1775-1780), A New Review (1782-1786), the English Review (1783-1796), incorporated in 1797 with the Analytical Review (1788-1799), the AntiJacobin Review and Magazine (1798-1821), and the British Critic (1793-1843), the organ of the High Church party, and first edited by Archdeacon Nares and Beloe.
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  • He was one of the early founders of the theory of determinants; in particular, he invented the functional determinant formed of the n 2 differential coefficients of n given functions of n independent variables, which now bears his name (Jacobian), and which has played an important part in many analytical investigations (see Algebraic Forms).
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  • The theoretical assumptions of Newton and Euler (hypotheses magis mathematicae quam naturales) of a resistance varying as some simple power of the velocity, for instance, as the square or cube of the velocity (the quadratic or cubic law), lead to results of great analytical complexity, and are useful only for provisional extrapolation at high or low velocity, pending further experiment.
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  • Hydrogen peroxide finds application as a bleaching agent, as an antiseptic, for the removal of the last traces of chlorine and sulphur dioxide employed in bleaching, and for various quantitative separations in analytical chemistry (P. Jannasch, Ber., 1893, 26, p. 2908).
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  • The equations to the tangent and normal at the point x' y are yy' = 2a(x+x) and aa(y - y')+y'(x - x')=o, and may be obtained by general methods (see Geometry, Analytical, and Infinitesimal Calculus).
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  • The great calculating engine was never completed; the constructor apparently desired to adopt a new principle when the first specimen was nearly complete, to make it not a difference but an analytical engine, and the government declined to accept the further risk (see Calculating Machines).
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  • He continued his labours in the theory of numbers and other analytical subjects, and communicated a long series of memoirs to the Royal Society of Sciences (Königliche Gesellschaft der Wissenschaften) at Göttingen.
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  • In the first volume of this treatise Plucker introduced for the first time the method of abridged notation which has become one of the characteristic features of modern analytical geometry (see Geometry, Analytical).
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  • These analytical methods of research were well known to the second Monro in Edinburgh, and to his pupils, one of whom, William Alexander, wrote a thesis in 1790 entitled "De partibus corporis animalis quae viribus opii parent."
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  • Advances in data handling and analytical technologies (eg. pyrolysis mass spectrometry), now offer additional potential for rapid research progress.
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  • Win 98/ME/NT/2000/XP Download 11 KB 10 sec 56k Analytical Eye Typing Tutor Typing Tutor is designed to help develop touch typing skills.
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  • Analytical factors are critical to generate high-resolution speleothem records.
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  • I will also add analytical material myself as well as transcripts of relevant conversations.
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  • Some people have a proclivity to like analytical data more than abstract concepts.
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  • Analytical and critical thinking skills can be taught using comic book themes and plots as well.
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  • Prospective students are encouraged to concentrate their studies before law school on courses that develop analytical skills and effective written and oral expression.
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  • Make the clues contain language riddles or historical facts in order to stimulate analytical thinking as well as creativity.
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  • The glaring problem with the theory is creatures that do not practice analytical thought sleep as well.
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  • If you take an analytical perspective, you may interpret the experience as the mind's way of working out feelings of repression and helplessness.
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  • Sometimes you have to assess a situation and make a choice quickly, which can help those become quick and analytical thinkers, more positive effects of video games.
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  • Writing skills and an incisive analytical sense are required to write a good bug report.
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  • Some children tend to approach life in a serious or analytical fashion while others respond to their immediate impressions of situations.
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  • A third analytical tool is the Titmus II Vision Tester Color Perception Test.
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  • What The traits Target looks for in interns include high energy, friendliness, communication skills, and analytical abilities.
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  • Other jobs available include analytical assistants, equipment technicians, sales managers, and account executives.
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  • Developing analytical skills is an important part of the requirements for this degree.
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  • If you enjoy the medical profession and working with people, have good communications and analytical skills, nursing may be a great career for you.
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  • This skill is important because they are responsible for so many different types of duties, such as interpersonal relations and analytical, number-crunching tasks.
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  • He needs to have the analytical skills involved in completing the bookkeeping tasks, payroll, and being careful not to go over the budget when working with vendors.
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  • Besides leadership abilities, analytical skills, and creativity, a general manager needs to be able to handle multitasking well.
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  • They possess active analytical minds and work hard to make sense of the natural relationships between objects, people, and information.
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  • Combining her analytical skills with a love of sewing turned out to be a winning combination combination.
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  • It bypasses the 'higher', more analytical centers of the brain.
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  • In general, Virgos are analytical people, especially when they are in love.
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  • This isn't necessarily a bad thing unless you become overly analytical, which will not only drive you crazy, but irritate your partner as well.
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  • Since both tend to be analytical, one is less likely to get frustrated because their partner has a hard time focusing on the facts and looking at a problem from several different perspectives.
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  • Your Virgo wants to see that you have the same analytical approach to life that he does.
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  • More mature Geminis have learned how to use their analytical mind to deduce the right course of action.
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  • Virgo is analytical and functions best when there are strict rules and plans to follow, while Pisces prefers to have the freedom to make adjustments and change course if the water grows turbulent.
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  • Virgo is very analytical when it comes to emotions, while Scorpio is anything but clinical.
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  • For example, an individual who is discerning and heavily analytical, marked by a tight, slender frame and dry skin would be described as a metal-dominant individual.
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  • The candidate should have excellent analytical skills in addition to the ability to work well with other people.
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  • 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.
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  • Uranyl nitrate is used in photography, and also in analytical chemistry as a precipitant for phosphoric acid (as uranyl ammonium phosphate, U02 NH4 P04).
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  • Its disintegration for analytical purposes can be effected by fusion with caustic alkali in silver basins, with the formation of soluble stannate, or by fusion with sulphur and sodium carbonate, with the formation of a soluble thiostannate.
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  • In astronomy, as in analytical geometry, the position of a point is defined by stating its distance and its direction from a point of reference taken as known.
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  • Game playing exercises the mind, as players hone their analytical and strategic skills.
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  • Advances in digital photo analytical processing bring the concept of robotic sight and object recognition much closer to reality.
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  • If you are a person that enjoys creative work rather than analytical work, then this career path may be more suited for you.
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  • This job deals with the back-end work of web design, so you will need to be very analytical and have a significant background in programming.
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  • Such is the basis of the algebraical or modern analytical geometry.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • But of the rest the majority, when treated with boiling sufficiently strong alkali, are attacked at least superficially; of ordinary metals only gold, platinum, and silver are perfectly proof against the reagents under consideration, and these accordingly are used preferably for the construction of vessels intended for analytical operations involving the use of aqueous caustic alkalis.
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  • His analytical skill enabled him to demonstrate the inaccuracy of the researches by which Berthollet attempted to support the opposite view, and to show among other things that some of the compounds which Berthollet treated as oxides were in reality hydrates containing chemically combined water, and the upshot was that by 1808 he had fully vindicated his position.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • 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).
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  • 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.
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  • Primary, secondary and spurious bows were formed, and their radii measured; a comparison of these observations exhibited agreement with Airy's analytical values.
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  • This latter work included the differential and integral calculus, the calculus of variations, the theory of attractions, and analytical mechanics.
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  • Fresenius, the founder of the Zeitschrift fiir analytische Chemie (1862), we are particularly indebted for perfecting and systematizing the various methods of analytical chemistry.
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  • In general analytical work the standard solution contains the equivalent weight of the substance in grammes dissolved in a litre of water.
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  • 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.
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  • In analytical invention, and mastery over the calculus, the Turin mathematician was admittedly unrivalled.
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  • It has the strength of an analytical treatise, the charm of a popular dissertation.
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  • By it his extraordinary analytical powers became strictly subordinated to physical investigations.
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  • 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.
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  • 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.
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  • In the former the author sets forth the analytical process by which the laws he discovered were deduced from facts.
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  • 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.
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