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The method of investigating the truth by analysis.

Originated or taught by Diophantus, the Greek writer on algebra. Diophantine analysis (Alg.), that branch of indeterminate analysis which has for its object the discovery of rational values that satisfy given equations containing squares or cubes; as, for example, to find values of x and y which make x2 + y2 an exact s…

That which is educed, as by analysis. Sir W. Hamilton.

A method of analysis developed by Newton, and based on the conception of all magnitudes as generated by motion, and involving in their changes the notion of velocity or rate of change. Its results are the same as those of the differential and integral calculus, from which it differs little except in notation and logica…

Of or pertaining to the measurement of gases; as, gasometric analysis.

reatise on this science. Analytical, or Coördinate, geometry, that branch of mathematical analysis which has for its object the analytical investigation of the relations and properties of geometrical magnitudes. -- Descriptive geometry, that part of geometry which treats of the graphic solution of all problems involvi…

ula. -- Graphic granite. See under Granite. -- Graphic method, the method of scientific analysis or investigation, in which the relations or laws involved in tabular numbers are represented to the eye by means of curves or other figures; as the daily changes of weather by means of curves, the abscissas of which repre…

to measurement by weight; measured by weight. -- Grav"i*met"ric*al*ly, adv. Gravimetric analysis (Chem.), analysis in which the amounts of the coastituents are determined by weight; -- in distinction from volumetric analysis.

ortion. -- Harmonic series or progression. See under Progression. -- Spherical harmonic analysis, a mathematical method, sometimes referred to as that of Laplace's Coefficients, which has for its object the expression of an arbitrary, periodic function of two independent variables, in the proper form for a large clas…

ixed; indefinite; not precise; as, an indeterminate number of years. Paley. Indeterminate analysis (Math.), that branch of analysis which has for its object the solution of indeterminate problems. -- Indeterminate coefficients (Math.), coefficients arbitrarily assumed for convenience of calculation, or to facilitate s…

y causing an appearance, disappearance, or change of color, as in titration or volumetric analysis.

An instrument for ascertaining the strength of an indigo solution, as in volumetric analysis. Ure.

r is a component part of any combination or mixture; an element; a constituent. By way of analysis we may proceed from compounds to ingredients. Sir I. Newton. Water is the chief ingredient in all the animal fluids and solids. Arbuthnot.

The act of liberating or the state of being liberated. This mode of analysis requires perfect liberation from all prejudged system. Pownall.

Geometry, including Trigonometry and Conic Sections. 3. Analysis, in which letters are used, including Algebra, Analytical Geometry, and Calculus. Each of these divisions is divided into pure or abstract, which considers magnitude or quantity abstractly, without relation to matter; and mixed or applied, which treats of…

urement of which a meter is the unit; as, the metric system; a metric measurement. Metric analysis (Chem.), analysis by volume; volumetric analysis. -- Metric system, a system of weights and measures originating in France, the use of which is required by law in many countries, and permitted in many others, including t…

determining the amount of nitrogen or some of its compounds in any substance subjected to analysis; an azotometer.

A vacuum tube, used in spectrum analysis, in which the part through which the discharge takes place is a capillary tube, thus producing intense incandescence of the contained gases.

To consider by a separate act of attention or analysis. Sir W. Hamilton.

Analysis into primary or elemental parts. [Archaic] Bacon.