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The Collaborative International Dictionary of English v.0.48 (gcide)

Mathematics \Math`e*mat"ics\, n. [F. math['e]matiques, pl., L.
mathematica, sing., Gr. ? (sc. ?) science. See {Mathematic},
and {-ics}.]
That science, or class of sciences, which treats of the exact
relations existing between quantities or magnitudes, and of
the methods by which, in accordance with these relations,
quantities sought are deducible from other quantities known
or supposed; the science of spatial and quantitative
relations.
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Note: Mathematics embraces three departments, namely: 1.
{Arithmetic}. 2. {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 magnitude as subsisting in
material bodies, and is consequently interwoven with
physical considerations.
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Analysis \A*nal"y*sis\, n.; pl. {Analyses}. [Gr. ?, fr. ? to
unloose, to dissolve, to resolve into its elements; ? up ?
to loose. See {Loose}.]
1. A resolution of anything, whether an object of the senses
or of the intellect, into its constituent or original
elements; an examination of the component parts of a
subject, each separately, as the words which compose a
sentence, the tones of a tune, or the simple propositions
which enter into an argument. It is opposed to
{synthesis}.
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2. (Chem.) The separation of a compound substance, by
chemical processes, into its constituents, with a view to
ascertain either (a) what elements it contains, or (b) how
much of each element is present. The former is called
{qualitative}, and the latter {quantitative analysis}.
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3. (Logic) The tracing of things to their source, and the
resolving of knowledge into its original principles.
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4. (Math.) The resolving of problems by reducing the
conditions that are in them to equations.
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5.
(a) A syllabus, or table of the principal heads of a
discourse, disposed in their natural order.
(b) A brief, methodical illustration of the principles of
a science. In this sense it is nearly synonymous with
synopsis.
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6. (Nat. Hist.) The process of ascertaining the name of a
species, or its place in a system of classification, by
means of an analytical table or key.
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{Ultimate}, {Proximate}, {Qualitative}, {Quantitative}, and
{Volumetric analysis}. (Chem.) See under {Ultimate},
{Proximate}, {Qualitative}, etc.
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