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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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Calculus \Cal"cu*lus\, n.; pl. {Calculi}. [L, calculus. See
{Calculate}, and {Calcule}.]
1. (Med.) Any solid concretion, formed in any part of the
body, but most frequent in the organs that act as
reservoirs, and in the passages connected with them; as,
biliary calculi; urinary calculi, etc.
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2. (Math.) A method of computation; any process of reasoning
by the use of symbols; any branch of mathematics that may
involve calculation.
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{Barycentric calculus}, a method of treating geometry by
defining a point as the center of gravity of certain other
points to which co["e]fficients or weights are ascribed.


{Calculus of functions}, that branch of mathematics which
treats of the forms of functions that shall satisfy given
conditions.

{Calculus of operations}, that branch of mathematical logic
that treats of all operations that satisfy given
conditions.

{Calculus of probabilities}, the science that treats of the
computation of the probabilities of events, or the
application of numbers to chance.

{Calculus of variations}, a branch of mathematics in which
the laws of dependence which bind the variable quantities
together are themselves subject to change.

{Differential calculus}, a method of investigating
mathematical questions by using the ratio of certain
indefinitely small quantities called differentials. The
problems are primarily of this form: to find how the
change in some variable quantity alters at each instant
the value of a quantity dependent upon it.

{Exponential calculus}, that part of algebra which treats of
exponents.

{Imaginary calculus}, a method of investigating the relations
of real or imaginary quantities by the use of the
imaginary symbols and quantities of algebra.

{Integral calculus}, a method which in the reverse of the
differential, the primary object of which is to learn from
the known ratio of the indefinitely small changes of two
or more magnitudes, the relation of the magnitudes
themselves, or, in other words, from having the
differential of an algebraic expression to find the
expression itself.
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