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.
2. A treatise on this science.
{Analytical, or Co["o]rdinate}, {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 involving three
dimensions.
{Elementary geometry}, that part of geometry which treats of
the simple properties of straight lines, circles, plane
surface, solids bounded by plane surfaces, the sphere, the
cylinder, and the right cone.
{Higher geometry}, that pert of geometry which treats of
those properties of straight lines, circles, etc., which
are less simple in their relations, and of curves and
surfaces of the second and higher degrees.