Section \Sec"tion\, n. [L. sectio, fr. secare, sectum, to cut; akin to E. saw a cutting instrument: cf. F. section. See Saw, and cf. Scion, Dissect, Insect, Secant, Segment.] 1. The act of cutting, or separation by cutting; as, the section of bodies. 2. A part separated from something; a division; a portion; a slice. Specifically: (a) A distinct part or portion of a book or writing; a subdivision of a chapter; the division of a law or other writing; a paragraph; an article; hence, the character [sect], often used to denote such a division. It is hardly possible to give a distinct view of his several arguments in distinct sections. --Locke. (b) A distinct part of a country or people, community, class, or the like; a part of a territory separated by geographical lines, or of a people considered as distinct. The extreme section of one class consists of bigoted dotards, the extreme section of the other consists of shallow and reckless empirics. --Macaulay. (c) One of the portions, of one square mile each, into which the public lands of the United States are divided; one thirty-sixth part of a township. These sections are subdivided into quarter sections for sale under the homestead and pre["e]mption laws. 3. (Geom.) The figure made up of all the points common to a superficies and a solid which meet, or to two superficies which meet, or to two lines which meet. In the first case the section is a superficies, in the second a line, and in the third a point. 4. (Nat. Hist.) A division of a genus; a group of species separated by some distinction from others of the same genus; -- often indicated by the sign [sect]. 5. (Mus.) A part of a musical period, composed of one or more phrases. See Phrase. 6. The description or representation of anything as it would appear if cut through by any intersecting plane; depiction of what is beyond a plane passing through, or supposed to pass through, an object, as a building, a machine, a succession of strata; profile. Note: In mechanical drawing, as in these Illustrations of a cannon, a longitudinal section (a) usually represents the object as cut through its center lengthwise and vertically; a cross or transverse section (b), as cut crosswise and vertically; and a horizontal section (c), as cut through its center horizontally. Oblique sections are made at various angles. In architecture, a vertical section is a drawing showing the interior, the thickness of the walls, ets., as if made on a vertical plane passed through a building. Angular sections (Math.), a branch of analysis which treats of the relations of sines, tangents, etc., of arcs to the sines, tangents, etc., of their multiples or of their parts. [R.] Conic sections. (Geom.) See under Conic. Section liner (Drawing), an instrument to aid in drawing a series of equidistant parallel lines, -- used in representing sections. Thin sections, a section or slice, as of mineral, animal, or vegetable substance, thin enough to be transparent, and used for study under the microscope. Syn: Part; portion; division. Usage: Section, Part. The English more commonly apply the word section to a part or portion of a body of men; as, a section of the clergy, a small section of the Whigs, etc. In the United States this use is less common, but another use, unknown or but little known in England, is very frequent, as in the phrases ``the eastern section of our country,'' etc., the same sense being also given to the adjective sectional as, sectional feelings, interests, etc.

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. 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.

Conic \Con"ic\, Conical \Con"ic*al\, a. [Gr. ?: cf. F. conique. See Cone.] 1. Having the form of, or resembling, a geometrical cone; round and tapering to a point, or gradually lessening in circumference; as, a conic or conical figure; a conical vessel. 2. Of or pertaining to a cone; as, conic sections. Conic section (Geom.), a curved line formed by the intersection of the surface of a right cone and a plane. The conic sections are the parabola, ellipse, and hyperbola. The right lines and the circle which result from certain positions of the plane are sometimes, though not generally included. Conic sections, that branch of geometry which treats of the parabola, ellipse, and hyperbola. Conical pendulum. See Pendulum. Conical projection, a method of delineating the surface of a sphere upon a plane surface as if projected upon the surface of a cone; -- much used by makers of maps in Europe. Conical surface (Geom.), a surface described by a right line moving along any curve and always passing through a fixed point that is not in the plane of that curve.

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