Diameter

Diameter (from the Gr. διά, through, μέτρον, measure), in geometry, a line passing through the centre of a circle or conic section and terminated by the curve; the “principal diameters” of the ellipse and hyperbola coincide with the “axes” and are at right angles; “conjugate diameters” are such that each bisects chords parallel to the other. The diameter of a quadric surface is a line at the extremities of which the tangent planes are parallel. Newton defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line. The word is also used as a unit of linear measurement of the magnifying power of a lens or microscope.

In architecture, the term is used to express the measure of the lower part of the shaft of a column. It is employed by Vitruvius (iii. 2) to determine the height of a column, which should vary from eight to ten diameters according to the intercolumniation: and it is generally the custom to fix the lower diameter of the shaft by the height required and the Order employed. Thus the diameter of the Roman Doric should be about one-eighth of the height, that of the Ionic one-ninth, and of the Corinthian one-tenth (see Order).

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