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The usage of the inter-related terms horizontal and vertical varies with context, There are important symmetries and asymmetries between the two terms which change as one goes from two to three dimensions, from a flat earth scenario to the spherical earth one. ==In two dimensions== In the context of a two-dimensional orthogonal Cartesian coordinate system on a Euclidean plane, to say that a line is horizontal or vertical, an initial designation has to be made. One can start off by designating the vertical direction, usually labelled the Y direction.〔For an example of identification of the ''y''-axis with the vertical, and the ''x''-axis with the horizontal, see G.S.Rehill's ''Interactive Maths Series, "Building a Strong foundation in Mathematics"'', accessible on http://www.mathsteacher.com.au/year8/ch15_graphs/05_hor/ver.htm.〕 The horizontal direction, usually labelled the X direction,〔For a definition of "Horizontal axis" see Math Dictionary at http://www.icoachmath.com/math_dictionary/Horizontal_Axis.html〕 is then automatically determined. Or, one can do it the other way around, i.e., nominate the ''x''-axis, in which case the ''y''-axis is then automatically determined. There is no special reason to choose the horizontal over the vertical as the initial designation: the two directions are on par in this respect. The following hold in the two-dimensional case: a) Through any point P in the plane, there is one and only one ''vertical line'' within the plane and one and only one ''horizontal line'' within the plane. This symmetry breaks down as one moves to the three-dimensional case. b) A ''vertical line'' is any line parallel to the vertical direction. A ''horizontal line'' is any line normal to a vertical line. c) Horizontal lines do not cross each other. d) Vertical lines do not cross each other. Not all of these elementary geometric facts are true in the 3-D context. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「horizontal and vertical」の詳細全文を読む スポンサード リンク
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