
In common usage, the abscissa refers to the (''x'') coordinate and the ordinate refers to the (''y'') coordinate of a standard
two-dimensional
In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise ...
graph
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discre ...
.
The distance of a point from the y-axis, scaled with the x-axis, is called abscissa or x coordinate of the point. The distance of a point from x-axis scaled with the y-axis is called ordinate.
For example, if (x, y) is an ordered pair in the Cartesian plane, then the first coordinate in the plane (x) is called the abscissa and the second coordinate (y) is the ordinate.
In
mathematics, the abscissa (; plural ''abscissae'' or ''abscissas'') and the ordinate are respectively the first and second
coordinate
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is si ...
of a
point in a
Cartesian coordinate system
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured ...
:
:abscissa
-axis (horizontal) coordinate
:ordinate
-axis (vertical) coordinate
Usually these are the horizontal and vertical coordinates of a point in
plane, the
rectangular coordinate system. An
ordered pair
In mathematics, an ordered pair (''a'', ''b'') is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (''a'', ''b'') is different from the ordered pair (''b'', ''a'') unless ''a'' = ''b''. (In co ...
consists of two terms—the abscissa (horizontal, usually ''x'') and the ordinate (vertical, usually ''y'')—which define the location of a point in two-dimensional rectangular space:
:
The abscissa of a point is the signed
measure of its projection on the primary axis, whose absolute value is the distance between the projection and the origin of the axis, and whose sign is given by the location on the projection relative to the origin (before: negative; after: positive).
The ordinate of a point is the signed measure of its projection on the secondary axis, whose absolute value is the distance between the projection and the origin of the axis, and whose sign is given by the location on the projection relative to the origin (before: negative; after: positive).
Etymology
Though the word "abscissa" (Latin; "linea abscissa", "a line cut off") has been used at least since ''De Practica Geometrie'' published in 1220 by
Fibonacci (Leonardo of Pisa), its use in its modern sense may be due to Venetian mathematician
Stefano degli Angeli in his work ''Miscellaneum Hyperbolicum, et Parabolicum'' of 1659.
In his 1892 work ' ("''Lectures on history of mathematics''"), volume 2, German
historian of mathematics Moritz Cantor writes:
At the same time it was presumably by tefano degli Angelithat a word was introduced into the mathematical vocabulary for which especially in analytic geometry the future proved to have much in store. ��We know of no earlier use of the word ''abscissa'' in Latin original texts. Maybe the word appears in translations of the Apollonian conics, where nBook I, Chapter 20 there is mention of ''ἀποτεμνομέναις,'' for which there would hardly be a more appropriate Latin word than .
The use of the word “ordinate” is related to the Latin phrase “linea ordinata applicata”, or “line applied parallel”.
In parametric equations
In a somewhat obsolete variant usage, the abscissa of a point may also refer to any number that describes the point's location along some path, e.g. the parameter of a
parametric equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric ...
.
Used in this way, the abscissa can be thought of as a coordinate-geometry analog to the
independent variable in a
mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
or experiment (with any ordinates filling a role analogous to
dependent variables).
See also
*
Dependent and independent variables
*
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the func ...
*
Relation (mathematics)
In mathematics, a relation on a Set (mathematics), set may, or may not, hold between two given set members.
For example, ''"is less than"'' is a relation on the set of natural numbers; it holds e.g. between 1 and 3 (denoted as 1 is an asymmetr ...
*
Line chart
References
External links
* {{Wiktionary-inline
Elementary mathematics
Coordinate systems
Dimension
de:Kartesisches Koordinatensystem#Das Koordinatensystem im zweidimensionalen Raum