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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 as s ...
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 Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 sign ...
of a
point Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland * 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 in t ...
: :abscissa \equiv x-axis (horizontal) coordinate :ordinate \equiv y-axis (vertical) coordinate Usually these are the horizontal and vertical coordinates of a point in
plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * ''Planes' ...
, the
rectangular 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 in t ...
. 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 con ...
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: :(\overbrace^, \overbrace^) The abscissa of a point is the signed
measure Measure may refer to: * Measurement, the assignment of a number to a characteristic of an object or event Law * Ballot measure, proposed legislation in the United States * Church of England Measure, legislation of the Church of England * Mea ...
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 Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western ...
(Leonardo of Pisa), its use in its modern sense may be due to Venetian mathematician
Stefano degli Angeli Stefano degli Angeli (Venice, September 23, 1623 – Padova, October 11, 1697) was an Italian mathematician, philosopher, and Jesuate. He was member of the Catholic Order of the Jesuats (Jesuati). In 1668 the order was suppressed by Pope Clemen ...
in his work ''Miscellaneum Hyperbolicum, et Parabolicum'' of 1659. In his 1892 work ' ("''Lectures on history of mathematics''"), volume 2, German
historian of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...
Moritz Cantor Moritz Benedikt Cantor (23 August 1829 – 10 April 1920) was a German historian of mathematics. Biography Cantor was born at Mannheim. He came from a Sephardi Jewish family that had emigrated to the Netherlands from Portugal Portugal, off ...
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 obj ...
. Used in this way, the abscissa can be thought of as a coordinate-geometry analog to the
independent variable Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
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 Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
).


See also

*
Dependent and independent variables Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
*
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 funct ...
*
Relation (mathematics) In mathematics, a relation on a 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 asymmetric relation, but ...
*
Line chart A line chart or line graph or curve chart is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a s ...


References


External links

* {{Wiktionary-inline Elementary mathematics Coordinate systems Dimension de:Kartesisches Koordinatensystem#Das Koordinatensystem im zweidimensionalen Raum