mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, 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 and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...

of a point in a

Cartesian coordinate system In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative number ...

: : abscissa

\equiv x

-axis (horizontal) coordinate : ordinate

\equiv y

-axis (vertical) coordinate Together they form an

ordered pair In mathematics, an ordered pair, denoted (''a'', ''b''), is a pair of objects in which their order is significant. The ordered pair (''a'', ''b'') is different from the ordered pair (''b'', ''a''), unless ''a'' = ''b''. In contrast, the '' unord ...

which defines the location of a point in two-dimensional rectangular space. More technically, the abscissa of a point is the signed measure of its projection on the primary axis. Its

absolute value In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if x is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), ...

is the distance between the projection and the origin of the axis, and its

sign A sign is an object, quality, event, or entity whose presence or occurrence indicates the probable presence or occurrence of something else. A natural sign bears a causal relation to its object—for instance, thunder is a sign of storm, or me ...

is given by the location on the projection relative to the origin (before: negative; after: positive). Similarly, the ordinate of a point is the signed measure of its projection on the secondary axis. In three dimensions, the third direction is sometimes referred to as the '' applicate''.

Etymology

Though the word "abscissa" () has been used at least since ''De Practica Geometrie'' (1220) by

Fibonacci Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italians, Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci ...

(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'' (1659). Historically, the term was used in the more general sense of a 'distance'. 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 History of mathematical notation, mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples ...

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, another branch ...

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 appliicata'' '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 expresses several quantities, such as the coordinates of a point (mathematics), point, as Function (mathematics), functions of one or several variable (mathematics), variables called parameters. In the case ...

. Used in this way, the abscissa can be thought of as a coordinate-geometry analog to the

independent variable A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function ...

in a

mathematical model A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...

or experiment (with any ordinates filling a role analogous to dependent variables).

References

{{Reflist Elementary mathematics Coordinate systems Dimension de:Kartesisches Koordinatensystem#Das Koordinatensystem im zweidimensionalen Raum pl:Układ współrzędnych kartezjańskich#Współrzędne

Etymology

In parametric equations

See also

References