Abscissa and ordinate


In common usage, the abscissa refers to the horizontal axis and the ordinate refers to the vertical axis of a standard two-dimensional graph.
In mathematics, the abscissa and the ordinate are respectively the first and second coordinate of a point in a coordinate system:
Usually these are the horizontal and vertical coordinates of a point in a two-dimensional rectangular Cartesian coordinate system. An ordered pair consists of two terms—the abscissa and the ordinate —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.
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.

Etymology

Though the word "abscissa" has been used at least since De Practica Geometrie published in 1220 by Fibonacci, 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 Vorlesungen über Geschichte der Mathematik, volume 2, German historian of mathematics Moritz Cantor writes:
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At the same time it was presumably by that 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 Book I, Chapter 20 there is mention of ἀποτεμνομέναις, for which there would hardly be a more appropriate Latin word than abscissa.

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. Used in this way, the abscissa can be thought of as a coordinate-geometry analog to the independent variable in a mathematical model or experiment.