# Abscissa and ordinate

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Illustration of a Cartesian coordinate plane, showing the absolute values (unsigned dotted line lengths) of the coordinates of the points (2, 3), (0, 0), (–3, 1), and (–1.5, –2.5). The first value in each of these signed ordered pairs is the abscissa of the corresponding point, and the second value is its ordinate.

In mathematics, the abscissa (/æbˈsɪs.ə/; plural abscissae or abscissæ or abscissas) and the ordinate are respectively the first and second coordinate of a point in a coordinate system.

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).

Usually these are the horizontal and vertical coordinates of a point in a two-dimensional rectangular Cartesian coordinate system. The terms can also refer to the horizontal and vertical axes respectively (typically x-axis and y–axis) of a two-dimensional graph. An ordered pair 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.

${\displaystyle (\overbrace {x} ^{\text{abscissa}},\overbrace {y} ^{\text{ordinate}})}$

## 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.[1]

In his 1892 work Vorlesungen über Geschichte der Mathematik, Volume 2, ("Lectures on history of mathematics") German historian of mathematics Moritz Cantor writes

"Wir kennen keine ältere Benutzung des Wortes Abssisse in lateinischen Originalschriften [than degli Angeli's]. Vielleicht kommt das Wort in Übersetzungen der Apollonischen Kegelschnitte vor, wo Buch I Satz 20 von ἀποτεμνομέναις die Rede ist, wofür es kaum ein entsprechenderes lateinisches Wort als abscissa geben möchte."[2]
"We know no earlier use of the word abscissa in Latin originals [than degli Angeli's]. Maybe the word descends from translations of the Apollonian conics, where in Book I, Chapter 20 there appears ἀποτεμνομέναις, for which there would hardly be as an appropriate Latin word as abscissa."

## 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.[3] 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 (with any ordinates filling a role analogous to dependent variables).

## References

1. ^ Dyer, Jason (March 8, 2009). "On the Word "Abscissa"". numberwarrior.wordpress.com. The number Warrior. Retrieved September 10, 2015.
2. ^ Cantor, Moritz (1900). Vorlesungen über Geschichte der Mathematik, Volume 2. Leipzig: B.G. Teubner. p. 898. Retrieved 10 September 2015.
3. ^ Hedegaard, Rasmus; Weisstein, Eric W. "Abscissa". MathWorld. Retrieved 14 July 2013.

This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.