# Abscissa

In mathematics, an **abscissa** (/æbˈsɪs.ə/; plural *abscissae* or *abscissæ* or *abscissas*) is the number whose absolute value (modulus) is the perpendicular distance of a point from the vertical axis. Usually this is the horizontal coordinate of a point in a two-dimensional rectangular Cartesian coordinate system. The term can also refer to the horizontal axis (typically *x*-axis) of a two-dimensional graph (because that axis is used to define and measure the horizontal coordinates of points in the space). 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.

## 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).

## Examples

- For the point (2, 3), 2 is called the abscissa and 3 the ordinate.
- For the point (−1.5, −2.5), −1.5 is called the abscissa and −2.5 the ordinate.

## See also

- Ordinate
- Dependent and independent variables
- Function (mathematics)
- Relation (mathematics)
- Line chart

## References

- ↑ Dyer, Jason (March 8, 2009). "On the Word "Abscissa"".
*https://numberwarrior.wordpress.com*. The number Warrior. Retrieved September 10, 2015. External link in`|website=`

(help) - ↑ Cantor, Moritz (1900).
*Vorlesungen über Geschichte der Mathematik, Volume 2*. Leipzig: B.G. Teubner. p. 898. Retrieved 10 September 2015. - ↑ 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.

## External links

- The dictionary definition of abscissa at Wiktionary