Editing Abscissa and ordinate

{{short description|Horizontal and vertical axes/coordinate numbers of a 2D coordinate system or graph}}
{{Citations needed|date=May 2024}}
[[File:Cartesian-coordinate-system.svg|thumb|right|250px|Cartesian plane with marked points (signed ordered pairs of coordinates). For any point, the ''abscissa'' is the first value (x coordinate), and the ''ordinate'' is the second value (y coordinate).]]
In [[mathematics]], the '''abscissa''' ({{IPAc-en|æ|b|ˈ|s|ɪ|s|.|ə}}; plural ''abscissae'' or ''abscissas'') and the '''ordinate''' are respectively the first and second [[coordinate]] of a [[Point (geometry)|point]] in a [[Cartesian coordinate system]]:<ref name="WolframAlpha" /><ref>{{Cite web |last=Hedegaard |first=Rasmus |last2=Weisstein |first2=Eric W. |title=Ordinate |url=https://mathworld.wolfram.com/Ordinate.html |access-date=14 July 2013 |website=[[MathWorld]] |language=en}}</ref>
: '''abscissa''' <math>\equiv x</math>-axis (horizontal) coordinate
: '''ordinate''' <math>\equiv y</math>-axis (vertical) coordinate

Together they form an [[ordered pair]] which defines the location of a point in two-dimensional [[rectangular coordinate system|rectangular space]].

More technically, the abscissa of a point is the signed measure of its projection on the primary axis. Its [[absolute value]] is the distance between the projection and the [[Origin (mathematics)|origin]] of the axis, and its [[Sign (mathematics)|sign]] 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. [[Cartesian_coordinate_system|In three dimensions]], the third direction is sometimes referred to as the ''[[wiktionary:applicate#Noun|applicate]]''.<ref>{{Cite web |title=Cartesian coordinates |url=https://planetmath.org/cartesiancoordinates |access-date=2025-04-02 |website=[[PlanetMath]] |archive-url=https://web.archive.org/web/20250221122412/https://planetmath.org/cartesiancoordinates |archive-date=2025-02-21 |url-status=live |quote='applicate' is rare in English, but its [equivalents]<!-- fixing typo in source --> in continental European, [such as]<!-- clarifying wording of source --> 'die Applikate' in German and 'aplikaat' in Estonian, are more known.}}</ref>

== Etymology ==
Though the word "abscissa" ({{ety|la|linea abscissa|a line cut off}}) has been used at least since ''De Practica Geometrie'' (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'' (1659).<ref>{{cite web |title =On the Word "Abscissa" |website =numberwarrior.wordpress.com |last=Dyer |first=Jason |publisher = The number Warrior |date = March 8, 2009 |url = https://numberwarrior.wordpress.com/2009/03/08/on-the-word-abscissa/ |access-date = September 10, 2015 }}</ref> Historically, the term was used in the more general sense of a 'distance'.<ref>{{Cite web |last=Miller |first=Jeff |date=June 24, 2017 |title=Earliest Known Uses of Some of the Words of Mathematics |url=https://jeff560.tripod.com/a.html |access-date=2025-01-06 |website=MacTutor |publisher=University of St. Andrews, Scotland}}</ref>

In his 1892 work ''{{lang|de|Vorlesungen über die Geschichte der Mathematik}}'' ("''Lectures on history of mathematics''"), volume 2, German [[history of mathematics|historian of mathematics]] [[Moritz Cantor]] writes:

<blockquote>{{lang|de|italic=yes|Gleichwohl ist durch [Stefano degli Angeli] vermuthlich ein Wort in den mathematischen Sprachschatz eingeführt worden, welches gerade in der analytischen Geometrie sich als zukunftsreich bewährt hat. […] Wir kennen keine ältere Benutzung des Wortes {{lang|de|italic=no|Abscisse}} in lateinischen Originalschriften. Vielleicht kommt das Wort in Uebersetzungen der [[Apollonius of Perga|Apollonischen Kegelschnitte]] vor, wo Buch I Satz 20 von {{lang|grc|italic=no|ἀποτεμνομέναις}} die Rede ist, wofür es kaum ein entsprechenderes lateinisches Wort als {{lang|la|italic=no|abscissa}} geben möchte.}}<ref>{{cite book |title=Vorlesungen über Geschichte der Mathematik |volume=2 |edition=2nd |lang=de |last=Cantor |first=Moritz |year=1900 |publisher=B.G. Teubner |location= Leipzig |page=898 |url=https://books.google.com/books?id=LejuAAAAMAAJ&q=%22Miscellaneum+Hyperbolicum%2C+et+Parabolicum.%22+%22abscissa%22&pg=PA898 |access-date=10 September 2015}}</ref><br/>
At the same time it was presumably by [Stefano degli Angeli] 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 [[Apollonius of Perga|Apollonian conics]], where [in] Book I, Chapter 20 there is mention of ''ἀποτεμνομέναις,'' for which there would hardly be a more appropriate Latin word than {{lang|la|abscissa}}.
</blockquote>

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]].<ref name="WolframAlpha">{{cite web |last1=Hedegaard |first1=Rasmus |last2=Weisstein |first2=Eric W. |title=Abscissa |work=[[MathWorld]] |url=http://mathworld.wolfram.com/Abscissa.html |access-date=14 July 2013}}</ref> Used in this way, the abscissa can be thought of as a coordinate-geometry analog to the [[Dependent and independent variables|independent variable]] in a [[mathematical model]] or experiment (with any ordinates filling a role analogous to [[Dependent and independent variables|dependent variables]]).

==See also==
{{Wiktionary|abscissa|ordinate}}
* [[Function (mathematics)]]
* [[Relation (mathematics)]]
* [[Line chart]]

==References==
{{Reflist}}

[[Category:Elementary mathematics]]
[[Category:Coordinate systems]]
[[Category:Dimension]]

[[de:Kartesisches Koordinatensystem#Das Koordinatensystem im zweidimensionalen Raum]]
[[pl:Układ współrzędnych kartezjańskich#Współrzędne]]