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Inmathematics, theabscissa (/æbˈsɪs.ə/; pluralabscissae orabscissas) and theordinate are respectively the first and secondcoordinate of apoint in aCartesian coordinate system:[1][2]
Together they form anordered pair which defines the location of a point in two-dimensionalrectangular space.
More technically, the abscissa of a point is the signed measure of its projection on the primary axis. Itsabsolute value is the distance between the projection and theorigin of the axis, and itssign 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 theapplicate.[citation needed]
Though the word "abscissa" (from Latin linea abscissa 'a line cut off') has been used at least sinceDe Practica Geometrie (1220) byFibonacci (Leonardo of Pisa), its use in its modern sense may be due to Venetian mathematicianStefano degli Angeli in his workMiscellaneum Hyperbolicum, et Parabolicum (1659).[3] Historically, the term was used in the more general sense of a 'distance'.[4]
In his 1892 workVorlesungen über die Geschichte der Mathematik ("Lectures on history of mathematics"), volume 2, Germanhistorian of mathematicsMoritz Cantor writes:
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 WortesAbscisse in lateinischen Originalschriften. Vielleicht kommt das Wort in Uebersetzungen derApollonischen Kegelschnitte vor, wo Buch I Satz 20 vonἀποτεμνομέναις die Rede ist, wofür es kaum ein entsprechenderes lateinisches Wort alsabscissa geben möchte.[5]
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 wordabscissa in Latin original texts. Maybe the word appears in translations of theApollonian conics, where [in] Book I, Chapter 20 there is mention ofἀποτεμνομέναις, for which there would hardly be a more appropriate Latin word thanabscissa.
The use of the wordordinate is related to the Latin phraselinea ordinata appliicata 'line applied parallel'.
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 aparametric equation.[1] Used in this way, the abscissa can be thought of as a coordinate-geometry analog to theindependent variable in amathematical model or experiment (with any ordinates filling a role analogous todependent variables).
